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When the transition temperature of a continuous phase transition is tuned to absolute zero, new ordered phases and physical behaviour emerge in the vicinity of the resulting quantum critical point. Sr3Ru2O7 can be tuned through quantum criticality with magnetic field at low temperature. Near its critical field Bc it displays the hallmark T-linear resistivity and a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T\,{{{{{{\mathrm{log}}}}}}}\,(1/T)$$\end{document}Tlog(1/T) electronic heat capacity behaviour of strange metals. However, these behaviours have not been related to any critical fluctuations. Here we use inelastic neutron scattering to reveal the presence of collective spin fluctuations whose relaxation time and strength show a nearly singular variation with magnetic field as Bc is approached. The large increase in the electronic heat capacity and entropy near Bc can be understood quantitatively in terms of the scattering of conduction electrons by these spin-fluctuations. On entering the spin-density-wave ordered phase present near Bc, the fluctuations become stronger suggesting that the order is stabilised through an “order-by-disorder” mechanism., Sr3Ru2O7 exhibits a quantum critical point tunable by magnetic field and has been widely used in the study of criticality. Here, by using inelastic neutron scattering, the authors measure collective magnetic excitations near the quantum critical point and relate them to thermodynamic properties and spin density wave order.

We propose a superconducting instability where microscopic supercurrent loops form spontaneously within a unit cell at the superconducting transition temperature with only uniform, onsite and intra-orbital singlet pairing. As a result of the circulating currents time-reversal symmetry is spontaneously broken in the superconducting state. Using Ginzburg-Landau theory, we describe in detail how these currents emerge in a toy model. We discuss the crystallographic symmetry requirements to realize such a state and show that they are met by the Re6X (X=Zr, Hf, Ti) family of time-reversal symmetry breaking, but otherwise seemingly conventional, superconductors. We estimate an upper bound for the resulting internal fields and find it to be consistent with recent muon-spin relaxation experiments., Comment: 10 pages, 3 figures (More references added)

The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $|C|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density matrix renormalization group simulations on a thin cylinder. We confirm the existence of fractional states in bands with Chern numbers $C=1,2,3,4,5$ at the filling fractions predicted by the generalized Jain series [Phys. Rev. Lett. 115, 126401 (2015)]. Moreover, we discuss their metal-to-insulator phase transitions, as well as the subtleties in distinguishing between physical and numerical stability. Finally, we comment on the relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications., 16 pages, 13 figures

We present a theoretical study of the potential of Principal Component Analysis to analyse magnetic diffuse neutron scattering data on quantum materials. To address this question, we simulate the scattering function $S\left(\mathbf{q}\right)$ for a model describing a cluster magnet with anisotropic spin-spin interactions under different conditions of applied field and temperature. We find high dimensionality reduction and that the algorithm can be trained with surprisingly small numbers of simulated observations. Subsequently, observations can be projected onto the reduced-dimensionality space defined by the learnt principal components. Constant-field temperature scans corresponds to trajectories in this space which show characteristic bifurcations at the critical fields corresponding to ground-state phase boundaries. Such plots allow the ground-state phase diagram to be accurately determined from finite-temperature measurements., 12 pages, 9 figures; author's accepted version with improved discussions and additional appendices

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as a tool to analyse the data from muon spectroscopy experiments. Specifically, we apply the ML technique to detect phase transitions in various materials. The measured quantity in muon spectroscopy is an asymmetry function, which may hold information about the distribution of the intrinsic magnetic field in combination with the dynamics of the sample. Sharp changes of shape of asymmetry functions - measured at different temperatures - might indicate a phase transition. Existing methods of processing the muon spectroscopy data are based on regression analysis, but choosing the right fitting function requires knowledge about the underlying physics of the probed material. Conversely, Principal Component Analysis focuses on small differences in the asymmetry curves and works without any prior assumptions about the studied samples. We discovered that the PCA method works well in detecting phase transitions in muon spectroscopy experiments and can serve as an alternative to current analysis, especially if the physics of the studied material are not entirely known. Additionally, we found out that our ML technique seems to work best with large numbers of measurements, regardless of whether the algorithm takes data only for a single material or whether the analysis is performed simultaneously for many materials with different physical properties., Comment: 11 pages, 7 figures, to be submitted to the Journal of Physics: Condensed Matter special issue on "Machine Learning in Condensed Matter Physics"

Chiral superconductors are novel topological materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He3. Chiral triplet superconductors are, however, topologically fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compound LaPt3P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temperature linear behaviour in the superfluid density indicating line nodes in the order parameter. Using symmetry analysis, first principles band structure calculation and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt3P is a chiral d-wave singlet., Nature Communications, 12 (1), ISSN:2041-1723

Superconductivity and magnetism are antagonistic states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms including the importance of multiple bands., 29 pages, 10 figures

We report the discovery of Zr$_3$Ir as a new type of unconventional noncentrosymmetric superconductor (with $T_c = 2.3$ K), here investigated mostly via muon-spin rotation/relaxation ($\mu$SR) techniques. Its superconductivity was characterized using magnetic susceptibility, electrical resistivity, and heat capacity measurements. The low-temperature superfluid density, determined via transverse-field $\mu$SR and electronic specific heat, suggests a fully-gapped superconducting state. The spontaneous magnetic fields, revealed by zero-field $\mu$SR below $T_c$, indicate the breaking of time-reversal symmetry in Zr$_3$Ir and, hence, the unconventional nature of its superconductivity. By using symmetry arguments and electronic-structure calculations we obtain a superconducting order parameter that is fully compatible with the experimental observations. Hence, our results clearly suggest that Zr$_3$Ir represents a new member of noncentrosymmetric superconductors with broken time-reversal symmetry., Comment: 6 pages, 4 figuress; supplementary materials can be accessed from corresponding authors

Ginzburg-Landau vortices in superconductors attract or repel depending on whether the value of the coupling constant is less than 1 or larger than 1. At critical coupling it was previously observed that a strongly localised magnetic impurity behaves very similarly to a vortex. This remains true for axially symmetric configurations away from critical coupling. In particular, a delta function impurity of a suitable strength is related to a vortex configuration without impurity by singular gauge transformation. However, the interaction of vortices and impurities is more subtle and depends not only on the coupling constant and the impurity strength, but also on how broad the impurity is. Furthermore, the interaction typically depends on the distance and may be attractive at short distances and repulsive at long distances. Numerical simulations confirm moduli space approximation results for the scattering of one and two vortices with an impurity. However, a double vortex will split up when scattering with an impurity, and the direction of the split depends on the sign of the impurity. Head-on collisions of a single vortex with different impurities away from critical coupling is also briefly discussed., 39 pages, 18 figures, this version is accepted for publication in PRD

The exceptionally low-symmetry crystal structures of the time-reversal symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an internally-antisymmetric non-unitary triplet (INT) state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the Density of States (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa$_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter. The latter is fixed by the critical temperature $T_c$ allowing parameter-free predictions. We compute the electronic specific heat and find excellent agreement with experiment. The size of the ordered moment in the superconducting state is compatible with zero-field muon spin relaxation experiments and the predicted spin-resolved DOS suggests the spin-splitting is within the reach of present experimental technology., Comment: Accepted in PRB as a rapid communication

The dynamics and behavior of ferromagnets have a great relevance even beyond the domain of statistical physics. In this work, we propose a Monte Carlo method, based on random graphs, for modeling their dilution. In particular, we focus on ferromagnets with dimension $D \ge 4$, which can be approximated by the Curie-Weiss model. Since the latter has as graphic counterpart a complete graph, a dilution can be in this case viewed as a pruning process. Hence, in order to exploit this mapping, the proposed strategy uses a modified version of the Erd\H{o}s-Renyi graph model. In doing so, we are able both to simulate a continuous dilution, and to realize diluted ferromagnets in one step. The proposed strategy is studied by means of numerical simulations, aimed to analyze main properties and equilibria of the resulting diluted ferromagnets. To conclude, we also provide a brief description of further applications of our strategy in the field of complex networks., Comment: 23 pages, 7 figures; accepted for publication in Complexity

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behaviour of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents emanating from the sample boundaries, and with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.

