Topological metals continue to attract attention as novel gapless states of matter. While there by now exists an exhaustive classification of possible topologically nontrivial metallic states, their observable properties, that follow from the electronic structure topology, are less well understood. Here we present a study of the electromagnetic response of three-dimensional topological metals with Weyl or Dirac nodes in the spectrum, which systematizes and extends earlier pioneering studies. In particular, we argue that a smoking-gun feature of the chiral anomaly in topological metals is the existence of propagating chiral density modes even in the regime of weak magnetic fields. We also demonstrate that the optical conductivity of such metals exhibits an extra peak, which exists on top of the standard metallic Drude peak. The spectral weight of this peak is transferred from high frequencies and its width is proportional to the chiral charge relaxation rate.
We study the spin conductivity of the bulk states of three-dimensional topological insulators within Kubo formalism. Spin Hall effect is the generation of the spin current that is perpendicular to the applied voltage. In the case of a three-dimensional topological insulator, applied voltage along $x$ direction generates transverse spin currents along $y$ and $z$ directions with comparable values. We found that a finite non-universal value of the spin conductivity exists in the gapped region due to the inversion of bands. Contribution to the spin conductivity from the vertex corrections enhance…
The lifetime of electrons on edge states of a two-dimensional topological insulator against the background of an allowed two-dimensional band has been determined. It has been shown that this time in the case of scattering on Coulomb impurities can be significantly larger than the mean free time of two-dimensional electrons. As a result, the conductivity of the metallic two-dimensional topological insulator strip can be determined primarily by edge states.
We investigate the influence of the hexagonal warping on the transport properties of the topological insulators. We study the charge conductivity within Kubo formalism in the first Born approximation using low energy expansion of the Hamiltonian near the Dirac point. The effects of disorder, magnetic field and chemical potential value are analyzed in details. We found that the presence of the hexagonal warping effects significantly the conductivity of the topological insulator. In particular, it gives rise to the growth of the longitudinal conductivity with the increase of the disorder and ani…
Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system. We illustrate the applications of this formalism by giving general expressions for optical conductivity of Floquet systems, including its homodyne and heterodyne components and beyond. We obtain the Floquet optical conductivity of specific driven models, including two-dimensional Dirac material such as the surface of a topological insulator, graphene, and the Haldane model irradiated with circularly or linearly polariz…
We consider the quantum Hall effect (QHE) in a system of interacting electrons. Our formalism is valid for systems in the presence of an external magnetic field, as well as for systems with a nontrivial band topology. That is, the expressions for the conductivity derived are valid for both the ordinary QHE and for the intrinsic anomalous QHE. The expression for the conductivity applies to external fields that may vary in an arbitrary way, and takes into account disorder. It is assumed that the ground state of the system is degenerate. We represent the QHE conductivity as $\frac{e^2}{h} \times …
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The quantum Hall conductivity is represented as the topological invariant in phase space in terms of the Wigner transformed two - point Green function.} This representation has been derived when the inter - electron interactions were neglected. It is natural to suppose, that in the presence of interactions the Hall conductivity is still given by the same expressi…
We consider a disordered topological insulator thin film placed on the top of a ferromagnetic insulator with a perpendicular exchange field $M$ and subjected to a perpendicular electric field. The presence of ferromagnetic insulator causes that bottom surface states of the topological insulator thin film become spin polarized and the electric field provides a potential difference $V$ between the two surface states, resulting in breaking of time-reversal and inversion symmetry in the system. Using Kubo formalism and employing the first Born approximation as well as the self-consistent Born appr…
