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arXiv · 1901.04467

Symmetry and Quantum Kinetics of the Non-linear Hall Effect

Snehasish Nandy·Inti Sodemann
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Abstract

We argue that the static non-linear Hall conductivity can always be represented as a vector in two-dimensions and as a pseudo-tensor in three-dimensions independent of its microscopic origin. In a single band model with a constant relaxation rate this vector or tensor is proportional to the Berry curvature dipole \cite{Sodemann_2015}. Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry Curvature Dipole term, there exist additional disorder mediated corrections to the non-linear Hall tensor that have the same scaling in impurity scattering rate. These can be thought of as the non-linear counterparts to the side-jump and skew-scattering corrections to the Hall conductivity in the linear regime. We illustrate our formalism by computing the different contributions to the non-linear Hall conductivity of two-dimensional tilted Dirac fermions.

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Snehasish Nandy, Inti Sodemann. 2019-12-03. Symmetry and Quantum Kinetics of the Non-linear Hall Effect. https://doi.org/10.1103/physrevb.100.195117

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