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The Fermi edge singularity, and related Anderson's orthogonality catastrophe, has been a touchstone of many body quantum physics for over 50 years. There are, however, a number of facets of this phenomenon that have, up until now, been left largely unexplored in the scientific literature. In this thesis we investigate two of these. Firstly we explore how the orthogonality catastrophe spatially spreads through a system, with particular considerations for the implications for quantum information processing implementations. We find that there is a propagating signal carrying the information about the Fermi edge singularity, but at long times the orthogonality catastrophe reasserts itself, posing a significant obstacle to the transmission of quantum information. We also found an "echo" formed by the interference of multiple Fermi edge singularities at different locations. Secondly we consider the effect of band structure on the Fermi edge singularity. Here we make significant progress in analytically understanding the effect of having a finite band bottom and of band curvature on the Fermi edge singularity. In the course of this we clarify some subtle points about the relationship between energy and time in non-relativistic quantum mechanics, which had been glossed over in the previous literature.

Superconducting circuits are well established as a viable candidate for the realisation of quantum computers. Circuits based on the transmon qubit are now ubiquitous, owing to its simple design and reduced control wiring overhead. An issue with transmon qubit-based architectures is the always-on unwanted interactions that impose limits on gate speeds and introduce errors into their operation. In addition, understanding sources of noise and decoherence is essential to the low-error operation quantum computers. This thesis describes the implementation of a multi-mode superconducting qubit in a coaxial circuit QED architecture. Constructed from three superconducting islands, connected via two Josephson junctions, the device possesses two transmon-like modes with orthogonal field symmetries. The unique polarisation of each mode allows for engineering dissipation and coupling in the system, extending functionality beyond the single-mode transmon. Experimental results on the unit-cell of the two-mode coaxial transmon are presented, demonstrating coherent control and simultaneous dispersive readout of the modes of the device. A predictive theory of charge sensitivity in a multi-mode superconducting qubit is presented, and experimental results in agreement of this theory are shown, observing sensitivity to four charge-parity configurations and two independent gate-charge offsets. The utility of a multi-mode qubit as a charge detector in spatially tracking local-charge drift of ≃ 100 µm length scales is also shown, demonstrating the use of these devices as tools in understanding charge noise in superconducting circuits. Finally, a system of a pair of coupled two-mode coaxial transmons is introduced, demonstrating a highly mode-selective coupling architecture. A suppressed quantum crosstalk of 2 kHz between protected modes of the devices is measured, along with equal single qubit gate fidelities when operated both individually and simultaneously. A first characterisation of a microwave activated conditional phase interaction between computational modes driven via ancillary transitions (AT-MAP) is presented. Whilst not shown in this work, this state-dependent two-qubit interaction can be used to generate entanglement. Combined with the low crosstalk demonstrated, this shows the multi-mode qubit architecture is a promising candidate for the construction of larger scale quantum processors with fast gates and low crosstalk-related errors.

Charge transfer (CT) states, which form at the interface between donor and acceptor molecules in organic solar cells (OSCs), strongly influence device performance, in particular the open-circuit voltage and the photogeneration of free charges. However, the connection between molecular properties, the resulting energetics at the donor-acceptor interface, and ultimately device performance is still incompletely understood. To address this knowledge gap, this thesis studies the impact of (1) molecular energy levels and donor:acceptor mixing ratios on exciton separation, and (2) blend morphologies on interfacial energetic disorder and voltage losses. CT state properties are studied via a custom-built sensitive external quantum efficiency (EQE) setup and fit from the resulting spectra. In the first part of this thesis, we establish a reliable and reproducible fitting methodology that considers both singlet and CT state absorption contributions in the EQE. We first apply this methodology to study the impact of molecular energy levels on exciton separation in low donor content blends of ZnPc or its fluorinated derivatives (FxZnPc, with x = 0, 4, 8, 16) and C60. We find that the fluorination-induced shifts of the donor energy levels result in an increasing CT state energy with C60 and a decreasing offset between local excitation (LE) and CT states. Through in-depth characterization of molecular and blend energy levels, we draw a comprehensive picture of how LE, CT, and charge separated (CS) energy levels and the energetic transitions between states change upon fluorination of ZnPc. We find that the CT → CS transition presents a major bottleneck for free charge generation in the low offset F8ZnPc and F16ZnPc blends. This study is further extended beyond the low donor content blends by gradually varying the donor:acceptor mixing ratio from neat FxZnPc to neat C60. We find that with increasing F8ZnPc or F16ZnPc content, the CT dissociation efficiency is further reduced, leading to very low photocurrents in these blends. The dependence of CT dissociation on donor concentration is attributed to charge-quadruple induced electrostatic shifts, caused by the positive quadrupole moments of F8ZnPc/F16ZnPc, which increase the CT dissociation barrier with increasing donor content. In comparison, ZnPc/F4ZnPc, which have negative quadrupole moments, experience the opposite electrostatic shifts and show efficient CT dissociation across all donor:C60 mixing ratios. These results not only motivate further studies of the CS state, but also show that improving the CT → CS transition, for instance via the design of molecules with suitable quadrupole moments, is an effective route for increasing the photocurrents of OSCs. Finally, we study the impact of interfacial energetic disorder on device performance and voltage losses for five small molecule donor:C60 systems. Through temperature-dependent EQE measurements, we disentangle the contributions of static (i.e. temperature independent) and dynamic (i.e. temperature-dependent) disorder. Contrary to what is often stated for evaporated blends of small molecules, static disorder is found to be significant, and often exceed the contribution of dynamic disorder in the CT linewidth. This motivates future studies of interfacial disorder in OSCs, linking bulk and interface morphologies to device performance, and finding ways to reduce disorder to decrease voltage losses.

Topological phases of matter are characterised by long-range entanglement between their constituent degrees of freedom, which allows them to host excitations with non-trivial exchange statistics. While topological phases in 2+1d are relatively well studied, less is known about their 3+1d counterparts. In this thesis, we examine features of these higher-dimensional phases in a tractable example model, based on a generalisation of lattice gauge theory called higher lattice gauge theory. As well as hosting point-like excitations, the model supports loop-like excitations with non-trivial loop-loop and point-loop braiding statistics. We explicitly construct operators to produce and move these excitations, and use these to find the loop-loop and point-loop braiding relations. These creation operators also reveal that some of the excitations are confined, costing energy to separate, while others are condensed and can be produced locally. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also explain a method for measuring topological charge and use explicit measurement operators to re-derive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the higher lattice gauge theory model on the 3-torus. From these measurement operators, we can see that the ground state degeneracy on the 3-torus is related to the number of types of linked loop-like excitations.

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as a key resource for applications including quantum information processing. In this thesis, we first develop a unifying framework based on non-Hermitian topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix and regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. Furthermore, we show that non-Hermitian topological amplification is robust against disorder as long as the disorder strength does not exceed the size of the point gap-the separation of the spectrum from the origin. In another part of this thesis, we revisit the bulk-boundary correspondence for non-Hermitian topological systems. It is a fundamental phenomenon of Hermitian topological phases, however, in non-Hermitian systems, it breaks down in the conventional form due to the non-Hermitian skin effect-the localisation of a macroscopic number of eigenvectors at the boundary. Here, we show that it is possible to restore the bulk-boundary correspondence by means of the singular value decomposition: when the system is topologically non-trivial, zero singular modes emerge leading to directional amplification with their number given by the topological invariant. In the final part, we extend the notion of non-reciprocity to unidirectional bosonic transport in time-reversal symmetric systems by exploiting interference between beamsplitter and two-mode-squeezing interactions. We develop a framework to identify the phenomenon we dub quadrature non-reciprocity based on features of the particle-hole graph representing the equations of motion. In addition to unidirectionality, these networks can exhibit an even-odd pairing between collective quadratures and an exponential end-to-end gain in the case of arrays of cavities. Our work opens up new avenues for signal routing, non-Hermitian topology, and amplification in bosonic systems.

In polar semiconductors and insulators, thermal vibrations of the ionic lattice give rise to long-ranged electric fields that can scatter electrons and holes very efficiently. This interaction is known as Fröhlich coupling, and it is the source for a range of intriguing many-body effects in these materials. We consider two scenarios: Firstly, the normal state, in which Fröhlich coupling can give rise to a coupled electron-phonon state, or "polaron", which causes a strong renormalisation of the electronic energy with major implications for excitation energies and charge-carrier mobilities in a material. A characteristic feature of polaron spectra, e.g. as observed in photoemission experiments, are low-energy sidebands near the main photoemission peak whose energetics are of the order of the most strongly coupled phonon modes. These sidebands are often referred to as "polaron satellites". Secondly, the superconducting state, in which Fröhlich coupling provides the attractive pairing potential required for the formation of Cooper pairs. A paradigmatic example for the large class of polar semiconductors is SrTiO₃, which hosts a strongly renormalised polaronic state in the conduction band, and whose phase diagram features a superconducting dome as a function of electron doping. In this thesis, we employ an analytical model of Fröhlich-type coupling between a parabolic electron band with finite electron occupation and a dispersionless LO phonon to study the coupled electron-phonon state in doped SrTiO₃. Our analytical approach allows us to model all the relevant interactions with arbitrary resolution and provides insights into the intriguing many-body effects in Fröhlich-type semiconductors. In the normal state, we calculate the interacting electron spectral function from a Green's function theory of electron phonon coupling for a range of doping levels and coupling strengths. Electron-phonon coupling is taken into account at the level of the Fan-Migdal self-energy. We compare the spectral functions obtained from two approximations to the interacting Green's function for a wide range of Fermi energies and coupling strengths, derive analytical expressions for the quasiparticle renormalisation as a function of electron doping, and discuss limiting cases of the second-order self-energy approximation. In the superconducting state, we employ Migdal-Eliashberg theory to calculate the critical temperature TC of doped SrTiO₃ as a function of doping level. In particular, our analytical approach allows us to explicitly model the attractive Fröhlich interaction and repulsive Coulomb interaction at generalised frequencies and momenta. Very good qualitative agreement of our results with experimental data is obtained. We emphasise the major contribution of free-carrier screening to the effective pairing potential, and we investigate promising avenues for improving the predictive power of ab initio calculations of the superconducting TC.

The direction of research in solid state physics and technology has changed since the discovery of graphene. Now, a plethora of two-dimensional materials are being thoroughly investigated for their unique properties as well as for their implementation in next-generation optoelectronic devices. Of course, much effort is needed in order to reach the current level of modern electronics which is based on decades of research and development. For example, the level of miniaturisation modern technology requires can be achieved with atomically thin materials, driving Moore's Law forward. Conventional dielectrics exhibit high leakage currents when their dimensions are reduced to the nano-scale and the need for alternative materials compatible with two-dimensional electronics arises. However, the techniques that are being used for the growth and processing of conventional semiconducting materials are not always suitable with two-dimensional materials, which need special handling. These are some of the points that will be addressed in this PhD dissertation. Here, a new method for generating a fundamentally two-dimensional high-k dielectric which can be automatically incorporated in atomically thin optoelectronics devices is presented. The photo-oxidation of hafnium disulfide, HfS2, is a straight-forward, non-invasive process that can be used to oxidise pristine few-layered HfS₂, opening new paths for applications ranging from optoelectronics to photonics. The resulting dielectric, Hafnium dioxide, HfO₂, exhibits outstanding properties that exceed those of silicon dioxide, SiO₂ and its atomically thin nature makes it an ideal insulating layer for next-generation nano-electronics. Finally, the last part of this thesis is dedicated to a novel, CVD-grown, n-type monolayer of tungsten diselenide, WSe2. This is the first time negatively doped CVD-grown WSe₂ is reported, which opens the possibility of choosing the doping of the two-dimensional semiconductor before fabrication. For investigating and characterising this novel material, field-effect transistors are fabricated and characterised optoelectronically, shining light on the carriers' behaviour and the ability of the material in light-detection applications. Vacuum and ambient annealing of the WSe2 based devices highlights a possible way to control the doping level of the material, and thus the electrical behaviour of the devices.

