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

Abstract

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunneling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $\ensuremath{\nu}$ of the underlying (integer) quantum Hall states. For $\ensuremath{\nu}=1$ 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 $\ensuremath{\nu}=2$, 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 $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these anomalous one-dimensional systems.