The spin ice materials Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$ are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour -- both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution -- is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange and dipolar fields from neighbouring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates which depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr$_{2}$Sn$_{2}$O$_{7}$ and Pr$_{2}$Zr$_{2}$O$_{7}$, we find an even more pronounced separation of timescales signalling the likelihood of coherent many-body dynamics., 5 pages, 2 figures, 1 table; supplemental material attached

An analytical model of electric field assisted diffusion of ions into glass is extended to include two indigenous mobile ion species that are initially uniformly distributed within the glass. A quasi-stationary state solution that includes diffusion effects and is applicable when the invasive ions have a lower mobility than the two indigenous species is presented. It is relevant to the electrical poling of soda-lime and borosilicate glasses with concentrations of mobile ions (Na+, K+) that are processed with a non-blocking anode where hydrogen ion injection occurs. The model is compared with numerical solutions based on the drift-diffusion equations and Poisson's equation and shows good agreement. The increase in the concentration of the indigenous species with the lower mobility (K+) below the poled layer within a pile-up region is accurately modelled.

Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows the introduction of elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of evolutionary game theory, where evolution constitutes an intrinsic mechanism. At the same time, the concept of innovation requires an opportune mathematical representation. Notably, innovation can be modeled as a strategy, or it can constitute the underlying mechanism that allows agents to change strategy. Here, we analyze the second case, investigating the behavior of a heterogeneous population, composed of imitative and innovative agents. Imitative agents change strategy only by imitating that of their neighbors, whereas innovative ones change strategy without the need for a copying source. The proposed model is analyzed by means of analytical calculations and numerical simulations in different topologies. Remarkably, results indicate that the mixing of mechanisms can be detrimental to cooperation near phase transitions. In those regions, the spatial reciprocity from imitative mechanisms is destroyed by innovative agents, leading to the downfall of cooperation. Our investigation sheds some light on the complex dynamics emerging from the heterogeneity of strategy revision methods, highlighting the role of innovation in evolutionary games.

We investigate whether by synthesising superconductors that are tuned to a topological, node-reconstruction transition point we could create superconducting wires that are intrinsically resilient to quenches. Recent work shows that the exponent characterising the temperature dependence of the specific heat of a nodal superconductor is lowered over a region of the phase diagram near topological transitions where nodal lines form or reconnect. Our idea is that the resulting enhancement of the low-temperature specific heat could have potential application in the prevention of superconductor quenches. We perform numerical simulations of a simplified superconductor quench model. Results show that decreasing the specific heat exponent can prevent a quench from occurring and improve quench resilience, though in our simple model the effects are small. Further work will be necessary to establish the practical feasibility of this approach., Comment: Accepted version for IEEE-TAS (Proceedings of EUCAS 2017)

We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy Luttinger liquid theory is gapped by interaction. This phase is of particular interest since it exhibits non-trivial interaction-induced topological properties. Using bosonization and an expansion in the tunneling strength, we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping the fractional spin the edge states can absorb or emit spinons and thus enable single electron tunneling across the impurity even though the bulk spectrum for these excitations is gapped. This results in a finite LDOS below the bulk gap and in a non-monotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase---which combines features of a topological spin insulator and a topological charge metal---in which the topology can be probed by measuring transport properties., Comment: 14 pages, 6 figures

Clustered quantum materials provide a new platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nano-magnet featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters., 14 pages, 11 Figures; minor changes; Phys. Rev. B (accepted)

We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects., 10 pages, 11 figures, including a Supplementary Material. Published version

