Layer Hall effect induced by altermagnetism

In this work, we propose a scheme to realize the layer Hall effect in the ferromagnetic topological insulator Bi$_2$Se$_3$ via proximity to $d$-wave altermagnets. We show that an altermagnet and an in-plane magnetic field applied near one surface gap the corresponding Dirac cone, yielding an altermagnet-induced half-quantized Hall effect. When altermagnets with antiparallel N\'{e}el vectors are placed near the top and bottom surfaces, giving rise to the layer Hall effect with vanishing net Hall conductance, i.e., the altermagnet-induced layer Hall effect. In contrast, altermagnets with parallel N\'{e}el vectors lead to a quantized Chern insulating state, i.e., the altermagnet-induced anomalous Hall effect. We further analyze the dependence of the Hall conductance on the orientation of the in-plane magnetic field and demonstrate that the layer Hall effect becomes observable under a perpendicular electric field. Our results establish a route to engineer altermagnet-induced topological phases in ferromagnetic topological insulators.