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Time dependent processes
Abstract:
We argue that static nonlinear Hall conductivity can always be represented as a vector in two dimensions and as a pseudotensor 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 I. Sodemann and L. Fu, Phys. Rev. Lett 115, 216806 (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 nonlinear Hall tensor that have the same scaling in the impurity scattering rate. These can be thought of as the nonlinear 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 nonlinear Hall conductivity of two-dimensional tilted Dirac fermions.
