# Magnetotransport on quantum spin Hall edge coupled to bulk midgap states

## TL;DR

This paper develops a theory for magnetoresistance in quantum spin Hall edges coupled to bulk midgap states, explaining experimental observations of cusp-like resistance behavior in monolayer WTe₂.

## Contribution

It introduces a model for hybridization-induced backscattering from bulk midgap states affecting edge transport under magnetic fields.

## Key findings

- Resonant midgap states cause cusp-like positive magnetoresistance.
- The theory fits experimental data for monolayer WTe₂.
- Magnetoresistance dependence on field direction matches incoherent transport predictions.

## Abstract

We consider magnetotransport on a helical edge of a quantum spin Hall insulator, in the presence of bulk midgap states ``side-coupled" to the edge. In the presence of a magnetic field, the midgap levels are spin-split, and hybridization of these levels with the itinerant edge states leads to backscattering, and the ensuing increase in the resistance. We show that there is a singular cusp-like contribution to the positive magnetoresistance stemming from resonant midgap states weakly coupled to the edge. The singular behavior persists for both coherent and incoherent edge transport regimes. We use the developed theory to fit the experimental data for the magnetoresistance for monolayer WTe$_2$ at liquid helium temperatures. The results of the fitting suggest that the cusp-like behavior of the resistance in weak magnetic fields observed in experiments on monolayer WTe$_2$ with long edge channels might indeed be explained by hybridization of the helical edge states with spin-split bulk midgap states. In particular, the dependence of the magnetoresistance on the direction of the external magnetic field is well described by the incoherent edge transport theory, at the same time being quite distinct from the one expected for a magnetic-field-induced edge gap.