This thesis studies the magnetism of the A'2A''A'''Mn4O12 columnar ordered quadruple perovskite manganites. The magnetic structures of five distinct members of this family of manganite perovskites has been determined using neutron scattering and magnetometry measurements. Point charge calculations of the crystal electric field, percolation calculations and a symmetry and group theoretical based approach to data analysis has been used to motivate the microscopic origins of the determined magnetic phases, and the physical mechanisms driving the observed magnetic phase transitions. Four regions of the magnetic phase diagram have been observed; a collinear ferrimagnetic phase, a Γ-point canted ferrimagnetic phase, a Z-point canted ferrimagnetic phase, and a magnetic phase characterised by well correlated collinear ferrimagnetic order punctuated by randomly dispersed clusters of antiferromagnetic order. We show that competing superexchange interactions and disorder can tune these manganites into different magnetically ordered phases. In these systems we observe two mechanisms for driving spin reorientation phase transitions. In Tm2MnMnMn4O12 the competition between rare-earth (Tm3+) and transition metal (Mn) anisotropies coupled via f-d exchange drives the spin reorientation, as is typical for distorted perovskites. In R2CuMnMn4O12 (R = Y or Dy) an alternative paradigm for spin reorientation was observed, which originated in frustrated Heisenberg exchange interactions, and the competition between Dzyaloshinskii- Moriya and single-ion anisotropies. Our studies on magnetic dilution in the Sm2MnMnMn4-xTixO12 systems have shown that they demonstrate an unusual variation in transition temperature, suggesting a departure from mean field physics. We observed a spin doped Griffiths phase in Y2MnMnMn4O12, and the coexistence of two magnetically distinct phases below Tc.

Superconducting circuits have been demonstrated at the ~50 qubit scale, with gate fidelities approaching the thresholds required for error correction using surface codes. It is generally considered that maintaining and improving this performance while scaling to >100 qubits will require 3D integration of control wiring, and techniques to prevent or mitigate the effects of unwanted electromagnetic modes which emerge in the circuit environment at larger scales. At the present time, no single design has emerged as the clear scaling "winner'', and many different modalities are being explored. In this thesis, we describe one potential scaling architecture for superconducting circuits, which is based on a unit cell containing a set of controllable, measurable qubits. In analogy to the unit cell of a crystal, this unit cell can be tiled, in this case to form 2D arrays of individually controllable and measurable qubits. This is enabled by three key technologies: 3D integrated off-chip control wiring, reverse-side readout resonators, and inductive shunting of the device enclosure with micromachined pillars. To validate this approach, we design and build a demonstration device featuring four transmon qubits and containing within it a single unit cell of the architecture. The device construction involves the fabrication of reverse-side circuits and the use of novel CNC drilling of the circuit substrate. We measure coherence times and single-qubit gate fidelities comparable with the state-of-the-art for transmon qubits (avg. T1 = 149 µs, avg. echoed pure dephasing T2 = 189 µs, avg. F > 99.98%), establishing that the design is compatible with high coherence. An important feature of the design is that the infinite construct formed by tiling the plane with the unit cell possesses a cutoff frequency, below which the circuit environment cannot sustain any electromagnetic modes. We develop models to predict this cutoff frequency, and predict that environment mediated crosstalk between qubits inside this structure decays exponentially with spatial separation. This crosstalk can be viewed as being mediated by evanescent waveguide modes, or by bound states formed by the interaction of qubits with the environmental modes around the cutoff. Both models provide quantitative predictions for the rate of crosstalk decay, which are shown to be in good agreement. We propose this architecture as a promising candidate for building 2D arrays of hundreds or thousands of nearest neighbour coupled superconducting qubits, which could provide a testbed of quantum error correction schemes such as the surface code.

Organic-inorganic metal-halide perovskites and narrow-gap semiconductors have been studied extensively over the last few decades. Their peculiar optoelectronic properties make them ideal candidates for future photovoltaic applications and ultrafast electronic devices. Specifically, knowledge of the charge-carrier transport and electronic band structure is key to understanding the fundamental principles that underpin their optoelectronic behaviors, and hence to improve the performance of devices based on them. Terahertz spectroscopy provides an ideal pathway to probe the optoelectronic properties of these semiconductor materials not only because of its non-contact nature which avoids damaging the sample and removes the complications arising from metallic contacts, but also due to its ability to measure the charge-carrier dynamics on an ultrafast (sub-picosecond) timescale. The versatility of terahertz spectroscopy allows a large phase space of optoelectronic parameters to be probed, such as charge-carrier mobility, carrier diffusion length, and photoconductivity. A comparative study on the prototypical metal-halide perovskite MAPbI3 as both single crystals and polycrystalline films suggests that Frohlich scattering is the dominant mechanism limiting charge-carrier mobility, which arises from the electron-phonon coupling effect. Further investigations of the phonon modes in MAPbI3 show a phonon-hardening effect under photo-excitation, which is attributed to the increase in dielectric screening due to photo-induced electron doping. In addition, grain-boundary scattering is shown to further reduce mobility in polycrystalline films at cryogenic temperature. By taking into account the effect of photon reabsorption, the wide range of values for charge recombination parameters and charge diffusion lengths reported previously is reconciled. The benign grain boundaries observed in polycrystalline films offer great promise for future high-performance devices. Time-resolved magneto-terahertz spectroscopy is utilized to investigate the cyclotron effective mass of a narrow-gap semiconductor InSb. A significant reduction of effective mass observed in the first 50ps after photoexcitation indicates a fast hot-electron cooling process. Meanwhile, the increase in effective mass with increasing carrier density agrees with the non-parabolic conduction band predicted by the ab initio calculations of the quasiparticle band structure based on the Kane model. This thesis, which combines a thorough experimental study utilizing terahertz spectroscopy with a complementary theoretical study based on first-principles calculations, helps to uncover a complete picture of the fundamental optoelectronic properties of metal-halide perovskites and narrow-gap semiconductors.

The discovery of electroluminescence from conjugated polymers was followed by tremendous academic and commercial interest in the field of polymer optoelectronics. Conjugated polymer materials have been shown to possess beneficial qualities for device fabrication such as low-cost, large area manufacturing and the potential for realizing flexible applications. Polyfluorenes, in particular, are a class of conjugated polymers which have been realized in a number of applications such as organic light emitting diodes, solar cells and field-effect transistors. The widespread commercialization of such products critically depends on improving device efficiencies. This can be accomplished by both advancing device engineering and improving material design. For the realization of the latter, fundamental understanding of the interplay between material chemistry and physics is required. This motivated the work in this thesis which is concerned with the structure-property relationship in polyfluorene containing copolymers. The well studied polyfluorene poly(9,9-dioctylfluorene) (PFO) was selected as the model polymer due to its complex phase morphology which allowed to additionally investigate the effect of film microstructure on the photophysics of the copolymers. The optoelectronic properties of PFO can be varied by the copolymerisation of suitable comonomers giving valuable insight into the relationship between chemical structure and photophysical properties that can guide future material design for device applications. In this work three different comonomers have been studied. Firstly, the hole mobility of four fluorene-arylamine copolymers has been investigated. It is shown that transport in these copolymers is controlled over a large range by the copolymerisation of different amounts of a lower ionisation potential transporting moiety. Next, the effect of increasing backbone rigidity on hole carrier transport is studied via the copolymerisation of fluorene and phenoxazine. The resulting copolymer has a high glass transition temperature suggesting a rigid polymer chain. Yet, its hole mobility is lower than for the chemically similar hole transporting material poly(9,9-dioctylfluorene-alt-N-(4-butylphenyl)-diphenylamine) (TFB) which possesses a greater number of torsions. Finally, the copolymerisation of PFO with a cyclometalated platinum complex has been investigated. The heavy platinum atom increases spin-orbit coupling leading to the radiative decay of the triplet state. It is shown that at low temperatures kinetic frustration of the triplet state is lifted in the planarised ß phase of the copolymer demonstrating that triplets can diffuse more effectively along highly conjugated polymer chains than along materials with short conjugation segments.

This thesis presents work exploring the use of pressure as a tuning parameter for exploring the phase diagrams and properties of magnetically ordered insulators, to add understanding to several areas of current interest in condensed matter research. It shows the versatility of pressure as an experimental technique for exploring material properties free from complicating factors which arise with similar techniques such as chemical doping. The properties of low-dimensional magnetic materials, and how these systems respond as they are pushed toward a more three-dimensional nature is explored through studies of both the crystal and magnetic structures of the family of quasi-two-dimensional magnetic insulators MPS3 (M = Fe, Ni, Mn). With previous work largely being specific to individual compounds, this thesis contributes to a more unified understanding of their properties. It shows that Ni and MnPS3 undergo similar structural transitions under pressure to those previous observed in FePS3, the highest pressure of which is linked to an insulator-to-metal transition in that system. Through record high-pressure neutron diffraction measurements, the evolution of the antiferromagnetic order in FePS3 through this metallisation is studied for the first time. In contradiction to previous indirect measurements, it is seen that magnetism persists into the metallic phase, with long range antiferromagnetism giving way to a previously unobserved short-range order. This work is relevant on a broader scale for numerous layered magnetic materials such as cuprate high temperature superconductors. Secondly, pressure is used to explore the magnetocaloric properties of the antiferromagnet EuTiO3. Recent work has shown that this compound compares favourably to many materials commonly used in magnetic refrigeration. Measurements show that these properties are suppressed by the application of pressure and point towards the potential existence of a previously undiscussed transition in the material between 0.4 GPa and 0.5 GPa.

The aim of this thesis it to contribute to three open problems in the theory of itinerant electron systems in two spatial dimensions. Firstly, the mechanism for charge density wave formation in the transition metal dichalcogenides is a debated subject. In this thesis it is shown that charge density wave formation is possible via a purely electronic mechanism in monolayer vanadium diselenide. The competition of superconductivity and density wave formation is taken into account using the renormalisation group. As the Fermi surface is tuned to perfect nesting, a charge density wave phase emerges when the Heisenberg exchange interaction is of the order of the contact Coulomb repulsion. Secondly, the search for materials which exhibit topological superconductivity is ongoing. Possible candidates are strongly spin-orbit-coupled metals. In this thesis a square-lattice Hubbard model with strong Rashba spin-orbit coupling and one of the Fermi surfaces close to a Lifshitz transition is examined. The metal is shown to be generically unstable to the formation of mixed-parity superconductivity with a helical triplet component via a renormalisation group analysis. Thirdly, the breakdown of Fermi liquid theory close to a quantum critical point is still not well understood. In this thesis a functional renormalisation group analysis is presented using a soft frequency cutoff, investigating a general class of Pomeranchuk instabilities with Nb flavours of boson. At small Nb the theory is characterised by weakly non-Fermi-liquid behaviour of the electrons and z ≈ 2 dynamics for the order parameter fluctuations. For large Nb, the theory crosses over to z ≈ 1 scaling and non-Fermi-liquid behaviour.