The study of magnetic correlations in dipolar-coupled nanomagnet systems with synchrotron x-ray scattering provides a means to uncover emergent phenomena and exotic phases, in particular in systems with thermally active magnetic moments. From the diffuse signal of soft x-ray resonant magnetic scattering, we have measured magnetic correlations in a highly dynamic artificial kagome spin ice with sub-70-nm Permalloy nanomagnets. On comparing experimental scattering patterns with Monte Carlo simulations based on a needle-dipole model, we conclude that kagome ice I phase correlations exist in our experimental system even in the presence of moment fluctuations, which is analogous to bulk spin ice and spin liquid behavior. In addition, we describe the emergence of quasi-pinch-points in the magnetic diffuse scattering in the kagome ice I phase. These quasi-pinch-points bear similarities to the fully developed pinch points with singularities of a magnetic Coulomb phase, and continually evolve into the latter on lowering the temperature. The possibility to measure magnetic diffuse scattering with soft x rays opens the way to study magnetic correlations in a variety of nanomagnetic systems., 8 pages, 5 figures; http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.224413

The Seebeck coefficient, thermoelectric power factor, electrical conductivity, and electronic thermal conductivity of the orthorhombic Pbnm phase of SrRuO3 are studied comprehensively by combining first-principles density functional calculations and Boltzmann transport theory. The influence of exchange-correlation functional on the Seebeck coefficient is carefully investigated. We show that the best agreement with experimental data is achieved when SrRuO3 is described as being at the limit of a half-metal. Furthermore, we analyze the role of individual symmetry-adapted atomic distortions on the Seebeck coefficient, highlighting a particularly strong sensitivity to R-4(+) oxygen rotational motions, which may shed light on how to manipulate the Seebeck coefficient. We confirm that the power factor of SrRuO3 can only be slightly improved by carrier doping. Our results provide a complete understanding of the thermoelectric properties of SrRuO3 and an interesting insight on the relationship between exchange-correlation functionals, atomic motions, and thermoelectric quantities.

The Jahn-Teller distortion, by its very nature, is often at the heart of the various electronic properties displayed by perovskites and related materials. Despite the Jahn-Teller mode being non- polar in nature, we devise and demonstrate in the present letter an electric field control of Jahn-Teller distortions in bulk perovskites. The electric field control is enabled through an anharmonic lattice mode coupling between the Jahn-Teller distortion and a polar mode. We confirm this coupling, and explicitly an electric field effect, through first principles calculations. The coupling will always exist within the P b2 1 m space group, which is found to be the favoured ground state for various perovskites under sufficient tensile epitaxial strain. Intriguingly, the calculations reveal that this mechanism is not only restricted to Jahn-Teller active systems, promising a general route to tune or induce novel electronic functionality in perovskites as a whole.

The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, $C$. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with $|C|>1$. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, $\nu$, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in $|C|=2$ bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions., Comment: v1: 7 pages, 4 figures; v2: 5+5 pages, 2+4 figures (final author formatted version)

We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in the light of these results., Comment: 4.5 pages, 3 figures

We study a quantum Hall bilayer system of bosons at total filling factor $\nu = 1$, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys.~Rev.~Lett.~{\bf 108}, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with $U(1)_2\times U(1)_2$ topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected $U(1)_4 \times U(1)$ structure., Comment: 20 pages, 4 figures, 3 tables

We study correlated phases occurring in the flat lowest band of the dice lattice model at flux density one half. We discuss how to realize the dice lattice model, also referred to as the T_3 lattice, in cold atomic gases. We construct the projection of the model to the lowest dice band, which yields a Hubbard-Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattice phases. At low density, we use exact diagonalization to identify three stable phases at fractional filling factors \nu of the lowest band, including a classical crystal at \nu=1/3, a supersolid state at \nu=1/2 and a Mott insulator at \nu=1., Comment: 5 pages, 4 figures; v2: final published version, title changed

We provide numerical evidence that a p_{x}-i p_{y} paired Bonderson--Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed nu=12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible nu = 12/5 quantum Hall state with shift S=2 on the sphere, matching that of the BS state. The exact ground state of the Coulomb interaction at S=2 is shown to have large overlap with the BS trial wave function. Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general p_{x}-i p_{y} weakly-paired states at nu=5/2. We perform a finite size scaling analysis of the ground state energies for nu=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered Read-Rezayi (S=-2) universality classes. This analysis reveals very tight competition between these two non-Abelian topological orders., Comment: 5 pages, 2 figures; v2: minor corrections; v3: new title, revised exposition, inclusion of neutral gap and finite well-width results; v4: minor corrections

