We develop a theory of quantum spin Hall insulators with arbitrary spin J. Our analysis demonstrates that such systems support J+21 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+21)-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.
@article{arxiv.2604.17479,
title = {Quantum higher-spin Hall insulators},
author = {Takuto Kawakami and Igor Kuzmenko and Yshai Avishai and Yigal Meir and Masatoshi Sato},
journal= {arXiv preprint arXiv:2604.17479},
year = {2026}
}