Hybrid metal halide perovskites have emerged over the last decade as highly promising materials for use in solar cells. Their advantages include low production costs, and rapidly increasing efficiencies to compete with those of commercially dominant silicon cells. Recently, increasing attention has been devoted to the use of perovskites in next-generation photovoltaic devices in order to overcome the efficiency limit for conventional single-junction cells. Work is still needed to identify the most promising perovskite materials for these applications, and to fully understand their relevant properties. This thesis contributes to both goals. The challenge of identifying the true timescale of charge-carrier cooling in metal halide perovskites, and whether certain compositions in fact show exceptionally slow cooling, is addressed. This is central to assessing the viability of hot-carrier extraction in perovskite solar cells. Key sources of error in previous approaches to determine charge-carrier temperature, which have produced an orders-of-magnitude range of reported cooling times, are identified. An improved model, which accounts for the full photoluminescence lineshape and enables a consistent approach that can be applied to studies across different perovskite compositions, is then described. Applying this improved model, charge-carrier cooling in FASnI3 is studied, revealing that observations of a secondary regime of slow charge-carrier cooling are in fact attributable to electronic relaxation, state-filling and recombination in this energetically disordered material. This result highlights that careful analysis of charge-carrier cooling dynamics is vital to assessing the realistic prospects for hot-carrier solar cells. Photoluminescence polarisation memory in FASnI3 is also examined, finding no persistent polarisation anisotropy within 270 fs. This points to a need for further study to identify the factors that lead such memory to arise from structural changes in certain perovskite compositions. Finally, the effects of the SnF2 additive commonly used to improve material quality of tin-containing perovskites are explored for FA0.83Cs0.17SnxPb1-xI3 across the lead-tin range. Significant beneficial effects from the suppression of tin oxidation and associated background hole doping, including reduced energetic disorder and increased charge-carrier mobilities and lifetimes, are found with as little as 1 mol% SnF2 added. The larger amounts of additive that have commonly been used are found to contribute to detrimental non-radiative recombination. These results, unravelling the impacts of SnF2 on both structural and optoelectronic properties, provide a foundation for control over the properties of mixed tin-lead perovskites for use as low-bandgap absorbers in all-perovskite tandem cells.

Organic semiconductors exhibit excellently suited material properties for a variety of applications and offer the possibility of low-cost and large-scale production. This thesis analyses photonic properties of several organic semiconductors, which are of great interest for different applications. To explore these materials, a combination of steady-state and time-resolved optical measurement techniques is employed and energy transfer dynamics within organic semiconductors are modelled. Research was focused on the following areas: The influence of the fraction of chain segments that adapt β-phase conformation on film microstructure of thin films of the blue-emitting polymer PFO is consistently investigated for the first time. An analysis of emission and absorption properties of PFO films with systematically varying β-phase content indicates that with increasing β-phase in PFO films, the chain conformation becomes more planar and includes more repeat units. Energy transfer, which occurs upon photoexcitation from glassy-phase to β-phase chain segments in PFO thin films is evaluated in terms of Förster resonant energy transfer theory. Differences in Förster radii calculated from ultrafast emission dynamics and spectral overlap between steady-state emission and absorption indicate that the energy transfer process is influenced by exciton diffusion within the glassy phase. Parasitic absorption of light in a molecular sun-facing charge extraction layer (CTL) of a metal halide perovskite (MHP)-based solar cell structure is addressed. Experimentally observed energy transfer between layers of photoexcited conjugated polymers and a MHP layer is combined with modelling the efficiency of the energy transfer process. Efficient energy transfer is found to counteract parasitic light absorption in the CTL for thin layers (≤ 10 nm) and/or high PLQE materials. Morphological changes in films of the hole-transport material P3HT deposited on MAPbI₃ are explored. Changes in aggregation are observed through careful analysis of absorption and emission spectra from P3HT films of varying thickness and spin speed during their fabrication on a MAPbI₃ layer.

Condensed matter physics spans molecules, fluids, and solids. Mathematical models have been developed to simulate physical systems, but exact solutions are special leaving the many-body Schr\"odinger equation analytically intractable. Therefore, approximations have to be constructed to make those difficult-to-solve problems tractable. This thesis adapts different levels of approximation, developing an exact formalism for a quantum operator, investigating the origins of intriguing phenomena in solids using first principle methods, and heuristic data-driven machine learning to guide biomedical developments. The quantum Monte Carlo method is used to study molecules where the formalism for force constants matrix is created for the first time using variational and diffusion Monte Carlo, which are the most accurate technique in electronic structure calculation but more resource demanding. We make the atomic relaxation and vibrational frequency calculation possible via the direct approach. The performance has been tested on a diverse set of case studies, with varying symmetries and mass distributions, and shows the established formalism outperforms leading computational methods over an order of magnitude in terms of the accuracy of vibrational frequency relative to experiment. This opens the way for self-contained quantum Monte Carlo simulations from relaxing atomic positions to calculating vibrational frequencies without being limited to the accuracy from density functional theory for structure relaxation. Density functional theory is applied to investigate the large and complex solids of perovskites and heterostructures efficiently. We explore the origins of Raman modes for transient photophysics in layered $2$D perovskites and discover the twisting of organic cations could influence the excitons in the inorganic layer. Understanding the coherent interplay of excitons, spins, and phonons facilitates the design of efficient light emission devices and solar cells. Inspired by an unexpected exchange bias effect in topological insulator superlattices, we introduce magnetic models to investigate the doping effect and predict the interfacial coupling between dopants induces exchange bias. We provide a new pathway for achieving the high-temperature quantum anomalous Hall effect in exchange bias stabilised magnetic systems by interface engineering. Finally, we show machine learning can deliver new insights for systems lacking theoretical models, and where data collection is expensive and difficult. We design a neural network model capable of handling missing data and estimating prediction uncertainties. We apply it to study the efficacy of biomedical stem cell fluids for cartilage repair and identify critical properties, optimal dose, and predicted therapeutic outcomes for personalised therapy. We provide references for scientists and clinicians to design better therapy strategies, and the technology can be adapted for addressing research problems across different subjects.

Strong light-matter interaction inside planar microcavities has been the object of intense scrutiny thanks to a wide variety of technological and theoretical achievements for which future applicability relies on understanding and controlling both photonic and excitonic environments. Recently, demonstrations of polariton lasing, non-equilibrium Bose Einstein Condensation (BEC) and superfluidity at room temperature have been reported thanks to the large oscillator strengths and exciton binding energies of Frenkel excitons in organic semiconductors. Among this class of material, semiconducting conjugated polymers are promising thanks to their versatility, remarkable optical properties and tunability. In this thesis, we explore different methods to manipulate the intra- and inter-chain properties of a subgroup of semiconducting polymers, the polyfluorenes, to shape the interactions of their excitons with light. We begin our work by examining the essential properties of semiconducting conjugated polymers, which we then embed inside microcavities to observe strong light-matter interactions. We present a brief overview of exciton-polaritons in organic microcavities, highlight recent developments in their understanding and introduce the measurement and fabrication techniques that we use throughout the thesis. In our first experimental investigation, we perform conformational changes to a polymer's backbone inside metallic microcavities thereby inducing two sub-populations of excitons with a pre-determined fraction. We present the mode characteristics of these structures with ultrastrong coupling (USC) of the first disordered population of excitons and a splitting of the lower polariton branch induced via gradual introduction of the second population of excitons. We measure the photoluminescence (PL) only emanating from the lowermost polariton branch, which allows us to exert conformational control over the emission energy and its angular variation to create dispersion-free cavities with highly saturated blue-violet emission. In our second experimental realization, we report an inter-chain tunability via the fabrication and optical characterization of organic microcavities containing liquid-crystalline conjugated polymers (LCCP)s aligned on top of a thin transparent Sulfuric Dye 1 (SD1) photoalignment layer. Transition dipole moment alignment enables a systematic increase in the interaction strength, with unprecedented solid-state Rabi splitting energies ~Ω0 of up to 1.80 eV, the first to reach energies comparable to those in the visible spectrum, accompanied by the highest-to-date organic microcavity coupling ratio: 65%. We also demonstrate that the coupling strength is polarization-dependent with bright polariton PL for TE polarization parallel to the polymer chains and either no emission or weakly coupled emission from the corresponding TM polarization. We finally examine the reflectivity and transmissivity of TE-polarized waves incident on microcavities containing excitons with in-plane uniaxially oriented transition dipole moments both theoretically and experimentally. We discuss the propagation of the electric field through the cavity and compare our results with previous reports. We confirm that in all cases, the reflected and transmitted electric fields derive from photons leaking parallel and perpendicular to the transition dipole moment orientation. We conclude our work by examining the opportunities that are enabled from our two experimental techniques for the future of polaritonics.

In this thesis superconductivity with unconventional pairing symmetries arising from repulsive interactions is investigated. Anyonic quasiparticles within the subclass of chiral p-wave superconductors are also examined. In Chapter 2 we study weak-coupling superconductivity in a repulsive Hubbard model on the tetragonal lattice. With the weak-coupling approximation we establish the superconducting phase diagram as the out-of-plane hopping strength and electron filling is varied. For four Fermi surface topologies we identify a total of five types of p- and d-wave ground state orders, several of which have accidental line nodes and break time-reversal symmetry. The weak-coupling scheme is adapted to strontium ruthenate (Sr₂RuO₄) in Chapter 3. We compute and compare odd- and even-parity superconducting order parameters using a realistic three-dimensional band structure. Two superconducting phases are identified: a helical p-wave spin triplet and a d-wave spin singlet phase. Both orders are roughly found to be compatible with specific heat data and recent nuclear magnetic resonance measurements [A. Pustogow et al., Nature 574, 72 (2019)]. We suggest that a d-wave order is likely involved in the superconducting phase, although certain experiments appear to remain incompatible with this conclusion. In Chapter 4 we describe anyonic (Majorana) quasiparticles in chiral p-wave superconductors at temperatures non-negligible compared to the superconducting gap. We consider the impact of thermally occupying in-gap vortex states on the hybridisation of two Majorana modes. The hybridisation, reflecting the state of the qubit defined by the two Majorana modes, is found to decay algebraically with temperature just above the first-excited state energy scale. In novel iron-based superconductors our results suggest that there is an appreciable temperature range in which qubit read-out can be achieved via the inter-vortex force derived from the hybridisation.

