Resonant nonlinear Hall effect in two-dimensional electron systems

We study the Hall conductivity of a two-dimensional electron gas under an inhomogeneous magnetic field . First, we prove using the quantum kinetic theory that an odd magnetic field can lead to a purely nonlinear Hall response. Second, considering a real-space magnetic dipole consisting of a sign-changing magnetic field and based on numerical semiclassical dynamics, we unveil a parametric resonance involving the cyclotron ratio and a characteristic width of , which can greatly enhance the Hall response. Different from previous mechanisms that rely on the bulk Berry curvature dipole, the effect largely stems from boundary states associated with the real-space magnetic dipole. Our findings pave a way to engineer current rectification and higher harmonic generation in two-dimensional materials having or not having crystal inversion symmetry.