Resonant Nonlinear Hall Effect in Two-Dimensional Electron Systems

TL;DR

This paper reveals a nonlinear Hall effect in 2D electron systems caused by inhomogeneous magnetic fields, highlighting a resonance mechanism that enhances Hall response through boundary states, independent of Berry curvature dipoles.

Contribution

It demonstrates a novel nonlinear Hall response driven by inhomogeneous magnetic fields and boundary states, distinct from previous Berry curvature-based mechanisms.

Findings

Odd magnetic fields induce nonlinear Hall effects.

Resonance enhances Hall response significantly.

Boundary states play a key role in the effect.

Abstract

We study the Hall conductivity of a two-dimensional electron gas under an inhomogeneous magnetic field $B(x)$. 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 $B(x)$, which can greatly enhance the Hall response. Different from previous mechanisms that rely on the bulk Berry curvature dipole, here, the effect largely stems from boundary states associated with the real-space magnetic dipole. Our findings pave a new way to engineer current rectification and higher harmonic generation in two-dimensional materials having or not crystal inversion symmetry.