The interest in vortices and vortex lattices was sparked by the prediction of quantisation of circulation by Onsager in the 1940s. The field has since developed dramatically and attracted a lot of interest across the physics community. In this dissertation we study vortices in two different systems: a rotating, Rabi-coupled, two-component Bose--Einstein condensate (BEC) and a rotating spinor-BEC, in two spatial dimensions. Vortex molecules can form in a two-component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in two dimensions, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of intercomponent interactions and strength of the Rabi field. In the limit of large field, when molecules are tightly bound, we develop a complementary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of two-dimensional quadrupoles, which may be written in terms of an elliptic function Q(z_ij;ω₁,ω₂). This allows for a numerical evaluation of the energy enabling us to find the ground state configuration of the molecules. In the 'polar' phase of a two-component BEC, in which the spin density is zero, the emergent 'spin-gauge rotation symmetry' of the order parameter allows for the presence of half-quantum vortices (HQVs). We numerically search for this object in the variational ground state of a spinor-BEC and find it in certain region of the phase diagram. We provide analytical arguments that suggest that this object is energetically favorable in the ground state. Matrix product state (MPS) based methods are currently regarded as one of the most powerful tools to study the low-energy physics of one-dimensional many-body quantum systems. In this work we find a connection between MPS in the left canonical form and the Stiefel manifold. This relation allows us to constrain the optimisation to this subspace of the otherwise larger MPS manifold. We find that our method suffers from two undesirable features. First, the need of a large unit cell to achieve machine precision. Second, because of the presence of the power method in the variational energy expression, it is possible for the convergence process to get stuck in regions of the Stiefel manifold where the modulus of the second largest eigenvalue of the transfer matrix is very close to one. Since the foundation of the field of 'Artificial Intelligence' (AI) in 1956, at a workshop held in Dartmouth College (New Hampshire, US), the excitement and optimism towards it has oscillated throughout the years. The last AI boom started in 2012 and we live in a time where people from 'all' disciplines, both in industry and academia, are getting involved in machine learning. We contribute to the field with a 'quantum-inspired' generative model for raw audio. Our model is based on continuous matrix product states and it takes the form of a 'stochastic Schrödinger equation', describing the continuous time measurement of a quantum system. We test our model on three different synthetic datasets and we find its performance promising.

The energy level tuning effect, observed when mixing halogenated versions of similar molecules, has recently been identified as a new way to modify the bulk ionisation energy and electron affinity of an organic semiconducting thin film, and increase the open-circuit voltage in organic solar cells. In this thesis, the energy level tuning effect is extended to organic field-effect transistors (OFETs). A method for the fabricating ambipolar devices with balanced hole and electron transport is established. This is achieved by using blends of two host molecules, zinc phthalocyanine (ZnPc) and its eight-times fluorinated derivative (F8ZnPc), with energy levels that shift based on mixing ratio. The semiconducting behaviour of the bottom-gate bottom-contact OFETs can be tuned continuously from unipolar p-type, through ambipolar, and finally to unipolar n-type. For the ambipolar devices, the optimum balance between the hole and electron mobilities is found for the blend of 1:1.5 weight ratio of ZnPc:F8ZnPc with hole and electron mobilities of (8.3 ± 0.2)×10 −7 cm2V−1s−1 and (5.5 ± 0.1)×10−7 cm2V−1s−1 , respectively. An application of the ambipolar devices in a complementary-like voltage inverter circuit, with performance comparable to an inverter based on separate ZnPc and F8ZnPc OFETs, is demonstrated. Next, a p-dopant (F6-TCNNQ) is introduced into the blend of ZnPc: F8ZnPc to investigate the impact of the energy level tuning effect on the molecular doping process. The doping efficiency is investigated using photothermal deflection spectroscopy and electron paramagnetic resonance spectroscopy, and is found to depend upon host mixing ratio. The experimentally observed trend is explained with a statistical model that includes both shifts of the host’s ionisation energies, and, importantly, the electron affinity of the dopant. The energy level shift in the model is in close agreement with the 0.86 eV shift in ionisation energy observed experimentally. As further validation, the model reproduces the measured trend at low temperature. The energy level tuning effect therefore has a crucial impact on the molecular doping process. The practice of comparing host and dopant energy levels must consider the long-range electrostatic shifts to consistently explain the doping mechanism in organic semiconductors.

The polaron is a quasiparticle formed by collectively dressing an electron with a phonon cloud. It emerges in a crystal lattice when an extra electron is trapped at the lattice distortion induced by itself. Due to its unique role and technological implications, this subject has consistently received attention for many years. To date, first-principle studies of polarons in materials are still based on direct calculations with large simulation cells. In this thesis we develop a theoretical and computational framework that allows for the modelling of lattice polarons in different materials of interest, but using unit-cell calculations of electronic, vibrational properties and electron-phonon couplings. We explain the architecture of the implementation in detail, and propose a self-interaction corrected DFT scheme for the validation of our methodology and implementation. We present extensive tests and benchmark for the code. We apply this new approach to investigate polaron properties in LiF and Li2O2 as prototypical bulk materials that host large and small polarons. We demonstrate that our method can describe both large and small polarons on the same footing, and capture both Fr ̈ohlich-type polar electron-phonon coupling and non-Fr ̈ohlich couplings to acoustic and optical phonons. Furthermore, we report cal- culations of formation energy, excitation energy, and wavefunction of polarons. To establish a quantitative understanding of which KS states and phonon modes con- tribute to the formation of polarons, we analysis the polaron spectral decomposition in a spirit similar to the Eliashberg spectral function. The last part of the thesis is devoted to explore the dimensionality effect on the polaron properties in h-BN. In this case, we compare the polaron energies for a localised hole between the h-BN in bulk and in monolayer, and show that the two-dimensional hole polaron trapped in the h-BN monolayer exhibits a layer formation energy in comparison to the bulk one. This work will open the door to predictive calculations of polarons in more complicated systems, such as van der Waals heterostructure and interfacial systems, and constitutes as a first step toward complete ab initio many-body calculations of polarons in real materials.

With each and every passing year, weather patterns seem to become less predictable and more chaotic due to changes to worldwide climate patterns. Greenhouse gas-free energy production is a boon to the aim of preventing further rises in global temperature increases. This thesis concerns itself with one major aspect of green energy, namely photovoltaics, and some materials with great potential for application in photovoltaics, namely single-walled carbon nanotubes (SWNT), and perovskites. SWNT have been known for almost thirty years by now, but their intrinsic fondness of bundling up due to their 2pz-orbitals has to date prevented any large scale application of them. Functionalising of SWNT offers a solution to this problem, either by dispersing them with surfactants in water, or by polymer functionalisation. Here, the latter method was applied to the problem, and the efficacy of deposition from solvents more advantageous than water is shown, achieving values of transmission and sheet resistance close to the necessary values for application in solar cells. Next, an inorganic contender for solar cell applications, Cs2AgBiBr6, is characterised by magneto-optical studies. With these, a direct and indirect gap are identified at 2.85 eV and 1.31eV. Moreover, a strongly Stokes shift influenced AgBi anti-site defect colour centre at 2.25 eV is shown to be part of a self-trapped exciton at low temperatures. Thereafter, the optical properties between 1.4 K and 370 K in conjunction with room temperature x-ray diffraction measurements of MAPbI3 single crystals and thin films grown/annealed at different temperatures are used to explain the double emission structure visible in photo- luminescence and reflectance. A dynamic Rashba effect, likely due to spontaneous alignment of the methylammonium-ions, causes a direct and indirect gap, where the former dominates the surface and the latter dominates the bulk of the samples. The remaining chapter is a study of the polaronic influence on the transitions observed for MAPbBr3 and MAPbI3. In comparison between high field, high energy, and low field, low energy, an almost two-fold difference in exciton binding energy, and an increase in effective mass can be observed due to exciton/lattice interactions in comparison to the established high field literature values. Interestingly, for both perovskites studied, single crystals show more favourable values, indicating that device application improvements could be possible by making thin films more single crystal-like.

Recently, the fast technological development of organic solar cells (OSCs) proves that it has a promising future in the sustainable energy market. Interlayers play a significant role in OSCs, which can enhance device performance and stability. However, many of the fundamental mechanism and design principles of the interlayers have not been adequately studied. The theoretical chapters of this thesis deliver a summary of the state-of-the-art photovoltaic (PV) technologies and the fundamentals of organic photovoltaics (OPVs). The basic knowledge of interlayers within OSCs is introduced, too. The methodology chapter introduces the materials used in this thesis. Besides, fundamentals and technical parameters of the methodologies are summarised in this chapter, e.g. X-ray diffraction (XRD), grazing-incidence wide-angle X-ray scattering (GIWAXS), photoluminescence (PL), spectroscopic ellipsometry, external quantum efficiency (EQE), and internal quantum efficiency (IQE). In the experimental chapters, a new molecule (hexapropyltruxene) is introduced as an interlayer material in small molecule organic solar cells (SMOSCs), and its functions within OSCs are investigated. Firstly, hexapropyltruxene is used as an interlayer in the SubPc/C60 solar cell stack. The experimental results show that hexapropyltruxene works well as an exciton blocking layer (ExBL) between the MoOx and SubPc layers. By adding 3.8 nm of hexapropyltruxene between MoOₓ and SubPc layers, the power conversion efficiency (PCE) of the SubPc/C60 solar cells is enhanced from 2.6 % to 3.0 %, achieving a ca. 15 % improvement. Besides, it is found that hexapropyltruxene has a weak molecular template growth effect on the growth of SubPc thin film. Secondly, the application of hexapropyltruxene as an interlayer in the solar cell stack first demonstrated by interuniversity microelectronics centre (IMEC) is also investigated. The results reveal that hexapropyltruxene has a very weak exciton blocking effect between MoOₓ layer and alpha-6T donor layer. The structural characterization also suggests that hexapropyltruxene can induce the growth of different alpha-6T polymorphs. In the final experimental chapter, the polymorphism of alpha-6T induced by different substrates with hole contact layers (HCLs) is studied. The competing growth of low temperature (LT)-, high temperature (HT)-, and beta-phases of alpha-6T is observed in the thin film growth. The results of the experiments suggest that widely-used HCLs such as MoOx, PEDOT:PSS, and MeO-TPD have the template growth effect on alpha-6T molecules. In addition, the substrate temperature in the deposition process is significant in the competing growth of alpha-6T polymorphs. Corresponding solar cell performances show a correlation with the polymorph composition within alpha-6T layers and the performances of OSCs. To conclude, less "standing-up" but more "lying-down" molecules lead to better light absorption, which results in better solar cell performance. PEDOT:PSS is the most appropriate HCL for our alpha-6T/SubPc solar cell stack, and low substrate temperature (20 C) is more suitable than high temperature (120 C) in the growth of alpha-6T thin films for solar cell application.

This dissertation reports on several experimental projects studying electronic transport in thin-film electronic devices. Self-assembly methods and graphene were used to realise devices contacting films of self-assembled PbS quantum dots. The devices have exhibited single-electron tunnelling with a high yield. The electrical properties of the junctions are studied individually and collectively using statistical tools to extract correlations between device geometries and electrical data. The dissertation includes discussion of the theory of relevant electronic transport including numerical simulations. Several initiated projects deriving from this work are introduced. A second device reported in this thesis is a memristive switch. Contacting thin films of Al2O3 with graphene delivered junctions which exhibit memristive behaviour with an ultrahigh on-off conductance ratio. The conduction state of the junctions is correlated with morphological changes in the devices, whereby conductive flament formation in the junction is found to lead to electrically-controllable and reversible gas encapsulation in bubbles in the structure. The device is measured electrically and topographically, and the correlation between the two aspects is studied. A discussion of memristive conduction is included with numerical simulations. A third section reports on a project studying thermoelectricity in self-assembled molecular junctions, as they show potential for improved thermoelectric efficiency for energy harvesting; this is discussed in the dissertation. Strategies to benchmark the studies are presented with relevant devices fabricated and measured. These include the development of a measurement protocol to study thermoelectricity in devices, studies of electrical coupling between various molecular structures and graphene electrodes, molecular-structure dependence of electrical and thermal conductance of junctions. Preliminary results and on-going work are discussed.

