# Interacting multi-channel topological boundary modes in a quantum Hall valley system

## TL;DR

This paper visualizes and analyzes boundary modes at domain walls between valley-polarized quantum Hall phases on bismuth, revealing interaction-driven behavior and the ability to tune between metallic and gapped regimes.

## Contribution

It provides the first direct visualization of interacting boundary modes in quantum Hall ferromagnets and demonstrates control over their electronic properties via valley occupation.

## Key findings

- Boundary modes are directly visualized using STM.
- Valley occupation controls whether channels are metallic or gapped.
- Coulomb interactions influence backscattering and Luttinger liquid behavior.

## Abstract

Symmetry and topology play key roles in the identification of phases of matter and their properties. Both concepts are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken symmetry QHFM phases are predicted to host gapless one-dimensional (1D) modes that emerge due to a topological change of the underlying electronic wavefunctions at such interfaces. Although a variety of QHFMs have been identified in different materials, probing interacting electronic modes at these domain walls has not yet been accomplished. Here we use a scanning tunneling microscope (STM) to directly visualize the spontaneous formation of boundary modes, within a sign-changing topological gap, at domain walls between different valley-polarized quantum Hall phases on the surface of bismuth. By changing the valley occupation and the corresponding number of modes at the domain wall, we can realize different regimes where the valley-polarized channels are either metallic or develop a spectroscopic gap. This behavior is a consequence of Coulomb interactions constrained by the symmetry-breaking valley flavor, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting Luttinger liquids.

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Source: https://tomesphere.com/paper/1902.02790