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First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

Pump-probe measurements of coherent-phonon-induced changes of refractive index in LaAlO3 are dominated by normally weak boundary effects. Atomic displacements in the range 50–500 μÅ were generated and probed by femtosecond laser pulses through impulsive Raman scattering. The absence of a bulk contribution is ascribed to phase mismatch due to domain disorder. Selection rules are consistent with a Raman model considering reflection and transmission at interfaces. Intensities and phonon parameters as a function of temperature agree well with incoherent Raman data.

The main focus of this work is to investigate how electronic excitation changes the forces between atoms in materials, causing large amplitude collective atomic motion, referred to as coherent phonon motion. The recent development of ultrafast optical spectroscopy has greatly advanced our understanding of these phenomena. However, many aspects of ultrafast phenomena are still poorly understood. For instance, experiments on a variety of different materials have shown that symmetry-breaking coherent modes have a much smaller amplitude than fully symmetric coherent modes. Recent experimental work in the group V semimetals have shown that the symmetry-breaking $E_g$ mode is driven by a force which decays in $\sim 10$ fs, a timescale much shorter than the period of the mode, explaining its small amplitude. However, the exact mechanism for this decay has remained unclear. We show that the $E_g$ force in optically excited group V semimetals decays due to coupling of the excited electrons to thermal vibrations. We propose a method for increasing the impact of photoexcitation on symmetry-breaking modes by a suitable choice of photon energy, which would apply to a variety of materials. We are also interested in the dynamics of the coherent phonons themselves. Recently, it has been shown that optical excitation can drive collective structural transformations to phases that do not exist on the equilibrium phase diagram of materials as diverse as transition metal oxides, transition metal chalcogenides, and the group V semimetals. Experimentally reaching many of these states requires a high degree of photoexcitation, with a significant fraction ($1$-$5$\%) of the valence electrons excited to the conduction bands. We use first-principles calculations to simulate coherent phonon dynamics in Sb, and show that at high enough excited carrier concentration, Sb undergoes a reversal of its Peierls distortion. Our results are in good agreement with pump-probe experiments carried out by our experimental collaborators, providing good evidence that such a reversal can be induced by optical excitation.

The thermoelectric figure of merit, ZT, is a dimensionless parameter used to characterise the efficiency of a thermoelectric material. One of the most common techniques to improve ZT is to suppress lattice thermal conductivity via nanostructuring. However, this approach often comes with the cost of reduced electrical conductivity and Seebeck coefficient, resulting in only modest increases to ZT. Using the first principles Boltzmann transport framework, we show that driving PbTe-based materials to the verge of the soft mode (ferroelectric) phase transition could be a powerful strategy to reduce their lattice thermal conductivity while potentially preserving the electrical properties beneficial for a large ZT. The proposed concept is based on the induction of considerably softened zone-centre transverse optical modes, increasing their anharmonic coupling with low-frequency heatcarrying acoustic phonons and reducing phonon lifetimes at all frequencies. We illustrate this concept by applying biaxial tensile (001) strain to PbTe and its alloys with PbSe; and by alloying PbTe with a rhombohedral material, GeTe, reducing the lattice thermal conductivity by a factor of 2−3 compared to PbTe. Furthermore, by tuning the chemical composition of Pb1−xGexTe alloys, we also investigate the roles of proximity to the phase transition, mass disorder, and phase of the alloy in reducing the lattice thermal conductivity. Finally, we take the first steps towards a fully ab initio calculation of the figure of merit of PbTe-based materials near the phase transition by considering electron-phonon interactions, and find fair agreement between the calculated electronic mobility of PbTe and experiment. Due to certain symmetry forbidden electron-phonon coupling, we anticipate that our outlined approach may not degrade electronic properties beneficial for a large ZT. This proposed concept is general and offers a promising new strategy to potentially increase thermoelectric efficiency.