Superconducting circuit QED is a promising approach for building a quantum computer. In order to realise superconducting circuits at a sufficient scale for useful near-term applications, an architecture with an extensible design is required which implements good connectivity between qubits, and allows for selective readout and control of the qubits without introducing detrimental crosstalk or decoherence. This thesis describes the development of a new coaxial circuit QED architecture that fulfils this requirement of extensibility by incorporating out-of-plane wiring into the sample holder. Single-qubit unit cells consisting of a transmon qubit and readout resonator with coaxial geometries are fabricated on opposing sides of a substrate, and selective control and readout of the qubits is achieved via a capacitance to coaxial wiring built into the device enclosure. Unit cells of qubit and resonator can be arranged in a 2D array without modification of the wiring scheme. A single-qubit unit cell of this architecture is used to implement dispersive circuit QED, and a full characterisation of the Hamiltonian is performed. The device is shown to have parameters comparable to those found in other approaches, such as a coupling between qubit-resonator of ~100 MHz and a coherence time of order ~10 μs. The extension of this scheme to 2D arrays of qubits is then presented, and realizations of two-qubits gates are demonstrated with fidelities all above 87% on a four qubit device. Further evaluations are performed on multi-qubit devices, including a characterisation of the drive isolation of the mode-matched drive ports, finding values in the range of 50 dB and 30 dB for measurement and control respectively. Similarly, the cross coupling between circuits is shown to have values ~2% of the coupling within a unit cell. The effective circuit temperatures are measured, finding typical values of ~100 mK, and the techniques of spin-locking and T2 spectroscopy are employed to probe the noise environment. Finally the architecture is extended to incorporate frequency tuning of qubits with gradiometric SQUID loops by way of off-chip flux bias lines (FBLs). These lines are used to tune qubits with a signal isolation of >99%. Furthermore, the ability of these FBLs to dynamically control the qubit frequency is shown by demonstrating switching of the frequency on a nanosecond time-scale, and parametric driving over a frequency range of gigahertz.

In hybrid mesoscopic systems the Meissner response of a superconducting film can be very different from its bulk behaviour. For instance, in normal (N) superconductor (S) bilayers screening can be greatly enhanced depending on the relative material properties and interface conditions. Furthermore, with the addition of ferromagnetic (F) layers comes the possibility of generating a paramagnetic screening response due to spin triplet pairs. Such pairs are produced from the mixing of opposing microscopic orders within S (which conventionally hosts electron pairs of opposite spin and momenta) and F (inside which spin symmetry is broken). The net result is a conversion of a fraction of the pairs to an odd-frequency s-wave triplet state. Any resultant modifications to the screening manifest in the flux profile across a sample which is directly probed using low energy muon spin rotation (LEμSR). Results of LEμSR experiments involving layered systems comprised of N, S and F elements are presented within chapter 3. A discrepancy between the pre-existing quasiclassical theory and measured flux profiles in the presence of an F layer was observed. A large enhancement to the flux lowering which could not be interpreted within the traditional S/F proximity picture was found. New theoretical developments have since suggested that coupled to direct electronic proximity effects within these systems is an additional electromagnetic component. Chapter 4 presents the results of analysing LEμSR data using a spatial flux profile consistent with new theory. In doing so, the observed anomalous enhancement could be successfully reconciled with the electromagnetic proximity effect. Subsequent experimental work in chapters 4 - 6 sought to test the main predictions of the theory by manipulating S/F interfaces within a variety of different structures. In all tested cases the theory provided an excellent description of experiment suggesting the importance of considering electromagnetic effects within S/F hybrid systems.

There is increasing interest in the role of materials with correlated structural disorder in mimicking the exotic properties exploited in electronic condensed matter phases. Spin ices, for example, are important class of frustrated magnets in which the spin configuration obeys the `two-in two-out' ice rules that govern proton order in water-ice. Such ice rules are implicated in a wide range of functional responses in different materials, from heavy-fermion behaviour to superconductivity. Ice-rules-obeying states are characterised by an absence of long range order, leading to a manifold of degenerate ground states, extensive residual entropy and exotic excitations; in spin-ices, these excitations correspond to topological defects in the form of effective magnetic monopoles. The main barrier to experimentation and application of these topological defects is the extremely low temperatures (~ 1 K) at which the spin-ice correlations develop. This thesis explores the structural ice analogue cadmium cyanide, Cd(CN)2, a cubic negative thermal expansion (NTE) material, in which the orientation of cyanide ions maps onto the spin orientation in spin-ices. Cd(CN)2 is shown here to display spin-ice physics at room temperature. Chapter 3 outlines the extreme sensitivity of Cd(CN)2 to X-ray irradiation, including unit-cell contraction, and the selection or suppression of particular phase transitions. These results explain earlier discrepancies regarding the phase behaviour and negative thermal expansion in Cd(CN)2 and motivated the development of a synthesis of isotopically-enriched 114Cd(CN)2 suitable for neutron scattering studies. The synthesis of Cd(CN)2 directly from Cd metal forms the basis of Chapter 4. The structure of previously-unreported intermediate phase, Cd(NH3)2[Cd(CN)4], is characterised, as well as its thermomechanical response. This represents the first variable-temperature study of this type of framework (PtS), shown to display anisotropic NTE and negative linear compressibility. The main result of this thesis is to demonstrate that by replacing the magnetic dipole in spin-ice with the electric dipole of the cyanide ion, cadmium cyanide displays spin-ice behaviour at temperatures nearly sixty times higher that in its magnetic analogue. I present the results of neutron scattering measurements on 114Cd(CN)2 along with density functional theory calculations, Monte Carlo simulations, total scattering and nuclear magnetic resonance measurements. Having confirmed the importance of spin-ice physics, chapter 6 explores the pressure and temperature dependence of the ice-like correlations. At least two phase transitions are identied at low pressure, kinetic trapping is observed and the extreme compressibility shown to be a function of cyanide reorientation and ice-like coordination. It is hoped that increase in energy scale, identified here, will enable further exploration that may shed further light on the physics of the spin and water-ices themselves.

This thesis presents studies of the spin dynamics in quantum magnets using inelastic neutron scattering (INS) and linear spin wave theory (LSWT). The first system considered is Ba2CuTeO6, proposed to realise weakly-coupled antiferromagnetic two-leg spin-1/2 ladders. Ba2CuTeO6 orders magnetically, but with a small Neel temperature relative to the exchange strength, suggesting that the interladder couplings are only just able to stabilise magnetic order and placing Ba2CuTeO6 close in parameter space to the critical point separating the singlet phase and Neel order. By comparing powder INS data with LSWT and quantum Monte Carlo (QMC) calculations, values are proposed for all relevant exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. High-field magnetisation data are also compared with the QMC predictions. In addition, single-crystal INS measurements are presented of the spin-1/2 triangular antiferromagnet Ba3CoSb2O9. Sharp magnons are observed throughout the Brillouin zone with a strong scattering continuum extending up to at least 4x the maximum one-magnon energy. The magnon energies are strongly renormalised downwards and the intensity decreases faster upon increasing energy than predicted by LSWT, which is attributed to a transfer of spectral weight to the continuum. An empirical model of renormalisations to the LSWT dispersion is proposed that can capture quantitatively the magnon dispersions throughout the Brillouin zone. Consistent with the observation of sharp magnons throughout, it is explicitly verified that kinematic constraints disallow one- to two-magnon decays for this renormalised dispersion. There is considerable structure and signal extending to much higher energies that cannot be explained by two-magnon simulations, suggesting significant quantum fluctuations beyond LSWT. The magnon dispersions have also been measured in fields up to 9 T, observing an evolution of the dispersion relations in field that is consistent with the presence of two equal-weight domains of opposite chirality.

Interacting Fermi gases are one of the chief paradigms of condensed matter physics. They have been studied since the beginning of the development of quantum mechanics, but continue to produce surprises today. Recent experimental developments in the field of ultracold atomic gases, as well as conventional solid state materials, have produced new and exotic forms of Fermi gases, the theoretical understanding of which is still in its infancy. This Thesis aims to provide updated tools and additional insights into some of these systems, through the application of both numerical and analytical techniques. The first Part of this Thesis is concerned with the development of improved numerical tools for the study of interacting Fermi gases. These tools take the form of accurate model potentials for the dipolar and contact interactions, as found in various ultracold atomic gas experiments, and a new form of Jastrow correlation factor that interpolates between the radial symmetry of the inter-electron Coulomb potential at short inter-particle distances, and the symmetry of the numerical simulation cell at large separation. These methods are designed primarily for use in quantum Monte Carlo numerical calculations, and provide high accuracy along with considerable acceleration of simulations. The second Part shifts focus to an analytical analysis of spin-imbalanced Fermi gases with an attractive contact interaction. The spin-imbalanced Fermi gas is shown to be unstable to the formation of multi-particle instabilities, generalisations of a Cooper pair containing more than two fermions, and then a theory of superconductivity is built from these instabilities. This multi-particle superconductivity is shown to be energetically favourable over conventional superconducting phases in spin-imbalanced Fermi gases, and its unusual experimental consequences are discussed.

A major area of interest in condensed matter physics over the past decades has been the emergence of new states of matter from strongly correlated electron systems. A few limited examples would be the emergence of unconventional superconductivity in the high-T$_c$ superconductors and heavy-fermion systems, the appearance of the skyrmion magnetic vortex state in MnSi and magnetically mediated superconductivity in UGe$_2$. While detailed studies of many of the emergent phases have been made, there are still many gaps in understanding of the underlying states and mechanisms that allow them to form. This work aims to add to knowledge of the basic physics behind such states, and the changes within them as they are tuned to approach new phases. The cubic perovskite material SrTiO$_3$ has been studied for many decades and is well-documented to be an incipient ferroelectric, theorised to exist in the absence of any tuning in the proximity of a ferroelectric quantum critical point. This work presents the first high-precision dielectric measurements under hydrostatic pressure carried out on a quantum critical ferroelectric, leading to a full pressure-temperature phase diagram for SrTiO$_3$. The influence of quantum critical fluctuations is seen to diminish as the system is tuned away from the quantum critical point and a novel low temperature phase is shown to be emergent from it. The Néel Temperature of the two-dimensional antiferromagnet FePS$_3$ was found to increase linearly with applied hydrostatic pressure. Evidence of an insulator-metal transition is also presented, and an unexplained upturn in the resistivity at low temperatures in the metallic phase.

We consider a series of problems regarding quantum Hall edges, focusing on both dynamics and the mathematical structure of edge states. We begin in Chapter 3 with a limiting case of the Laughlin state placed in a very steep confining potential, but which is weak compared to the interactions. We find that the eigenstates have a Jack polynomial structure and an energy spectrum which is extremely different from the well-known Luttinger liquid edge. In Chapter 5 we analyse the inner products of edge state wavefunctions, using an effective description given by a large-N expansion ansatz proposed by J. Dubail, N. Read and E. Rezayi, PRB 86, 245310 (2012). As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check the conjecture by calculating overlaps exactly for small system sizes and comparing the numerics with our high-order expansion to find excellent agreement. Finally, Chapter 6 considers the behaviour of quantum Hall edges close to the Luttinger liquid fixed point that occurs in the low energy, large system limit. We construct effective Hamiltonians using a local field theory description and then consider the effect of bulk symmetries on this edge. The symmetry analysis produces remarkable simplifications which allow for very accurate descriptions of the low-energy edge physics even relatively far away from the Luttinger liquid fixed point.