We investigate the spin conductivity of topological insulators taking into account both the surface and quasi-two-dimensional bulk states. We apply a low-energy expansion of the Hamiltonian up to the third order in momentum and take into account the vertex corrections arising due to the short range disorder. Hexagonal warping gives rise to the additional anisotropic components in the spin conductivity tensor. Typically, isotropic part of the spin conductivity is larger than anisotropic one. The helical regime for the bulk states, in which the electrons in the Fermi level have the same projecti…
It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE), which, in addition, may be represented as one in momentum space composed of the two point Green's functions. We propose the generalization of this expression to the QHE in the presence of non-uniform magnetic field. The proposed expression is the topological invariant in phase space composed of the Weyl symbols of the two-point Green's function. It is applicab…
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
We theoretically investigate the spin Hall conductivity (SHC) in topological Dirac semimetals (TDSMs) whose Dirac points are protected by rotational symmetry. On the basis of a general phase diagram of the system with time-reversal, inversion and four-fold rotational symmetries, we reveal that the SHC is sensitive to the phase to which the system belong. The phase and the SHC are characterized by the mirror Chern numbers and the presence or absence of gapless bulk Dirac points. It is also found that the representative TDSM Cd$_3$As$_2$ supports a large and negative SHC $σ_{xy}^z\sim -10^4 (\hb…
Hall conductivity for the intrinsic quantum Hall effect in homogeneous systems is given by the topological invariant composed of the Green function depending on momentum of quasiparticle. This expression reveals correspondence with the mathematical notion of the degree of mapping. A more involved situation takes place for the Hall effect in the presence of external magnetic field. In this case the mentioned expression remains valid if the Green function is replaced by its Wigner transformation while ordinary products are replaced by the Moyal products. Such an expression, unfortunately, is muc…
It is textbookly regarded that phonons, i.e., an energy quantum of propagating lattice waves, are the main heat carriers in perfect crystals. As a result, in many crystals, e.g., bulk silicon, the temperature-dependent thermal conductivity shows the classical 1/T relationship because of the dominant Umklapp phonon-phonon scattering in the systems. However, the thermal conductivity of many crystalline metal-organic frameworks is very low and shows no, a weakly negative and even a weakly positive temperature dependence (glass-like thermal conductivity). It has been in debate whether the thermal …
We show that in a model of a metal photoexcited by a transient pump pulse resonant with a phonon mode the absolute dc conductivity may become negative, depending on the interplay between the electronic structure, the phonon frequency and the pump intensity. The analysis includes the effects of inelastic scattering and thermal relaxation. Results for the time evolution of the negative conductivity state are presented; the associated non-equilibrium physics may persist for long times after the pulse. Our findings provide a theoretical justification for previously proposed phenomenology and indic…
ZrSiS is one of the strong candidates for realistic nodal-line semimetal. We theoretically investigate the dynamical conductivity in ZrSiS by using a multi-orbital theoretical model based on the first-principles band calculation. We find that the dynamical conductivity in the clean limit is actually not frequency independent unlike the ideal Dirac model, while nearly flat dependence is achieved by introducing the energy broadening possibly induced by the disorder. The results can be applied to other compounds with the similar crystal structure, such as ZrSiSe, ZrSiTe, and HfSiS.
The third-rank tensor of the static spin Hall conductivity is investigated for two-dimensional (2D) topological insulators by electronic structure calculations. Its seeming quantization is numerically demonstrated for highly symmetric systems independent of the gap size. 2D crystals with hexagonal and square Bravais lattice show similar effects, while true rectangular translational symmetry yields conductivity values much below the quantum $e^2/h$. Field-induced lifting the inversion symmetry does not influence the quantum spin Hall state up to band inversion but the conductivity quantization.…
Quantum transport in magnetic topological insulators reveals the strong interplay between the magnetism and topology of electronic band structures. A recent experiment on magnetically doped topological insulator Bi2Se3 thin films showed the anomalous temperature dependence of the magnetoconductivity while their field dependence presents a clear signature of weak anti-localization [Tkac et al., Phys. Rev. Lett. 123, 036406(2019)]. Here we demonstrate that the tiny mass of the surface electrons induced by the bulk magnetization leads to a temperature-dependent correction to the πBerry phase, and…
