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arXiv · 1907.00577

Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics

Cong Xiao·Z. Z. Du·Qian Niu
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Abstract

We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows from the interband-coherence effect of dc electric-fields during scattering and is related to the interband Berry connection. As an application, we demonstrate it in the second-order nonlinear Hall effect of the tilted massive Dirac model. The intuitive Boltzmann constructions are confirmed by a quantum kinetic theory, which shows that arbitrary $n$th-order nonlinear dc response up to the first three leading contributions in the weak disorder potential is handled by the same few gauge-invariant semiclassical ingredients.

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Cong Xiao, Z. Z. Du, Qian Niu. 2019-09-28. Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics. https://doi.org/10.1103/physrevb.100.165422

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