Nonlinear Layer Hall Effect and Detection of the Hidden Berry Curvature Dipole in $\mathcal{PT}$-Symmetric Antiferromagnetic Insulators

Abstract

Recent experimental and theoretical studies have revealed the emergence of a linear layer Hall effect (LHE) induced by hidden Berry curvature in \textrm{MnBi}$_{2}$\textrm{Te}$_{4}$ thin films. This phenomenon underscores the layer degree of freedom as a novel mechanism for generating Hall transport in layered materials, providing a new pathway to probe and manipulate the internal structure of fully compensated topological antiferromagnets (AFMs). In this work, we predict a nonlinear LHE in $\mathcal{PT}$-symmetric layered AFMs, which manifests as a detectable nonlinear Hall conductivity even with respect to the AFM order and odd with respect to the vertical electric field, in contrast to the linear LHE. Furthermore, we demonstrate that the nonlinear Hall currents induced by the hidden BCD and quantum metric dipole (QMD) obey distinct symmetries and flow in different directions. Our proposed nonlinear LHE establishes an experimentally advantageous framework for exclusively probing the hidden BCD quantum geometry.