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arXiv2013

Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling

We theoretically investigate the spectral properties and the spatial dependence of the local density of states (LDoS) in disordered two-dimensional electron gases (2DEG) in the quantum Hall regime, taking into account the combined presence of electrostatic disorder, random Rashba spin-orbit in- teraction, and finite Zeeman coupling. To this purpose, we extend a coherent-state Green's function formalism previously proposed for spinless 2DEG in the presence of smooth arbitrary disorder, that here incorporates the nontrivial coupling between the orbital and spin degrees of freedom into the electronic drift states. The formalism allows us to obtain analytical and controlled nonperturbative expressions of the energy spectrum in arbitrary locally flat disorder potentials with both random electric fields and Rashba coupling. As an illustration of this theory, we derive analytical microscopic expressions for the LDoS in different temperature regimes which can be used as a starting point to interpret scanning tunneling spectroscopy data at high magnetic fields. In this context, we study the spatial dependence and linewidth of the LDoS peaks and explain an experimentally-noticed correlation between the spatial dispersion of the spin-orbit splitting and the local extrema of the potential landscape.

cond-mat.mes-hall↗

arXiv2014

Phase Transition in 3d Heisenberg Spin Glasses with Strong Random Anisotropies, through a Multi-GPU Parallelization

We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark the presence of strong finite-size effects on the chiral sector. We find a unique phase transition for the chiral and spin glass sector, in the Universality class of Ising spin glasses. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 64x64x64 spins, over a vast range of temperatures.

cond-mat.dis-nn↗

arXiv2013

Diffusive transport in Weyl semimetals

Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic quantum materials, recently of considerable interest. In order to do this, we first explicitly implement the analytical scheme by which disorder with anisotropic scattering amplitude is incorporated into the diagrammatic response-function formalism for calculating the `diffuson'. The result thus obtained is consistent with transport coefficients evaluated from the Boltzmann transport equation or the renormalized uniform current vertex calculation, as it should be. We thus demonstrate that the computation of the diffusion coefficient should involve the transport lifetime, and not the quasiparticle lifetime. Using this method, we then calculate the density response function in Weyl semimetals and discover an unconventional diffusion process that is significantly slower than conventional diffusion. This gives rise to relaxation processes that exhibit stretched exponential decay, instead of the usual exponential diffusive relaxation. This result is then explained using a model of thermally excited quasiparticles diffusing with diffusion coefficients which are strongly dependent on their energies. We elucidate the roles of the various energy and time scales involved in this novel process and propose an experiment by which this process may be observed.

cond-mat.mes-hall↗

arXiv2014

Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass

The long-range one-dimensional Ising spin-glass with random couplings decaying as $J(r) \propto r^{-σ}$ presents a spin-glass phase $T_c(σ)>0$ for $0 \leq σ<1$ (the limit $σ=0$ corresponds to the mean-field SK-model). We use the eigenvalue method introduced in our previous work [C. Monthus and T. Garel, J. Stat. Mech. P12017 (2009)] to measure the equilibrium time $t_{eq}(N)$ at temperature $T=T_c(σ)/2$ as a function of the number $N$ of spins. We find the activated scaling $\ln t_{eq}(N) \sim N^ψ$ with the same barrier exponent $ψ\simeq 0.33$ in the whole region $0\leqσ<1$.

cond-mat.dis-nn↗

arXiv2014

Do Se vacancies electron dope monolayer FeSe?

Following the discovery of the potentially very high temperature superconductivity in monolayer FeSe we investigate the doping effect of Se vacancies in these materials. We find that Se vacancies pull a vacancy centered orbital below the Fermi energy that absorbs most of the doped electrons. Furthermore we find that the disorder induced broadening causes an effective hole doping. The surprising net result is that in terms of the band structure Se vacancies behave like hole dopants rather than electron dopants. Our results exclude Se vacancies as the origin of the large electron pockets measured by angle resolved photoemission spectroscopy.

cond-mat.supr-con↗

arXiv2014

Critical behavior of spin and chiral degrees of freedom in three-dimensional disordered XY models studied by the nonequilibrium aging method

The critical behavior of the gauge-glass and the XY spin-glass models in three dimensions is studied by analyzing their nonequilibrium aging dynamics. A new numerical method, which relies on the calculation of the two-time correlation and integrated response functions, is used to determine both the critical temperature and the nonequilibrium scaling exponents, both for spin and chiral degrees of freedom. First, the ferromagnetic XY model is studied to validate this nonequilibirum aging method (NAM), since for this nondisordered system we can compare with known results obtained with standard equilibrium and nonequilibrium techniques. When applied to the case of the gauge-glass model, we show that the NAM allows us to obtain precise and reliable values of its critical quantities, improving previous estimates. The XY spin-glass model with both Gaussian and bimodal bond distributions, is analyzed in more detail. The spin and the chiral two-time correlation and integrated response functions are calculated in our simulations. The results obtained mainly for Gaussian and, to a lesser extent, for bimodal interactions, support the existence of a spin-chiral decoupling scenario, where the chiral order occurs at a finite temperature while the spin degrees of freedom order at very low or zero temperature.