This thesis describes the application of various techniques to the study of magnetic phenomena in condensed matter systems with a particular focus given to a.c. magnetic susceptibility. This is accomplished by briefly discussing the basic theory of condensed matter magnetism before describing measurement techniques employed in this thesis. I discuss magnetometry in detail, contrasting d.c. susceptibility with a.c. susceptibility in the context of the applicability of the latter to the study of slow magnetic dynamics. In order to understand the a.c. response of materials containing slow magnetic dynamics I take a theoretical approach and show how the commonly used models for describing such behaviour arise from the more overarching linear response theory. I then show common treatments of a.c. susceptibility data before reviewing the a.c. response of various classes of material while discussing the origin of the associated magnetic sluggishness. Subsequently, I show studies of two different classes of material showing magnetic sluggishness. In the first study of single-molecule magnets two families are examined: the simpler Co3+2Ln3+ family (Ln = Gd, Ho, Tb and Er) and the more complex Ni2+4Ln3+4 family (Ln = Gd, Ho, Dy, and Tb). By beginning with the Co2Ln family in which only the central Ln3+ ion possesses a magnetic moment I use a.c. susceptibility to show the Tb and Er analogues to display field-induced slow magnetic relaxation consistent with single-molecule magnet behaviour while the Gd and Ho analogues do not. Combining these results with d.c. magnetic measurements in the context of the structure of these compounds allows the origin of this behaviour to be shown to be associated with the relevant Ln3+ ions. This sets out the process utilised for elucidating the magnetic behaviour of the more complex Ni2+4Ln3+4 family in which both transition metal ions and lanthanide ions possess a magnetic moment. As such, the possible magnetic exchanges between ions are evaluated using d.c. techniques and I propose the Dy and Tb analogues to form Ni-Ln dimers (ferromagnetic and antiferromagnetic respectively). Using a.c. susceptibility I demonstrate Ni4Dy4 and Ni4Tb4 to display field-induced slow magnetic relaxation of single-molecule magnet origin only in Ni4Dy4. The second study I present focuses on the low temperature magnetism associated with the superconducting family Li1-xFex(OH)Fe1-ySe which is comprised of alternating two-dimensional layers of Fe1-ySe and Li1-xFex(OH). The Fe2+ ions of the hydroxide layer possess a magnetic moment and by considering a random distribution of these ions in such a layer I suggest the low temperature magnetic state to likely be disordered and spin glass-like. Taking advantage of samples provided by synthetic chemists of superconducting and nonsuperconducting members of this family I show that d.c. magnetometry and heat capacity measurements support a spin glass-like state. A.c. susceptibility and μSR measurements demonstrate that the magnetic state of Li1-xFex(OH)Fe1-ySe contains slow relaxation of a spin glass type.

Two dimensional (2D) materials with interesting fundamental physics and potential applications attract tremendous efforts to study. The versatile properties of 2D materials can be further tailored by tuning the electronic structure with the layer-stacking arrangement, of which the main adjustable parameters include the thickness and the in-plane twist angle between layers. The Angle-Resolved Photoemission Spectroscopy (ARPES) has become a canonical tool to study the electronic structure of crystalline materials. The recent development of ARPES with sub-micrometre spatial resolution (micro-ARPES) has made it possible to study the electronic structure of materials with mesoscopic domains. In this thesis, we use micro-ARPES to investigate the spatially-resolved electronic structure of a series of few-layer materials: 1. We explore the electronic structure of the domains with different number of layers in few-layer graphene on copper substrate. We observe a layer- dependent substrate doping effect in which the Fermi surface of graphene shifts with the increase of number of layers, which is then explained by a multilayer effective capacitor model. 2. We systematically study the twist angle evolution of the energy band of twisted few-layer graphene over a wide range of twist angles (from 5° to 31°). We directly observe van Hove Singularities (vHSs) in twisted bilayer graphene with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is observed in trilayer graphene. The large tuning range of vHS binding energy in twisted few-layer graphene provides a promising material base for optoelectrical applications with broad-band wavelength selectivity. 3. To better extract the energy band features from ARPES data, we propose a new method with a convolutional neural network (CNN) that achieves comparable or better results than traditional derivative based methods. Besides ARPES study, this thesis also includes the study of surface reconstruction for the layered material Bi2O2Se with the analysis of Scanning Tunnelling Microscopy (STM) images. To explain the origin of the pattern, we propose a tile model that produces the identical statistics with the experiment.

This thesis explores a range of photoactive metal halide perovskite materials for use in photovoltaic applications. These materials are of huge interest due to their outstanding optoelectronic properties which result in high photovoltaic power conversion efficiencies. In particular, this thesis discusses perovskites with stoichiometry ABX3 where A is a singly charged cation, for example methylammonium (MA), B is predominantly lead (Pb2+), and X is iodide (I-) and/or bromide (Br-). At present the commercial applications of these materials are limited by the chemical instability of the A-site cation. In this thesis, the effect of chemical substitution of the A-site is investigated as a way to increase the stability of the perovskite material. Full replacement with the inorganic cation caesium (Cs+) is shown to significantly improve the chemical stability. However, the inorganic lead halide perovskites with ideal bandgaps for photovoltaic applications exhibit structural instability. Routes to achieve both chemical and structural stability for these perovskites are discussed. Consequently, this thesis represents pioneering work in the field of inorganic halide perovskites and will greatly assist the development of stable inorganic perovskite materials for optoelectronic applications such as tandem photovoltaics and LEDs. Chapters 1 and 2 of this thesis present the motivation for perovskite materials to be used in solar cells, along with relevant background information about these materials and solar cell operation in general. Chapter 3 details the methods utilised in the experimental results chapters which follow. The first experimental results chapter, Chapter 4, shows how incorporation of Br- in place of I- in CsPbI3 leads to increased ambient stability of the perovskite structure, and the first solar cells with CsPbI2Br as the absorbing photovoltaic material are reported. Chapter 5 remedies the deficit of information about the optoelectronic properties of the CsPbI3-xBrx (0 ≤ x ≤ 3) perovskites through magneto-optical measurements on thin-films. These measurements raise questions about the room temperature perovskite structure of the CsPbI3-xBrx compositions with small x, previously thought to be cubic perovskite, which is shown in Chapter 6 to be an orthorhombic perovskite polymorph. This finding motivates preliminary work presented in Chapter 7 aimed at chemical stabilisation of this orthorhombic perovskite polymorph. Finally, Chapter 8 summarises the work presented in this thesis, and recommends further research for the development of stable perovskite materials for photovoltaics.

The proposed final resting place for radioactive waste in the UK is a geological disposal facility that will be built at a location in the UK, which has yet to be chosen, at some unspecified time in the future. To safely commit a waste material into this facility requires knowledge about the long-term behaviour of the material in the disposal conditions. It is critical to consider what effect the ionising radiation introduced by contaminants will have. In the case of Magnox sludge, a complex material that exists in large quantities, it is known that hydrogen gas will be produced by radiolysis. It is clear that fundamental understanding of this process is required to build confidence in the proposed disposal plans. In this investigation, we start with a simple model of bulk brucite, the main component of the Magnox sludge. When a high-energy ionising particle interacts with matter, its initial passage leaves a cylindrical track where there will be a high density of ions and radical species created. This process will spawn many secondary electrons with a lower energy than the initial particle and these will create small secondary tracks, known as spurs, near the main track. Additional electrons will be created at successively lower energies, and this cascade will continue until the electrons can no longer induce ionisations. The end result is that the largest population of electrons contains those with low energies, around the ionisation potential of the material being irradiated. Thus, in our calculations, using density functional theory, the effects of two types of electronic structure defect were considered. The first is the addition of an excess electron into the system, representing one of these many low energy electrons. The second is the addition of an excess hole, which simulates an ionisation. Molecular dynamics simulations were used to give insight into the effects of the defects on the material at room temperature. Complexity was added to the model by the creation of a surface. Initially, this surface was in contact with vacuum. Subsequently, water was added to the system, first as monolayers adsorbed on the slab surface, and then later as bulk water. This work shows that excess holes are particularly damaging to brucite, potentially leading to the dissociation of hydroxide groups at room temperature, while excess electrons are relatively inert. This process could be the first step in a reaction pathway that may directly or indirectly lead to molecular hydrogen formation. The presence of a water interface has a considerable effect on the results, the most significant of which is that an excess hole will localise near the surface of the bulk brucite or even in the bulk water, which could reduce damage to brucite mineral. Similarly, an excess electron will localise at the surface and will become solvated by the water monolayer. These results suggest that the water in the sludge, rather than the brucite itself, is a larger problem with regard to the stability of the waste following disposal.

Nuclear magnetic resonance (NMR) is a powerful experimental technique for probing the local environment of nuclei in materials. However, it can be difficult to separate the large number of interactions that are recorded in the resulting spectra. First-principles calculations based on quantum mechanics therefore provide much-needed support for interpreting experimental spectra. In this way, the underlying mechanisms recorded in experimental spectra can be investigated on an atomic level, and trends can be noted with which to guide the direction of future experiments. This thesis presents two cases in which first-principles calculations do just that. The first is an investigation of the perovskite structures of NaNbO3, KNbO3, LiNbO3 and the related solid solutions of NaxK1-xNbO3, KxNa1-xNbO3 and LixNa1-xNbO3 in order to study how structural disorder affects their NMR parameters. The second investigation involves the calculation of the Knight shift in platinum, palladium and rhodium---in their elemental bulk forms and in a set of surface structures. The Knight shift is a systematic shift in the NMR frequencies of metallic systems. It arises from the hyperfine interaction between the nuclear spins and the spins of the unpaired conduction electrons. When calculating the Knight shift, it is found that the Brillouin zone must be very finely sampled. A discussion of core polarisation is also presented. This is the polarisation of core electrons as a result of their interaction with valence electrons. In the case of Curie paramagnets, core polarisation can have a significant effect on the calculation of hyperfine parameters.

This thesis investigates a number of novel magnetic materials and high temperature superconductors using high-field magnetometry and muon spin spectroscopy (μSR). The main measurement techniques are briefly described and a study of the dimer material [Cu(pyrazine)(glycine)]ClO4 is presented to demonstrate the use of the proximity detector oscillator as a susceptometer in high magnetic fields. μSR is a highly effective tool for probing magnetic order, spin freezing and spin dynamics. However, in some circumstances its performance may be impaired by the extent to which it perturbs the material under study. Using μSR, density functional theory and crystal field calculations, I identify an experimental situation in the family of candidate quantum spin ices Pr2B2O7 (B = Sn, Zr, and Hf), in which the measured response is dominated by a muon-induced distortion of the local structure. This issue is also addressed in a study of the spin dynamics in the canonical spin ice Ho2Ti2O7. Although computational work indicates a similar muon-induced effect in both Ho2Ti2O7 and Dy2Ti2O7, the μSR data is not dominated by this perturbation. The remainder of this thesis is concerned with studying the superconducting properties of a number of Fe-based materials, including LiFeP which is found to have an enhanced superfluid stiffness in relation to its transition temperature. Also reported is the effect of structural disorder on the superconducting state in recently discovered Sr0.3(NH2)y(NH3)1-yFe2Se2. Pulsed magnetic field measurements are used to probe the temperature dependence of the upper critical field, giving a maximum value of μ0Hc2(0)≈33(2) T. I also investigate the effect of intercalating additional ammonia, via reversible adsorption and desorption in the related superconductor Lix[(NH2)y(NH3)1-y]zFe2Se2 (z = 1, 2). These reactions were carried out in situ on the muon beamline so that the superfluid stiffness could be measured using transverse-field μSR on a single sample.

