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

Conventional topological classification dictates that time-reversal symmetry confines the quantum spin Hall (QSH) effect to a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> classification, permitting only a single pair of gapless helical edge states. Here, we utilize altermagnetism to circumvent this fundamental constraint. We demonstrate a unique QSH phase possessing multiple pairs of gapless helical edge states in altermagnetic multilayers. This QSH phase, characterized by a mirror-spin Chern number, emerges from the interplay of spin-orbit coupling and <i>d</i>-wave altermagnetic ordering. Moreover, using first-principles calculations, we identify altermagnetic Fe₂Se₂O multilayers as promising material candidates, in which the number of gapless helical edge states scales with the number of layers, leading to a large, exactly quantized, and experimentally accessible spin-Hall conductance. Our findings unveil a new mechanism for stabilizing multiple pairs of gapless helical edge states, expanding the scope of QSH effects, and providing a blueprint for utilizing altermagnetism to engineer topological phases.