cond-mat.stat-mech↗

arXiv2014

Interplay of Coulomb Blockade and Ferroelectricity in Nano-Granular Materials

We study electron transport properties of composite ferroelectrics --- materials consisting of metallic grains embedded in a ferroelectric matrix. In particular, we calculate the conductivity in a wide range of temperatures and electric fields, showing pronounced hysteretic behavior. In weak fields, electron cotunneling is the main transport mechanism. In this case, we show that the ferroelectric matrix strongly influences the transport properties through two effects: i) the dependence of the Coulomb gap on the dielectric permittivity of the ferroelectric matrix, which in turn is controlled by temperature and external field; and ii) the dependence of the tunneling matrix elements on the electric polarization of the ferroelectric matrix, which can be tuned by temperature and applied electric field as well. In the case of strong electric fields, the Coulomb gap is suppressed and only the second mechanism is important. Our results are important for i) thermometers for precise temperature measurements and ii) ferrroelectric memristors.

cond-mat.mes-hall↗

arXiv2013

The renormalization flow of the hierarchical Anderson model at weak disorder

We study the flow of the renormalized model parameters obtained from a sequence of simple transformations of the 1D Anderson model with long-range hierarchical hopping. Combining numerical results with a perturbative approach for the flow equations, we identify three qualitatively different regimes at weak disorder. For a sufficiently fast decay of the hopping energy, the Cauchy distribution is the only stable fixed-point of the flow equations, whereas for sufficiently slowly decaying hopping energy the renormalized parameters flow to a delta peak fixed-point distribution. In an intermediate range of the hopping decay, both fixed-point distributions are stable and the stationary solution is determined by the initial configuration of the random parameters. We present results for the critical decay of the hopping energy separating the different regimes.

cond-mat.dis-nn↗

arXiv2013

Network Models of Photonic Floquet Topological Insulators

A recently-proposed class of photonic topological insulators is shown to map onto Chalker-Coddington-type networks, which were originally formulated to study disordered quantum Hall systems. Such network models are equivalent to the Floquet states of periodically-driven lattices. We show that they can exhibit topologically protected edge states even if all bands have zero Chern number, which is a characteristic property of Floquet bandstructures. These edge states can be counted by an adiabatic pumping invariant based on the winding number of the coefficient of reflection from one edge of the network.

cond-mat.mes-hall↗

arXiv2014

A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions

We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low and large disorder regimes, and allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a cell-selective fashion. As a function of cluster size, our method systematically recovers the re-entrance behavior of the mobility edge and obtains the correct critical disorder strength for Anderson localization in 3D.

cond-mat.dis-nn↗

arXiv2014

Non-homogeneity of the density of states of tunneling two-level systems at low energies

Amorphous solids, and many disordered lattices, exhibit a remarkable qualitative and quantitative universality in their acoustic properties at temperature $\lesssim 3$K. This phenomenon is attributed to the existence of tunneling two level systems (TTLSs), characterized by a homogenous density of states (DOS) at energies much lower than the disorder energy ($\approx 0.1$eV). Here we calculate numerically, from first principles, the DOS of KBr:CN glass, the archetypal disordered lattice showing universality. In contrast to the standard tunneling model, we find that the DOS diminishes abruptly at $\approx 3$ K, and that tunneling states differ essentially by their symmetry under inversion. This structure of the TTLSs dictates the low temperature below which universality is observed, and the quantitative universality of the acoustic properties in glasses. Consequences to the properties of glasses at intermediate temperatures, as well as to the microscopic structure of amorphous solids, are discussed.

cond-mat.mes-hall↗

arXiv2014

Short-range disorder effects on electronic transport in 2D semiconductor structures

We study theoretically the relative importance of short-range disorder in determining the low-temperature 2D mobility in GaAs-based structures with respect to Coulomb disorder which is known to be the dominant disorder in semiconductor systems. We give results for unscreened and screened short-range disorder effects on 2D mobility in quantum wells and heterostructures, comparing with the results for Coulomb disorder and finding that the asymptotic high-density mobility is always limited by short-range disorder which, in general, becomes effectively stronger with increasing `carrier density' in contrast to Coulomb disorder. We also predict an intriguing re-entrant metal-insulator transition at very high carrier densities in Si-MOSFETs driven by the short-range disorder associated with surface roughness scattering.

