Bulk spin conductivity of three-dimensional topological insulator

TL;DR

This paper investigates the bulk spin conductivity in three-dimensional topological insulators using the Kubo formalism, revealing finite spin conductivity in the gapped region and explaining large observed values.

Contribution

It provides a theoretical analysis of bulk spin conductivity, including vertex corrections, in 3D topological insulators, highlighting non-universal values and band inversion effects.

Findings

Finite non-universal spin conductivity in the gapped region

Vertex corrections enhance spin conductivity from filled states

Explains large spin conductivity observed experimentally

Abstract

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 enhances the spin conductivity from the filled states. These findings explain the large spin conductivity that has been observed in topological insulators.