# Mesoscopic transport in electrostatically-defined spin-full channels in quantum Hall ferromagnets

## TL;DR

This paper investigates electron transport through individual domain walls in quantum Hall ferromagnets, demonstrating electrostatic control and analyzing mesoscopic fluctuations, advancing understanding of helical domain walls for topological quantum computing.

## Contribution

It introduces a method to electrostatically control and study single helical domain walls in quantum Hall ferromagnets, revealing their transport properties and potential for topological applications.

## Key findings

- Long domain walls are insulating with localization length 4-6 μm.
- Short domain walls show non-zero resistance saturation at low temperatures.
- Transport through impurity states aligns with spin-orbit interaction models.

## Abstract

In this work we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to hybridization of two counter-propagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with localization length 4 - 6~$\mu$m. In shorter DWs the resistance saturates to a non-zero value at low temperatures. Mesoscopic resistance fluctuations in a magnetic field are investigated. The theoretical model of transport through impurity states within the gap induced by spin-orbit interactions agrees well with the experimental data. Helical DWs have required symmetry for the formation of synthetic p-wave superconductors. Achieved electrostatic control of a single helical domain wall is a milestone on the path to their reconfigurable network and ultimately to a demonstration of braiding of non-Abelian excitations.