Over the last 4 years, perovskite solar cells emerged as an attractive, highly efficient, and low-cost alternative to established, conventional photovoltaic technologies. The power conversion efficiency of these devices recorded an unprecedented rise, currently exceeding certified values of 20%. This thesis covers a number of technological advancements which lead to improved photovoltaic performance, as well as vital insight into some more fundamental aspects of the perovskite device operation. The focus of this body of work is primarily directed towards the electric contact in the PV stack which is responsible for electron collection. The motivation of the study presented here is given in Chapter 1, and includes a brief summary of the current energy landscape. Chapter 2 introduces the theoretical background of photovoltaic technology, starting from the basics of semiconductor physics, through to the principles of solar cell operation, as well as some characteristic properties of the perovskite materials. Details of the experimental methods used in this study are reported in Chapter 3. Chapter 4 reports the development of a low temperature process (sub-150 °C) for the manufacture of perovskite solar cells. Dispersions of pre-synthesised, highly crystalline TiO2 nanoparticles were used as an electron selective contact, which eliminated the high temperature sintering step. Chapters 5, 6 and 7, report the interface modification of an n-type contact, resulting in a substantially improved device operation and suppression of hysteresis phenomenon which is characteristic of perovskite photovoltaics. Fullerene-based materials have been found to make excellent electronic contact with halide perovskite materials, and are shown to be far superior to commonly used metal oxides. The facilitated electron collection allows enhancements in the photovoltaic performance of these devices. Furthermore, the organic layers used in this study can be processed at low temperatures. Finally, the development of transparent conductive electrodes based on silver nanowires is presented in Chapter 8. The fabricated electrodes exhibit low sheet resistance, high degree of transparency, and can be processed at low temperatures, allowing them to be compatible with processing on flexible substrates and multi-junction architectures. The application of silver nanowires in different perovskite solar cell architectures is also reported.

Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.

The three key areas of this thesis are crystal synthesis strategies, growth mechanisms, and new types of quantum materials nanowires. The highlights are introduction of a new catalyst (TiO2) for nanowire growth and application to Bi2Se3, Bi2Te3, SnO2, and Ge nanowires; demonstration of step-flow growth, a new growth mechanism, for Bi2Te3 sub-micron belts; and the characterisation of the first quasi-one dimensional topological insulator (orthorhombic Sb-doped Bi2Se3) and topological Dirac semimetal nanowires (Cd3As2). Research into new materials has been one of the driving forces that have contributed to the progress of civilisation from the Bronze Age four thousand years ago to the age of the semiconductor in the 20th century. At the turn to the 21st century novel materials, so-called quantum materials, started to emerge. The fundamental theories for the description of their properties were established at the beginning of the 20th century but expanded significantly during the last three decades based, for example, on a new interpretation of electronic states by topological invariants. Hence, topological insulator (TI) materials such as mercury-telluride are one manifestation of a quantum material. In theory, TIs are characterised by an insulating interior and a surface with spin-momentum locked conduction. In real crystals, however, the bulk can be conducting due to crystal imperfections. Nanowires suppress this bulk contribution inherently by their high surface-to-volume ratio. Additionally, trace impurity elements can be inserted into the crystal to decrease the conductance further. These optimised TI nanowires could provide building blocks for future electronic nanodevices such as transistors and sensors. Initial synthesis efforts using vapour transport techniques and electronic transport studies showed that TI nanowires hold the promise of reduced bulk contribution. This thesis expands the current knowledge on synthesis strategies, crystal growth mechanisms, and new types of quantum materials nanowires. Traditionally, gold catalyst nanoparticles were used to grow TI nanowires. We demonstrate that they are suitable to produce large amounts of nanowires but have undesired side-effects. If a metaloxide catalyst nanoparticle is used instead, quality and even quantity are significantly improved. This synthesis strategy was used to produce a new TI which is built from chains of atoms and not from atomic layers as in case of previously known TIs. The growth of large nanowires with a layered crystal structure leads to step-flowgrowth, an intriguing phenomenon in the growth mechanism: New layers grow on top of previous layers with a single growth frontmoving fromthe root to the tip. These wires are ideal for further electronic characterisation that requires large samples. The nanowire growth of tin-oxide will also be discussed, a side project that arose from my growth studies, which is useful for sensor applications. Under certain conditions it forms tree-like structures in a single synthesis step. All of the aforementioned growth studies are carried out at atmospheric pressure. A separate growth study is carried out in ultra-high vacuum to assess the transferability of the growth process towards the cleanliness requirements of the semiconductor industry. If two quantum materials are joined together, exotic physics may emerge at the interface. One of the goals of TI research is the experimental observation of Majorana fermions, exotic particles which are their ownantiparticles with potential applications in quantum computing that may appear in superconductor/TI hybrid structures. We have synthesised such structures and initial characterisation suggests that the resistivity increases when they are cooled below the critical temperature of the superconductor. Beyond TIs, a new type of quantum material, called a topological Dirac semimetal, opens new realms of exotic physics to be discovered. Nanowires are grownfroma material which has recently been discovered to be a topological Dirac semimetal. Their growth mechanism is characterised and an extremely high electron mobility at room temperature is measured. The contribution of this thesis to the field is summarised in Fig. 1. Its core is the study of the growth mechanism of quantum materials which will be vital for future development of applications and fundamental research.

Graphene, a single atomic layer of graphite, has many exciting electronic and mechanical properties. On a fundamental level, the quasi-relativistic behaviour of the charge carriers in graphene arises from the honeycomb-like atomic structure. Deforming the lattice changes the lengths of the carbon-carbon bonds, breaking the hopping symmetry between carbon sites. Mathematically, elastic strain in a graphene membrane can be described by additional terms in the low-energy effective Hamiltonian, analogous to the vector potential of an external magnetic field. Hence, certain non-uniform strain geometries produce so-called `pseudo-magnetic fields', leading to a predicted zero-field quantum Hall effect. These fictitious magnetic fields are distinct from an external magnetic field in that they are only observed by charge carriers within the membrane, and have opposing polarity for electrons in the K and K' valleys, preserving time-reversal symmetry of the lattice as a whole. Deforming graphene in the non-uniform manner required to produce a homogeneous pseudo-magnetic field has proven to be a huge technological challenge, however, restricting experimental evidence to scanning tunnelling spectroscopy measurements on, for example, highly deformed nanobubbles formed by the thermal expansion of an epitaxially grown sheet on a platinum substrate. These results stimulated a large amount of interest in strain-engineering electron transport in graphene, partly due to the extreme magnitude of the observed pseudo-magnetic field, a direct consequence of the strain components strongly varying over the space of a few nanometres, but the formation of nanobubbles is a highly stochastic process which cannot be reliably reproduced. Subsequent research found a way to fabricate nanobubbles with a high degree of consistency, but the measurements were still limited to local-probe techniques due to the nanoscale size of the devices. As such, a method to reliably induce a homogeneous pseudo-magnetic field within a micron-sized membrane would be an attractive proposition, and is the basis for the work presented within this thesis. The non-uniform strain required precludes a simple bending or elongation of the substrate, hence a more local method is required. A novel nanostructure consisting of suspended gold beams surrounding a graphene membrane will deform upon cooling to cryogenic temperatures, and crucially, the actuation mechanism can be designed to produce any configuration of strain, including uniaxial strain, triaxial strain and a fan-shaped deformation, the latter two of which are predicted to create homogeneous pseudo-magnetic fields within a membrane. Strain patterns which are predicted to produce experimentally significant pseudo-magnetic fields (~1 T) may be generated with complex actuation beams that are physically achievable. Furthermore, the actuation mechanisms may be utilised as electrical contacts to the membrane, allowing its conductivity to be measured in the context of a two- or multi-terminal measurement, in conjunction with an external magnetic field. The design of the devices was developed using finite-element analysis, and the behaviour verified by low-temperature imaging of prototypes. While, after careful annealing, some conventional two-terminal suspended devices exhibited quantum Hall features at very low fields, the fabricated strain-inducing devices did not display pseudo-Landau quantisation, nor Landau quantisation, due to the difficulties of using current annealing to clean devices post-fabrication. The presented work, however, could pave the way towards observing signatures of pseudo-magnetic fields in a range of experimental measurements, as well as creating alternative strain geometries.

With the overriding goal of developing functional multiferroic systems with technological potential, this thesis focuses on the role of orbital and charge ordering in coupling magnetism and ferroelectricity in synthetic quadruple perovskites. Using x-ray diffraction as the primary characterisation tool, modulations to crystal ordering have been interpreted in terms of orbital occupation and charge variation. Expanding on previous magnetic structure studies and polarisation measurements, structural analysis of CaMn7O12 has led to the experimental realisation of a new mechanism for multiferroicity, resulting from a "magneto-orbital helix". Motivated by the idea of tuning multiferroic properties through varying manganese valence, the doped system CaCuxMn7-xO12 has been studied. Structural models considering the possibility of domain formation and multiple coexisting modulations have been tested against x-ray diffraction data. Finally, motivated by theoretical predictions of ferroelectric phases and multiferroicity in doped, simple, manganite perovskites, a structural model for the low temperature phase of NaMn7O12 has been developed, based upon theoretical predictions for orbital ordering and the experimentally determined magnetic structure. This model has been tested against previously measured neutron diffraction data. The importance of understanding crystal formation and domain structures when applying theoretical models has been highlighted, and has prompted the consideration of future work involving viewing and manipulating twin formation.

Spin properties of donor impurities in silicon have been investigated by electron spin resonance (ESR) techniques for more than sixty years. These studies gave us a contribution towards understanding some of the physics of doped semiconductor materials in general, which is the platform for much of our current technology. Despite the fact that donor electron and nuclear spins have been researched for so long, ESR studies of their properties are still giving us interesting insights. With the introduction of the concept of quantum information in the 1980s, some properties of donor spins in silicon, that were known from the fifties (such as long relaxations), have been reinterpreted for their potential application in this field. Since then, incredible experimental results have been achieved with magnetic resonance control, including manipulation and read-out of individual spins. However, some open questions are still to be answered before the realisation of a spin-based silicon quantum architecture will be achieved. Currently, ESR studies still contribute to help answering some of those questions. In this thesis, we demonstrate electrical and optical methods for donor charge state manipulation measured by ESR. Recent experiments have demonstrated that coherence time of nuclear spins may be enhanced by manipulating the state of donors from neutral to singly charged. We investigate electric field ionisation/neutralisation of arsenic donors in a silicon SOI device measured by ESR. Below ionisation threshold, we also measure the hyperfine Stark shift of arsenic donors spins in silicon. These results have, for instance, implications on how fast individual addressability of donor spins may be achieved in certain quantum computer architectures. Here, we also study optical-driven charge state manipulation of selenium impurities in silicon. Selenium has two additional electrons when it replaces an atom in the silicon crystal (i.e. double donor). The electronic properties of singly-ionised selenium make it potentially advantageous as spin qubit, compared to the more commonly studied group-V donors. For instance, we find here that the electron spin relaxation and coherence times of selenium are up to two orders of magnitude longer than phosphorus at the same temperature. Finally, we demonstrate that it is possible to bring selenium impurity in singly-charged state and subsequently re-neutralise them leaving a potential long-lived 77Se nuclear spin.

