Nonlinear Hall effect on a disordered lattice

TL;DR

This paper investigates the nonlinear Hall effect on disordered lattices, revealing disorder-induced Berry curvature fluctuations and an Anderson localization phenomenon, advancing understanding for realistic device applications.

Contribution

It introduces a numerical study of the nonlinear Hall effect on disordered lattices, uncovering Berry curvature fluctuations and localization effects not seen in previous theories.

Findings

Disorder causes fluctuations in Berry curvature.

Fluctuations increase nonlinear Hall conductivity at higher energies.

Evidence of Anderson localization in nonlinear Hall response.

Abstract

The nonlinear Hall effect has recently attracted significant interest due to its potential as a promising spectral tool and device applications. A theory of the nonlinear Hall effect on a disordered lattice is a crucial step towards explorations in realistic devices, but has not been addressed. We study the nonlinear Hall response on a lattice, which allows us to introduce strong disorder numerically. We reveal a disorder-induced fluctuation of the Berry curvature that was not discovered in the previous perturbation theories. The fluctuating Berry curvature induces a fluctuation of the nonlinear Hall conductivity, which anomalously increases as the Fermi energy moves from the band edges to higher energies. More importantly, the fluctuation may explain those observations in the recent experiments. We also discover an "Anderson localization" of the nonlinear Hall effect. This work shows a territory of the nonlinear Hall effect yet to be explored.