Magnetic field induced localization in 2D topological insulators

TL;DR

This paper models how weak magnetic fields cause localization of edge states in 2D topological insulators, revealing a quadratic dependence of localization length on magnetic field strength and providing estimates for experimental systems.

Contribution

It introduces a scattering theory model for magnetic field-induced localization of helical edge states in 2D topological insulators, with quantitative predictions.

Findings

Localization length scales as B^2 at small B

Localization length saturates at large B

Estimated localization length for HgTe/CdTe quantum wells

Abstract

Localization of the helical edge states in quantum spin Hall insulators requires breaking time reversal invariance. In experiments this is naturally implemented by applying a weak magnetic field B. We propse a model based on scattering theory that describes the localization of helical edge states due to coupling to random magnetic fluxes. We find that the localization length is proportional to B^{2} when B is small, and saturates to a constant when B is sufficiently large. We estimate especially the localization length for the HgTe/CdTe quantum wells with known experimental parameters.