Effects of disorder on electron tunneling through helical edge states

TL;DR

This paper studies how disorder affects electron tunneling in helical edge states, revealing that phase fluctuations due to disorder can significantly influence transmission properties and localization length.

Contribution

It introduces models of phase disorder in tunneling amplitudes and analyzes their impact on transmission and localization in quantum spin Hall edge states.

Findings

Phase fluctuations can dramatically alter energy-dependent transmission.

The way phase fluctuates influences the localization length.

Different disorder models have distinct effects on transport properties.

Abstract

A tunnel junction between helical edge states, realized via a constriction in a Quantum Spin Hall system, can be exploited to steer both charge and spin current into various terminals. We investigate the effects of disorder on the transmission coefficient $T_p$ of the junction, by modelling disorder with a randomly varying (complex) tunneling amplitude $\Gamma_p=|\Gamma_p| \exp[i \phi_p]$. We show that, while for a clean junction $T_p$ is only determined by the absolute value $|\Gamma_p|$ and is independent of the phase $\phi_p$, the situation can be quite different in the presence of disorder: phase fluctuations may dramatically affect the energy dependence of $T_p$ of any single sample. Furthermore, analysing three different models for phase disorder (including correlated ones), we show that not only the amount but also the way the phase $\phi_p$ fluctuates determines the localisation length $\xi_{loc}$ and the sample-averaged transmission. Finally, we discuss the physical conditions in which these three models suitably apply to realistic cases.