Intrinsic Magnetoelectric Hall Effect from Layer-Orbital Quantum Geometry

Original Abstract

Intrinsic Hall effects, such as the anomalous Hall effect, originate from the orbital quantum geometry of Bloch states. However, in layered materials, the combined action of out-of-plane electric and magnetic fields couples to layer polarization and orbital moment, generating a mixed layer-orbital quantum geometry in field-dressed Bloch states. We show that this geometry produces an intrinsic magnetoelectric Hall effect that is bilinear in the electric and magnetic fields. The response is scattering-time independent and can arise in nonmagnetic systems without spin-orbit coupling. Its origin lies in interband coherence involving layer polarization and orbital moment, leading to a finite, non-quantized Hall response that persists in the band gap. The Hall coefficient is odd under gate reversal and tracks layer polarization. A symmetry analysis identifies the classes of layered materials that host this effect. As a representative realization, we demonstrate the effect in rhombohedral pentalayer graphene, where the conductivity reaches values of order $0.05\,e^2/h$. These results establish mixed layer-orbital quantum geometry as a mechanism for intrinsic magnetoelectric Hall transport and a direct probe of layer-resolved quantum geometry in Bloch bands.