Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

TL;DR

This paper investigates the properties of domain walls in nematic quantum Hall ferromagnets, revealing how their conduction behavior depends on the filling factor and symmetries, with implications for topological phases and experimental detection.

Contribution

It introduces a detailed analysis of domain wall conduction in quantum Hall nematics, showing the dependence on filling factor and connecting to topological insulator physics.

Findings

At =1, domain walls host a single-channel Luttinger liquid due to valley and charge conservation.

At =2, domain walls support a two-channel Luttinger liquid that can become a symmetry-preserving thermal metal.

The physics at =2 is equivalent to a bosonic topological insulator protected by U(1)nd U(1) symmetries.

Abstract

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $\nu$ of the underlying (integer) quantum Hall states. For $\nu=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $\nu=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems.