Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

TL;DR

This paper analytically investigates how Rashba spin-orbit coupling affects the energy dispersion and spin orientation of helical edge states in 2D topological insulators, revealing finite size effects and potential implications for transport properties.

Contribution

It provides analytical expressions for the dispersion relations and spin orientations of generic helical edge states with Rashba coupling, including finite size effects within the BHZ model.

Findings

Weak energy dependence of spin orientation in single-edge case for HgTe quantum wells

Finite size effects cause avoided crossings and increased spin variation

Analytical results agree well with numerical tight-binding simulations

Abstract

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.