Heat transport in Weyl semimetals in the hydrodynamic regime

We study heat transport in a Weyl semimetal with broken time-reversal symmetry in the hydrodynamic regime. At the neutrality point, the longitudinal heat conductivity is governed by the momentum relaxation (elastic) time, while longitudinal electric conductivity is controlled by the inelastic scattering time. In the hydrodynamic regime this leads to a large longitudinal Lorenz ratio. As the chemical potential is tuned away from the neutrality point, the longitudinal Lorenz ratio decreases because of suppression of the heat conductivity by the Seebeck effect. The Seebeck effect (thermopower) and the open circuit heat conductivity are intertwined with the electric conductivity. The magnitude of Seebeck tensor is parametrically enhanced, compared to the non-interacting model, in a wide parameter range. While the longitudinal component of Seebeck response decreases with increasing electric anomalous Hall conductivity $\sigma_{xy}$, the transverse component depends on $\sigma_{xy}$ in a non-monotonous way. Via its effect on the Seebeck response, large $\sigma_{xy}$ enhances the longitudinal Lorenz ratio at a finite chemical potential. At the neutrality point, the transverse heat conductivity is determined by the Wiedemann-Franz law. Increasing the distance from the neutrality point, the transverse heat conductivity is enhanced by the transverse Seebeck effect and follows its non-monotonous dependence on $\sigma_{xy}$

Elementary models of 3D topological insulators with chiral symmetry

We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of $\mathbb{Z}$ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For $\mathbb{Z}$ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in $\mathbb{Z}$ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in $\mathbb{Z}_2$ topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected

Quantum corrections to the magnetoconductivity of surface states in three-dimensional topological insulators

The interplay between quantum interference, electron-electron interaction (EEI), and disorder is one of the central themes of condensed matter physics. Such interplay can cause high-order magnetoconductance (MC) corrections in semiconductors with weak spin-orbit coupling (SOC). However, it remains unexplored how the magnetotransport properties are modified by the high-order quantum corrections in the electron systems of symplectic symmetry class, which include topological insulators (TIs), Weyl semimetals, graphene with negligible intervalley scattering, and semiconductors with strong SOC. Here, we extend the theory of quantum conductance corrections to two-dimensional (2D) electron systems with the symplectic symmetry, and study experimentally such physics with dual-gated TI devices in which the transport is dominated by highly tunable surface states. We find that the MC can be enhanced significantly by the second-order interference and the EEI effects, in contrast to the suppression of MC for the systems with orthogonal symmetry. Our work reveals that detailed MC analysis can provide deep insights into the complex electronic processes in TIs, such as the screening and dephasing effects of localized charge puddles, as well as the related particle-hole asymmetry

Elementary models of three-dimensional topological insulators with chiral symmetry

We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of ℤ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For ℤ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in ℤ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in ℤ2 topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected

One-dimensional non-interacting topological insulators with chiral symmetry

We construct microscopical models of one-dimensional non-interacting topological insulators in all of the chiral universality classes. Specifically, we start with a deformation of the Su-Schrieffer-Heeger (SSH) model that breaks time-reversal symmetry, which is in the AIII class. We then couple this model to its time-reversal counterpart in order to build models in the classes BDI, CII, DIII and CI. We find that the ℤ topological index (the winding number) in individual chains is defined only up to a sign. This comes from noticing that changing the sign of the chiral symmetry operator changes the sign of the winding number. The freedom to choose the sign of the chiral symmetry operator on each chain independently allows us to construct two distinct possible chiral symmetry operators when the chains are weakly coupled -- in one case, the total winding number is given by the sum of the winding number of individual chains while in the second case, the difference is taken. We find that the chiral models that belong to ℤ classes, AIII, BDI and CII are topologically equivalent, so they can be adiabatically deformed into one another so long as the chiral symmetry is preserved. We study the properties of the edge states in the constructed models and prove that topologically protected edge states must all be localised on the same sublattice (on any given edge). We also discuss the role of particle-hole symmetry on the protection of edge states and explain how it manages to protect edge states in ℤ2 classes, where the integer invariant vanishes and chiral symmetry alone does not protect the edge states anymore. We discuss applications of our results to the case of an arbitrary number of coupled chains, construct possible chiral symmetry operators for the multiple chain case, and briefly discuss the generalisation to any odd number of dimensions

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher--Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment. Unlike the method of bosonization, the Fisher--Hartwig formula correctly takes into account the discreteness of charge. Furthermore, we check numerically the precision of the generalized Fisher--Hartwig formula, find that it has a higher precision than rigorously proven so far, and conjecture the form of the next-order correction to the existing formula.Comment: 17 pages, 2 figures, Latex, iopart.cl

Current Fluctuations and Electron-Electron Interactions in Coherent Conductors

We analyze current fluctuations in mesoscopic coherent conductors in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of the current noise on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission of the $n$-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large voltages we recover two different interaction corrections entering with opposite signs. The net result is proportional to $\sum_nT_n(T_n-1)(1-2T_n)$, i.e. Coulomb interaction decreases the shot noise at low transmissions and increases it at high transmissions.Comment: 16 pages, 2 figure

Quantum corrections to the magnetoconductivity of surface states in three-dimensional topological insulators

Abstract The interplay between quantum interference, electron-electron interaction (EEI), and disorder is one of the central themes of condensed matter physics. Such interplay can cause high-order magnetoconductance (MC) corrections in semiconductors with weak spin-orbit coupling (SOC). However, it remains unexplored how the magnetotransport properties are modified by the high-order quantum corrections in the electron systems of symplectic symmetry class, which include topological insulators (TIs), Weyl semimetals, graphene with negligible intervalley scattering, and semiconductors with strong SOC. Here, we extend the theory of quantum conductance corrections to two-dimensional (2D) electron systems with the symplectic symmetry, and study experimentally such physics with dual-gated TI devices in which the transport is dominated by highly tunable surface states. We find that the MC can be enhanced significantly by the second-order interference and the EEI effects, in contrast to the suppression of MC for the systems with orthogonal symmetry. Our work reveals that detailed MC analysis can provide deep insights into the complex electronic processes in TIs, such as the screening and dephasing effects of localized charge puddles, as well as the related particle-hole asymmetry