Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems

Abstract

Nonlinear Hall effects provide a powerful probe of quantum geometry in solids and enable rectification phenomena beyond the constraints of linear response. In this Letter, we predict a \emph{layer nonlinear Hall effect} (LNHE) in stacked bilayer systems composed of nonmagnetic or antiferromagnetic materials with a vanishing linear Hall conductivity. In such systems, the second- or third-order nonlinear Hall responses are intrinsically layer odd: the contributions from the two constituent layers have equal magnitude but opposite sign, resulting in exact cancellation under layer-exchange symmetry. An out-of-plane electric field $E_z$ can break this symmetry, thereby unveiling the hidden response and converting it into a switchable macroscopic nonlinear Hall signal. Using a minimal $k\!\cdot\!p$ model, we demonstrate that the LNHE can originate from the Berry curvature dipole mechanism. A systematic symmetry analysis of all 80 layer groups further yields a complete classification of the symmetry constraints and stacking configurations that allow for this type of LNHE. Beyond this mechanism, additional symmetry analysis reveals that LNHE may also arise from quantum metric dipole or inversed mass dipole. Remarkably, even in cases where second-order nonlinear Hall responses are symmetry forbidden, a third-order LNHE can still survive in certain stacked bilayer configurations. First-principles calculations on representative bilayers---nonmagnetic 1T$'$-WTe$_2$ and 1T$'$-ReS$_2$---explicitly demonstrate electrically reversible second-order LNHE, in full agreement with our symmetry-based predictions. Overall, our results establish LNHE as a universal phenomenon in a wide range of layered quantum materials and provide a robust route toward electrically tunable nonlinear transport.