Quantum higher-spin Hall insulators

TL;DR

This paper generalizes quantum spin Hall insulators to arbitrary spin J, revealing new edge modes, transport phenomena, and magnetic effects, with potential realization in ultracold atomic gases.

Contribution

It introduces a theoretical framework for higher-spin quantum spin Hall insulators, identifying protected edge modes and novel magnetic phenomena.

Findings

Support for J+1/2 pairs of helical edge modes

Edge modes exhibit non-linear voltage responses

Magnetic domain walls host degenerate bound states

Abstract

We develop a theory of quantum spin Hall insulators with arbitrary spin $J$. Our analysis demonstrates that such systems support $J+\tfrac{1}{2}$ pairs of helical edge modes protected by nontrivial mirror Chern numbers. We establish that the corresponding edge theory is described by a generalized Dirac fermion with higher-order dispersion. These modes produce unique transport responses that are non-linear with voltage. An in-plane magnetic field opens a mass gap in the edge spectrum, and magnetic domain walls host $(J+\tfrac{1}{2})$-fold degenerate bound states characterized by nontrivial winding numbers. Our results extend quantum spin Hall physics to higher-spin systems and suggest possible realizations in ultracold atomic gases.