Quantum Spin Hall Effect with Extended Topologically Protected Features in Altermangetic Multilayers

TL;DR

This paper introduces a new quantum spin Hall phase in altermagnetic multilayers that hosts multiple pairs of edge states, expanding the possibilities for topological phases beyond traditional constraints.

Contribution

It demonstrates, both theoretically and via first-principles calculations, that altermagnetism enables multiple edge state pairs, breaking the conventional $ ext{Z}_2$ classification limit.

Findings

Multiple pairs of gapless helical edge states in altermagnetic multilayers.

Number of edge states scales linearly with the number of layers.

Large, quantized spin-Hall conductance in candidate materials.

Abstract

Conventional topological classification theory dictates that time-reversal symmetry confines the quantum spin Hall (QSH) effect to a $\mathbb{Z}_2$ classification, permitting only a single pair of gapless helical edge states. Here, we utilize the recently discovered altermagnetism to circumvent this fundamental constraint. We demonstrate the realization of a unique QSH phase possessing multiple pairs of gapless helical edge states in altermagnetic multilayers. This exotic QSH phase, characterized by a mirror-spin Chern number, emerges from the interplay of spin-orbit coupling and $d$-wave altermagnetic ordering. Moreover, using first-principles calculations, we identify altermagnetic Fe$_2$Se$_2$O multilayers as promising material candidates, in which the number of gapless helical edge states scales linearly with the number of layers, leading to a correspondingly large, exactly quantized, and experimentally accessible spin-Hall conductance. Our findings unveil a new mechanism for stabilizing multiple pairs of gapless helical edge states, significantly expanding the scope of QSH effects, and provide a blueprint for utilizing altermagnetism to engineer desired topological phases.