Nonlinear Hall effect on a disordered lattice

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.

References in corpus (11)

• Anderson Transitions
• The Kernel Polynomial Method
• Robustness of the Spin-Chern number
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• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
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• Real-space calculation of the conductivity tensor for disordered topological matter
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Cited by in corpus (7)

• Light-enhanced nonlinear Hall effect
• Planar Hall Plateau in Magnetic Weyl Semimetals
• Electric field induced second-order anomalous Hall transport in unconventional Rashba systems
• Nonlinear Hall effects with an exceptional ring
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Identifying geometric third-order nonlinear transport in disordered materials