# Disordered contacts can localize helical edge electrons

## TL;DR

This paper demonstrates that contact disorder in quantum spin Hall systems can induce localization of helical edge electrons, leading to measurable deviations in resistance that depend on contact disorder and are nullified by inelastic scattering.

## Contribution

It reveals that disordered contacts can cause localization effects in helical edge states, a phenomenon not previously understood, and quantifies how contact disorder affects transport properties.

## Key findings

- Disordered contacts induce localization corrections in QSH edge modes.
- Resistance deviations increase with contact disorder and decrease with more contacts.
- Inelastic scattering can eliminate the localization correction.

## Abstract

It is well known that quantum spin Hall (QSH) edge modes being helical are immune to backscattering due to non-magnetic disorder within the sample. Thus, quantum spin Hall edge modes are non-localized and show a vanishing Hall resistance along with quantized 2-terminal, longitudinal and non-local resistances even in presence of sample disorder. However, this is not the case for contact disorder. This paper shows that when all contacts are disordered in an N-terminal quantum spin Hall sample, then transport via these helical QSH edge modes can have a significant localization correction. All the resistances in an N-terminal quantum spin Hall sample deviate from their values derived while neglecting the phase acquired at disordered contacts, and this deviation is called the quantum localization correction. This correction term increases with the increase of disorderedness of contacts but decreases with the increase in the number of contacts in an N terminal sample. The presence of inelastic scattering, however, can completely destroy the quantum localization correction.