We use particle entanglement spectra to characterize bosonic quantum Hall states on lattices, motivated by recent studies of bosonic atoms on optical lattices. Unlike for the related problem of fractional Chern insulators, very good trial wavefunctions are known for fractional quantum Hall states on lattices. We focus on the entanglement spectra for the Laughlin state at $\nu=1/2$ for the non-Abelian Moore-Read state at $\nu=1$. We undertake a comparative study of these trial states to the corresponding groundstates of repulsive two-body or three-body contact interactions on the lattice. The magnitude of the entanglement gap is studied as a function of the interaction strength on the lattice, giving insights into the nature of Landau-level mixing. In addition, we compare the performance of the entanglement gap and overlaps with trial wavefunctions as possible indicators for the topological order in the system. We discuss how the entanglement spectra allow to detect competing phases such as a Bose-Einstein condensate., Comment: 12 pages, 9 figures

We have employed large scale exact numerical diagonalization in Haldane spherical geometry in a comparative analysis of the correlated many-electron states in the half-filled low Landau levels of graphene and such conventional semiconductors as GaAs, including both spin and valley (i.e., pseudospin) degrees of freedom. We present evidence that the polarized Fermi sea of essentially non-interacting composite fermions remains stable against a pairing transition in both lowest Landau levels of graphene. However, it undergoes spontaneous depolarization, which in (ideal) graphene is unprotected for the lack of a single-particle pseudospin splitting. These results point to the absence of the non-Abelian Pfaffian phase in graphene.

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux N_\phi=2N-3 can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-Abelian statistics of the Ising model with degenerate fusion channels 1 and \psi.

It is now well established that in two-dimensional chiral p-wave paired superfluids, the vortices carry zero-energy modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation. In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices. We study the properties of these subgap states, and argue that their presence affects the topological protection of the zero modes. In conventional superconductors where the chemical potential is of the order of the Fermi energy of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult to cool the system to below the mini-gap and at experimentally available temperatures, transitions between the subgap states, including the zero modes, will occur and can alter the quantum states of the zero-modes. We show that compound qubits involving the zero-modes and the parity of the occupation number of the subgap states on each vortex are still well defined. However, practical schemes taking into account all subgap states would nonetheless be difficult to achieve. We propose to avoid this difficulty by working in the regime of small chemical potential mu, near the transition to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored, and explicitly evaluate mu_c in a Feshbach resonant K-40 gas., 19 pages, 10 figures; v2: main text as published version, additional detail included as appendices

We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene., Comment: 3 pages, 4 figures (revision: reference update)

We study charged excitations of the non-abelian Moore-Read liquid at filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of non-zero well widths, we find that at sufficiently low Zeeman energy it is energetically favourable for charge e/4 quasiholes to bind into "skyrmions" of charge e/2. We show that skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations. We comment on the consequences for the activated transport., 4 pages, 3 figures

We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both s-wave and p-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor in the lowest Landau level and in terms of the ratio between s- and p-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or composed of spin-singlets. In the regime with no phase separation, we give evidence for fractional quantum Hall states. Most notably, we find two distinct singlet states at the filling nu =2/3 for different interactions. One of these states is accounted for by the composite fermion theory while the other one is a paired state for which we identify two competing descriptions with different topological structure. This paired state may be an Abelian liquid of composite spin-singlet Bose molecules with Laughlin correlations. Alternatively, it may be a known non-Abelian paired state, indicated by good overlaps with the corresponding trial wavefunction. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for nu =1/2 and the permanent state of Moore and Read for nu =1. For purely repulsive interactions, we also find evidence for a gapped Halperin state at nu=2/5., 12 pages, 9 figs (best viewed in color), published version with additional evidence for a non-Abelian spin singlet state at filling nu=2/3

