# Counterflowing edge current and its equilibration in quantum Hall devices with sharp edge potential: Roles of incompressible strips and contact configuration

## TL;DR

This study observes counterflowing edge currents in InAs quantum wells causing quantum Hall effect breakdown at high magnetic fields, highlighting the roles of incompressible strips and contact configuration in edge state equilibration.

## Contribution

It provides the first detailed measurement of counterflowing edge modes and their equilibration length in InAs quantum wells, emphasizing the influence of incompressible strips and contact setup.

## Key findings

- Counterflowing edge channels cause QH breakdown at high fields.
- Equilibration length increases exponentially with magnetic field.
- Contact configuration significantly affects edge state transport.

## Abstract

We report the observation of counterflowing edge current in InAs quantum wells which leads to the breakdown of quantum Hall (QH) effects at high magnetic fields. Counterflowing edge channels arise from the Fermi-level pinning of InAs and the resultant sharp edge potential with downward bending. By measuring the counterflow conductance for varying edge lengths, we determine the effective number $\langle N_\text{C} \rangle$ of counterflowing modes and their equilibration length $\lambda_\text{eq}$ at bulk integer filling factor $\nu = 1$--$4$. $\lambda_\text{eq}$ increased exponentially with magnetic field $B$, reaching $200~\mu$m for $\nu = 4$ at $B \geq 7.6$~T. Our data reveal important roles of the innermost incompressible strip with even filling in determining $\langle N_\text{C} \rangle$ and $\lambda_\text{eq}$ and the impact of the contact configuration on the QH effect breakdown. Our results show that counterflowing edge channels manifest as transport anomalies only at high fields and in short edges. This in turn suggests that, even in the integer QH regime, the actual microscopic structure of edge states can differ from that anticipated from macroscopic transport measurements, which is relevant to various systems including atomic-layer materials.