Layer Hall Effect in Multiferroic Two-Dimensional Materials

The layer Hall effect (LHE) is of fundamental and practical importance in condensed-matter physics and material science; however, it was rarely observed and usually based on the paradigms of persistent electric field and sliding ferroelectricity. Here, a new mechanism of LHE is proposed by coupling layer physics with multiferroics using symmetry analysis and a low-energy k·p model. Due to time-reversal symmetry breaking and valley physics, the Bloch electrons on one valley will be subject to a large Berry curvature. This combined with inversion symmetry breaking gives rise to layer-polarized Berry curvature and can force the electrons to deflect in one direction of a given layer, thereby generating the LHE. We demonstrate that the resulting LHE is ferroelectrically controllable and reversible. Using first-principles calculations, this mechanism and predicted phenomena are verified in the multiferroic material of bilayer Co₂CF₂. Our finding opens a new direction for LHE and 2D materials research.