Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals

TL;DR

This paper develops a comprehensive microscopic theory for the nonlinear and anomalous Hall effects in topological semimetals, incorporating quantum interference and impurity scattering, with applications to multifold fermions.

Contribution

It introduces a systematic derivation of the semiclassical Boltzmann equation including quantum interference effects for topological semimetals.

Findings

Derived a generic formula for skew scattering rate from Pancharatnam phase.

Formulated a theory suitable for studying nonlinear Hall and photogalvanic effects.

Applied the framework to multifold fermions, revealing new insights into their Hall responses.

Abstract

We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied side-jump and skew-scattering processes, quantum interference diffractive contributions are now explicitly incorporated within the developed framework. This theory is applied to multifold fermions in topological semimetals, for which the generic formula for the skew scattering rate from the Pancharatnam phase is obtained along with the corresponding anomalous Hall conductivity.