The layer Hall effect: concepts, realizations, and recent advances

Arising from layer-blocked Berry curvature, the layer Hall effect(LHE) causes carriers in different layers to deflect in opposite transverse directions. This leads to layer-resolved Hall responses even when the net Hall signal vanishes due to interlayer compensation. In this review, we provide recent progress on the LHE including its basic physical mechanism and discuss prototypical systems, with particular emphasis on MnBiTebased antiferromagnetic topological insulators. Theoretically proposed material platforms, including MnBiTederived structures, topological insulator heterostructures, valleytronic and multiferroic bilayers, altermagnetic systems, magnetoelectric antiferromagnets, and quantized regimes of the effect are reviewed. Furthermore, experimental advances in detecting both conventional and quantized layer dependent Hall responses are summarized. Finally, we discuss the broader conceptual significance of the LHE for real space-resolved Berry phase engineering, layertronics, and multi degree of freedom coupling in quantum materials, and conclude with an outlook on open challenges and future directions.