cond-mat.mes-hall↗

arXiv2014

Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors

We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as "pseudomagnetic" fields (abelian and non-abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wavefunctions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel'stein non-linear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders, and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII we show that interactions are always irrelevant, while in class AIII there is a finite window of stability, controlled by the disorder. Outside of this window we identify new interaction-stabilized fixed points.

cond-mat.dis-nn↗

arXiv2014

Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach

The role of disorder in the field of three-dimensional time reversal invariant topological insulators has become an active field of research recently. However, the computation of Z2 invariants for large, disordered systems still poses a considerable challenge. In this paper we apply and extend a recently proposed method based on the scattering matrix approach, which allows the study of large systems at reasonable computational effort with few-channel leads. By computing the Z2 invariant directly for the disordered topological Anderson insulator, we unambiguously identify the topological nature of this phase without resorting to its connection with the clean case. We are able to efficiently compute the Z2 phase diagram in the mass-disorder plane. The topological phase boundaries are found to be well described by the self consistent Born approximation, both for vanishing and finite chemical potential.

cond-mat.mes-hall↗

arXiv2014

Signatures of Rashba Spin-Orbit Interaction in Charge and Spin Properties of Quantum Hall Systems

We study the local equilibrium properties of two-dimensional electron gases at high magnetic fields in the presence of random smooth electrostatic disorder, Rashba spin-orbit coupling, and the Zeeman interaction. Using a systematic magnetic length ($l_B$) expansion within a Green's function framework we derive quantum functionals for the local spin-resolved particle and current densities which can be useful for future studies combining disorder and mean-field electron-electron interaction in the quantum Hall regime. We point out that the spin polarization presents a peculiar spatial dependence which can be used to determine the strength of the Rashba coupling by local probes. The spatial structure of the current density, consisting of both compressible and incompressible contributions, also essentially reflects the effects of Rashba spin-orbit interaction on the energy spectrum. We show that in the semiclassical limit $l_B \rightarrow 0$ the local Hall conductivity remains, however, still quantized in units of $e^2/h$ for any finite strength of the spin-orbit interaction. In contrast, it becomes half-integer quantized when the latter is infinite, a situation which corresponds to a disordered topological insulator surface consisting of a single Dirac cone. Finally, we argue how to define at high magnetic fields a spin Hall conductivity related to a dissipationless angular momentum flow, which is characterized by a sequence of plateaus as a function of the inverse magnetic field (thus free of resonances).

cond-mat.mes-hall↗

arXiv2014

Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene

We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A frozen regime can occur for strong disorder in these systems, wherein a single wavefunction presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a Quantum Hall critical metal. For the case of two valleys and non-abelian disorder, we verify predictions of conformal field theory. Our results for the non-abelian case imply that both delocalization and conformal invariance are topologically-protected for multivalley topological superconductor surface states.

cond-mat.dis-nn↗

arXiv2014

Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy

For the Ising model with Gaussian random coupling of average $J_0$ and unit variance, the zero-temperature spinglass-ferromagnetic transition as a function of the control parameter $J_0$ can be studied via the size-$L$ dependent renormalized coupling defined as the domain-wall energy $J^R(L) \equiv E_{GS}^{(AF)}(L)-E_{GS}^{(F)}(L)$ (i.e. the difference between the ground state energies corresponding to AntiFerromagnetic and and Ferromagnetic boundary conditions in one direction). We study numerically the critical exponents of this zero-temperature transition within the Migdal-Kadanoff approximation as a function of the dimension $d=2,3,4,5,6$. We then compare with the mean-field spherical model. Our main conclusion is that in low dimensions, the critical stiffness exponent $θ^c$ is clearly bigger than the spin-glass stiffness exponent $θ^{SG}$, but that they turn out to coincide in high enough dimension and in the mean-field spherical model. We also discuss the finite-size scaling properties of the averaged value and of the width of the distribution of the renormalized couplings.

cond-mat.dis-nn↗

arXiv2014

Unconventional quantum criticality in the kicked rotor

The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies realizes the universality class of $d$-dimensional disordered metals. For $d>3$, the system exhibits an Anderson metal-insulator transition which has been observed within the framework of an atom optics realization. However, the absence of genuine randomness in the QKR reflects in critical phenomena beyond those of the Anderson universality class. Specifically, the system shows strong sensitivity to the algebraic properties of its effective Planck constant $\tilde h \equiv 4π/q$. For integer $q$, the system may be in a globally integrable state, in a `super-metallic' configuration characterized by diverging response coefficients, Anderson localized, metallic, or exhibit transitions between these phases. We present numerical data for different $q$-values and effective dimensionalities, with the focus being on parameter configurations which may be accessible to experimental investigations.

cond-mat.stat-mech↗