Altermagnetic quantum spin Hall effect in a Chern homobilayer

Altermagnetism, combing advantages of ferromagnetism and antiferromagnetism, exhibits rich fundamental physics with great interest in both theory and experiment. Here, we explicitly demonstrated the emergence of quantum spin Hall effect (QSHE) in two-dimensional altermagnets, i.e., altermagnetic QSHE, and propose that stacked Chern insulators with opposite chiralities offers a rational way to achieve the altermagnetic QSHE. In particular, through spin space group analysis and first-principles calculations, ${\mathrm{RuCS}}_{3}$ is revealed as a suitable candidate for material realization, where chiral and helical edge states appear in the monolayer and stacked bilayer, characterized by Chern number $\mathcal{C}=1$ and spin Chern number ${\mathcal{C}}_{S}=\ensuremath{-}1$, respectively. Moreover, the robustness of both the altermagnetic spin-splitting and QSHE with vanishing net magnetic moments is confirmed by strain engineering. Our results greatly enrich the prominent physical phenomena and expand the domain of QSHE, which are expected to draw great experimental attentions.