We study a frustrated dipolar array recently manufactured lithographically by Wang {\em et al.} [Nature {\bf 439}, 303 (2006)] in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck., Comment: 4 pages, 4 figures; v2: minor modifications in typesetting, figures 1 and 3 updated

The method of Jain and Kamilla [PRB {\bf 55}, R4895 (1997)] allows numerical generation of composite fermion trial wavefunctions for large numbers of electrons in high magnetic fields at filling fractions of the form nu=p/(2mp+1) with m and p positive integers. In the current paper we generalize this method to the case where the composite fermions are in an effective (mean) field with opposite sign from the actual physical field, i.e. when p is negative. We examine both the ground state energies and the low energy neutral excitation spectra of these states. Using particle-hole symmetry we can confirm the correctness of our method by comparing results for the series m=1 with p>0 (previously calculated by others) to our results for the conjugate series m=1 with p 0, m=2 cases., 11 pages

ECRYS 2005 International Workshop on Electronic Crystals; In Quantum Hall bilayers, at total filling factor one, a transition from a compressible phase with weak interlayer correlations to an incompressible phase with strong interlayer correlations is observed as the distance between the two layers is reduced. The transition between these two regimes can be understood using a trial wavefunction approach based on the composite particle picture.

By means of first-principles calculations, various properties of SrRuO3 are investigated, focusing on its lattice dynamical properties. Despite having a Goldschmidt tolerance factor very close to 1, the phonon dispersion curves of the high-temperature cubic phase of SrRuO3 show strong antiferrodistortive instabilities. The energetics of metastable phases with different tilt patterns are discussed, concluding that the coupling of oxygen-rotation modes with anti-polar Sr motion plays a key role in stabilizing the Pnma phase with respect to alternative rotation patterns. This not only explains the ground state of SrRuO3 but also contributes to rationalize why most ABO3 perovskites exhibit an orthorhombic ground state. The zone-center phonon modes of the Pnma phase have been computed, from which we propose partial reassignment of available experimental data. The full dispersion curves have also been obtained, constituting benchmark results for the interpretation of future measurements and providing access to thermodynamical properties., Comment: Also see LabTalk (http://iopscience.iop.org/0953-8984/labtalk-article/55704) and HighLight of 2014 (http://iopscience.iop.org/0953-8984/page/Highlights-of-2014)

Rare-earth co-doping in inorganic materials has a long-held tradition of facilitating highly desirable optoelectronic properties for their application to the laser industry. This study concentrates specifically on rare-earth phosphate glasses, (R2O3)x(R'2O3)y(P2O5)(1-(x+y)), where (R, R') denotes (Ce, Er) or (La, Nd) co-doping and the total rare-earth composition corresponds to a range between metaphosphate, RP3O9, and ultraphosphate, RP5O14. Thereupon, the effects of rare-earth co-doping on the local structure are assessed at the atomic level. Pair-distribution function analysis of high-energy X-ray diffraction data (Q(max) = 28 Å(-1)) is employed to make this assessment. Results reveal a stark structural invariance to rare-earth co-doping which bears testament to the open-framework and rigid nature of these glasses. A range of desirable attributes of these glasses unfold from this finding; in particular, a structural simplicity that will enable facile molecular engineering of rare-earth phosphate glasses with 'dial-up' lasing properties. When considered together with other factors, this finding also demonstrates additional prospects for these co-doped rare-earth phosphate glasses in nuclear waste storage applications. This study also reveals, for the first time, the ability to distinguish between P-O and P[double bond, length as m-dash]O bonding in these rare-earth phosphate glasses from X-ray diffraction data in a fully quantitative manner. Complementary analysis of high-energy X-ray diffraction data on single rare-earth phosphate glasses of similar rare-earth composition to the co-doped materials is also presented in this context. In a technical sense, all high-energy X-ray diffraction data on these glasses are compared with analogous low-energy diffraction data; their salient differences reveal distinct advantages of high-energy X-ray diffraction data for the study of amorphous materials.