Highly doped polar semiconductors are essential components of today’s semiconductor industry. Most strikingly, transistors in modern electronic devices are polar semiconductor heterostructures. It is important to thoroughly understand carrier transport in such structures. In doped polar semiconductors, collective excitations of the carriers (plasmons) and the atoms (polar phonons) couple. These coupled collective excitations affect the electrical conductivity, here quantified through the carrier mobility. In scattering events, the carriers and the coupled collective modes transfer momentum between each other. Carrier momentum transferred to polar phonons can be lost to other phonons through anharmonic decay, resulting in a finite carrier mobility. The plasmons do not have a decay mechanism which transfers carrier momentum irretrievably. Hence, carrier-plasmon scattering results in infinite carrier mobility. Momentum relaxation due to either carrier–plasmon scattering or carrier–polar-phonon scattering alone are well understood. However, only this thesis manages to treat momentum relaxation due to both scattering mechanisms on an equal footing, enabling us to properly calculate the mobility limited by carrier–coupled plasmon–polar phonon scattering. We achieved this by solving the coupled Boltzmann equations for the carriers and the collective excitations, focusing on the “drag” term and on the anharmonic decay process of the collective modes. Our approach uses dielectric functions to describe both the carrier-collective mode scattering and the decay of the collective modes. We applied our method to bulk polar semiconductors and heterostructures where various polar dielectrics surround a semiconducting monolayer of MoS2, where taking plasmons into account can increase the mobility by up to a factor 15 for certain parameters. This screening effect is up to 85% higher than if calculated with previous methods. To conclude, our approach provides insight into the momentum relaxation mechanism for carrier–coupled collective mode scattering, and better tools for calculating the screened polar phonon and interface polar phonon limited mobility.

A quantum mechanical density functional theory approach was used to investigate the structural atomic configuration, vibration mode frequencies and electronic structure of surfaces and interfaces using germanium. Initially, we investigated the H2S and H2Opassivated germanium surfaces. A supercell approach is used with the local density (LDA), generalized gradient (GGA) approximations and van der Waals (vdW) interactions. The frozen phonon method was used to calculate the vibrational mode frequencies of these surfaces. The calculated frequencies produce stretch, bond bending and wag modes. The differences between the functionals including vdW terms and the LDA or GGA are less than the differences between LDA and GGA for the vibrational mode frequencies. Some of these modes provide useful vibrational signatures of bonding of both sulfur and oxygen on germanium surfaces, which may be compared with vibrational spectroscopy measurements. A bare germanium surface is bonded to a bare silicon surface to form a Ge-Si interface. As germanium has a 4% larger lattice constant than silicon this implies there are regions on the interface where the germanium and silicon match perfectly (aligned) and are completely mismatched (misaligned). The atomic structure of the GeSi aligned interface shows the original crystal structure and the projected band structure (PBS) shows no interface states in the band gap. The GeSi misaligned structure forms a (2x1) configuration. The electronic PBS shows interface states in the band gap. To remove the interface states seen in the GeSi interface, sulfur with its six valence electrons and its flexible chemical bonds is suggested to improve the interface bonding and remove interface states. The PBS in both the aligned and misaligned GeSSi interfaces shows states around the germanium and silicon interface atomic layers and a charge density localised around the sulfur interface atoms. A sulfur terminated germanium surface results in a (1x1) configuration with surface states present in the band gap. However, a H2S terminated germanium surface results in a (2x1) configuration with symmetric Ge-Ge dimers and pushes the surface states into the bulk region, implying the presence of hydrogen results in no surface states. Including hydrogen on our GeSSi interfaces, the atomic configuration remains the same with the hydrogen molecule in the channels. However, upon looking at the PBS, states are clearly visible in the band gap and when we investigate the charge density contour plots, interface states do exist. Therefore, the presence of hydrogen here does not influence the interfaces.

The substitution of a small fraction x of nitrogen atoms, for the group V elements in conventional III-V semiconductors such as GaAs and GaSb strongly perturbs the conduction band of the host semiconductor. In this thesis we investigate the effects of nitrogen states on the band dispersion, carrier scattering and mobility of dilute nitride alloys. In the supercell model we solve the single particle Hamiltonian for a very large supercell containing randomly placed nitrogen. This model predicts a gap in the density of states of GaNxAs1−x, where this gap is filled in the Green’s function model. Therefore we develop a self-consistent Green’s function (SCGF) approach, which provides excellent agreement with supercell calculations and reveals a gap in the DOS, in contrast with the results of previous non-self-consistent Green’s function calculations. However, including the distribution of N states destroys this gap, as seen in experiment. We then examine the high field transport of carriers by solving the steadystate Boltzmann transport equation and find that it is necessary to include the full distribution of N levels in order to account for the small, low-field mobility and the absence of a negative differential velocity regime observed experimentally with increasing x. Overall the results account well for a wide range of experimental data. We also investigate the band structure, scattering and mobility of carriers by finding the poles of the SCGF, which gives lower carrier mobility for GaNxAs1−x, compared to those already calculated, in better agreement with experiments. The calculated optical absorption spectra for InyGa1−yNxAs1−x and GaNxSb1−x using the SCGF agree well with the experimental data, confirming the validity of this approach to study the band structure of these materials.

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.