Hexagonal Warping Effects on the Surface Transport in Topological Insulators

TL;DR

This paper studies how hexagonal warping affects charge transport and spin polarization on the surface of topological insulators, revealing density-dependent effects and weak anti-localization.

Contribution

It provides general expressions for conductivity and spin polarization including hexagonal warping effects, applicable in classical and quantum regimes.

Findings

Hexagonal warping introduces quadratic carrier density dependence.

Surface states exhibit weak anti-localization despite warping.

Dielectric function becomes momentum-angle-dependent with warping.

Abstract

We investigate the charge conductivity and current-induced spin polarization on the surface state of a three-dimensional topological insulator by including the hexagonal warping effect of Fermi surface both in classical and quantum diffusion regimes. We present general expressions of conductivity and spin polarization, which are reduced to simple forms for usual scattering potential. Due to the hexagonal warping, the conductivity and spin polarization show an additional quadratic carrier density dependence both for Boltzmann contribution and quantum correction. In the presence of warping term, the surface states still reveal weak anti-localization. Moreover, the dielectric function in the random phase approximation is also explored, and we find that it may be momentum-angle-dependent.