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 Néel 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 Néel 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.