Bulk and surface spin conductivity in topological insulators with hexagonal warping

TL;DR

This paper studies how hexagonal warping affects spin conductivity in topological insulators, revealing anisotropic effects, robustness of surface contributions, and disorder sensitivity of bulk states, aligning with experimental observations.

Contribution

It provides a detailed analysis of bulk and surface spin conductivity considering hexagonal warping and disorder effects, highlighting the robustness of surface contributions and the conditions for bulk conductivity suppression.

Findings

Hexagonal warping introduces anisotropic components in spin conductivity.

Surface states' spin conductivity is robust and independent of chemical potential.

Bulk spin conductivity increases in the helical regime and is sensitive to disorder.

Abstract

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 projection of the spin on the direction of momentum, have been studied in a more detail. In this regime, a substantial increase of the spin conductivity contribution from the bulk states at the Fermi level is observed. We find that the bulk spin conductivity is insensitive to disorder if Rashba spin-orbit coupling is larger than disorder strength, otherwise, it is strongly suppressed. The contribution to the spin conductivity from the surface states is almost independent of the chemical potential, robust to disorder and its value is comparable to the spin conductivity contribution from the bulk states per layer. The obtained results are in agreement with experimental data.