Topological insulators (TIs) are recently predicted, and much studied, new quantum materials. These materials are characterised by their unique surface electronic properties; namely, behaving as band insulators within their bulk, but with spin-momentum locked surface or edge states at their interface. These surface/edge crossing states are protected by the underlying time-reversal symmetry (TRS) of the bulk band structure, leading to a robust topological surface state (TSS) that is resistant to scattering from impurities which do not break TRS. Their surface band dispersion has a characteristic crossing at time reversal invariant momenta (TRIM) called a Dirac cone. It has been predicted that the introduction of a TRS breaking effect, through ferromagnetic order for instance, will open a band-gap in this Dirac cone. It can be seen that magnetic fields are not time reversal invariant by considering a solenoid. If time is reversed, the current will also reverse in the solenoid and so the magnetic field will also be reversed. So it can be seen that magnetic fields transform as odd under time reversal, the same will be true of internal magnetisation. By manipulating this gapped surface state a wide range of new physical phenomena are predicted, or in some cases, already experimentally observed. Of particular interest is the recently observed quantum anomalous Hall effect (QAHE) as well as, e.g., topological magneto-electric effect, surface Majorana Fermions and image magnetic monopoles. Building on these novel physical effects, it is hoped to open new pathways and device applications within the emerging fields of spintronics and quantum computation. This thesis presents an investigation of the nature of magnetic doping of the chalcogenide TIs Bi2Se3 and Bi2Te3 using 3d transition-metal dopants (Mn and Cr). Samples were grown by molecular beam epitaxy (MBE), an ideal growth method for the creation of high-quality thin film TI samples with very low defect densities. The grown films were investigated using a range of complementary lab-based and synchrotron-based techniques to fully resolve their physical structure, as well as their magnetic and electronic properties. The ultimate aim being to form a ferromagnetic ground state in the insulating material, which may be expanded into device applications. Samples of bulk Mn-doped Bi2Te3 are presented and it is shown that a ferromagnetic ground state is formed below a measured TC of 9-13 K as determined by a range of experimental methodologies. These samples are found to have significant inhomogeneities within the crystal, a problem that is reduced in MBE-grown crystals. Mn-doped Bi2Se3 thin films were grown by MBE and their magnetic properties investigated by superconducting quantum interference device (SQUID) magnetometry and x-ray magnetic circular dichroism (XMCD). These reveal a saturation magnetisation of 5.1 μB/Mn and show the formation of short-range magnetic order at 2.5 K (from XMCD) with indication of a ferromagnetic ground state forming below 1.5 K. Thin films of Cr-doped Bi2Se3 were grown by MBE, driven by the recent observation of the QAHE in Cr-doped (Bi1−xSbx)2Te3. Investigation by SQUID shows a ferromagnetic ground state below 8.5 K with a saturation magnetisation of 2.1 μB/Cr. Polarised neutron reflectometry shows a uniform magnetisation profile with no indication of surface enhancement or of a magnetic dead layer. Further studies by extended x-ray absorption fine structure (EXAFS) and XMCD elucidate the electronic nature of the magnetic ground state of these materials. It is found that hybridisation between the Cr d and Se p orbitals leads to the Cr being divalent when doping on the Bi3+ site. This covalent character to the electronic structure runs counter to the previously held belief that divalent Cr would originate from Cr clusters within the van der Waals gap of this material. The work overall demonstrates the formation of a ferromagnetic ground state for both Cr and Mn doped material. The transition temperature, below which ferromagnetic order is achieved, is currently too low for usable device applications. However, these materials provide a promising test bed for new physics and prototype devices.

Inwardly rectifying potassium (Kir) channels are essential for controlling the excitability of eukaryotic cells, forming a key part of the inter-cellular signalling system in multi-cellular organisms. However, as prokaryotic (KirBac) channels are less technically challenging to study in vitro and have been shown to be directly homologous to eukaryotic channels, they are often studied in lieu of their mammalian counterparts. A vital feature of Kir and KirBac channels is their mechanism for opening and closing, or their gating: this study predominantly features observations of open and/or closed channel populations. A well-characterised member of the KirBac family, KirBac1.1, has been successfully expressed, purified into detergent micelles, and doubly labelled with fluorescent maleimide dyes in order to enable observation of confocal-in-solution Förster Resonance Energy Transfer (FRET) at the single molecule level. Results demonstrate single-molecule FRET signals from KirBac1.1 and therefore represent the first single-molecule FRET observations from a KirBac channel. Perturbation of the open-closed dynamic equilibrium was performed via activatory point mutations, changes in pH, and ligand binding. A protocol for reconstitution into nanodiscs was optimised in order to more closely approximate native conditions, and the single-molecule FRET observations repeated. This thesis presents a comparison between measurements made using the detergent solubilisation system and those made using nanodiscs.

There is a strong need to develop a mechanical method to apply external torque to the bacterial flagellar motor. Such a method will allow us to probe the behaviour of the motor at a range of different speeds under different external conditions. In this thesis, I explored various methods to deliver torque at the single-molecule level, in particular the use of angular optical trapping and magnetic tweezers. I have identified rutile particles as suitable handles for use in angular optical trapping due to their high birefringence. Further progress was not achieved using angular optical trapping due to the lack of a suitable method to attach birefringent particles to the bacterial flagellar motor. On the other hand, I was able to make further progress using magnetic tweezers. A highly-reproducible and high-yielding magnetic bead assay was developed along with electromagnets capable of generating fast-rotating magnetic fields at magnitudes on the order of tens of mT. Using the system of delivering magnetic torque developed, I was able to stall and rotate the motor forward at speeds up to 220 Hz and in the reverse direction. Stalling experiments carried out on the motor revealed the stator mechanosensing depends on torque and not rotation. Signatures of stators dropping out at low load experiments further confirm the load dependence of stators.

Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.

This thesis studies lead suphide (PbS) colloidal quantum dots and their photovoltaic applications. Different sizes of PbS QDs were synthesised and characterised using absorption spectroscopy and transmission electron microscopes. PbS QD Schottky junction devices were fabricated with AM1.5 power conversion efficiency up to 1.8 %. The Schottky junction geometry limits the device performance. A semiconductor heterojunction using ZnO as an electron acceptor was built and the device efficiency increased to 3%. By studying the light absorption and charge extraction profile of the bilayer device, the absorber layer has a charge extraction dead zone which is beyond the reach of the built-in electric field. Therefore, strategies to create a QD bulk heterojunction were considered to address this issue by distributing the junction interface throughout the absorber layer. However, the charge separation mechanism of the QD heterojunction is not clearly understood: whether it operates as an excitonic or a depleted p-n junction, as the junction operating mechanism determines the scale of phase separation in the bulk morphology. This study shows a transitional behaviour of the PbS/ZnO heterojunction from excitonic to depletion by increasing the doping density of ZnO. To utilise the excitonic mechanism, a PbS/ZnO nanocrystal bulk heterojunction was created by blending the two nanocrystals in solution such that a large interface between the two materials could facilitate fast exciton dissociation. However, the devices show poor performance due to a coarse morphology and formation of germinate pairs. To create a bulk heterojunction where a built-in electric field could assist the charge separation, a TiO2 porous structure with the pore size matching with the depletion width was fabricated and successfully in-filled by PbS QDs. The porous device produces 5.7% power conversion efficiency, among one of the highest in literature. The enhancement comes from increased light absorption and suppression of charge recombination.

This thesis presents details of x-ray and neutron scattering experiments used to probe quantum magnets with strong spin-orbit interaction. The first of these systems are the three-dimensional iridate compounds, in which the three-fold co-ordination of IrO6 octahedra has been theoretically hypothesized to stabilize anisotropic exchange between Ir4+ ions. This novel interaction between these spin-orbital entangled, Jeff=1/2 moments is described by a Hamiltonian first proposed by Kitaev, and would be the first physical realization of this Hamiltonian in a condensed matter system. This thesis details the determination of the structure of a new polytype within these compounds, the 'stripyhoneycomb' γ-Li2IrO3. Furthermore, through resonant magnetic x-ray diffraction experiments on single crystals of β-Li2IrO3 and γ-Li2IrO3, an incommensurate, non-coplanar structure with counter-rotating moments is found. The counter-rotating moment structure is a rather counter-intuitive result, as it is not stabilizied by Heisenberg exchange between magnetic sites, however, the Kitaev exchange naturally accounts for this feature. As such, these experiments reveal, for the first time, systems which exhibit dominant Kitaev interactions. The ordering wavevector of both β- and γ-Li2IrO3 polytypes are found to be identical, suggesting that the same magnetic interactions are responsible for stabilizing magnetic order in both materials, despite their different lattice topologies. Following this, the spinel FeSc2S4 is considered. Here, despite the presence of strong exchange between Fe^{2+,/sup>, and the fact that these ions sit in a Jahn-Teller active environment, the system does not order in the spin or orbital degrees of freedom. A 'spin-orbital singlet' has been theoretically proposed to describe the groundstate of this system, and here inelastic neutron scattering (INS) is used to probe the resulting triplon excitations. This allows determination of microscopic parameters in the single ion and exchange Hamiltonians, and moreover experiments in external magnetic field reveal the true spin-and-orbital nature of these triplon excitations. Finally, Ba3CoSb2O9, a physical realization of the canonical triangular antiferromagnet model is explored with INS and the high energy excitations from the 120 degree magnetic structure are found to display significant differences from those calculated by linear spin wave theory, suggesting the presence of quantum dynamics not captured in the 1/S linear spin wave expansion.}

Metal oxides are of immense technological importance. Their wide variety of structural and electronic characteristics leads to a flexibility unrivalled by other groups of materials. However, there is still much debate about the fundamental properties of some of the most widely used oxides, including TiO2 and In2O3. This work presents high quality, in-depth characterisation of these two oxides in pure and doped form, including soft and hard X-ray photoelectron spectroscopy and X-ray diffraction. Bulk samples as well as thin film samples were prepared analysed. For the preparation of thin films a high quality sol-gel dip-coating method was developed, which resulted in epitaxial films. In more detail the organisation of the thesis is as follows: Chapter 1 provides an introduction to key ideas related to metal oxides and presents the metal oxides investigated in this thesis, In2O3, Ga2O3, Tl2O3, TiO2, and SnO2. Chapter 2 presents background information and Chapter 3 gives the practical details of the experimental techniques employed. Chapters 4 presents reciprocal space maps of MBE-grown In2O3 thin films and nanorods on YSZ substrates. Chapters 5 and 6 investigate the doping of In2O3 bulk samples with gallium and thallium and introduce a range of solid state characterisation techniques. Chapter 7 describes the development of a dip-coating sol-gel method for the growth of thin films of TiO2 and shows 3D reciprocal space maps of the resulting films. Chapter 8 concerns hard x-ray photoelectron spectroscopy of undoped and Sn-doped TiO2. Chapter 9 interconnects previous chapters by presenting 2D reciprocal space maps of nano structured epitaxial samples of In2O3 grown by the newly developed sol-gel based method. Chapter 10 concludes this thesis with a summary of the results.