Boltzmann transport from density matrix theory: interband and intraband coherences

TL;DR

This paper derives a systematic approach to include interband and intraband coherence effects in Boltzmann transport theory for strongly spin-orbit coupled systems, explaining anomalous Hall effects.

Contribution

It provides a rigorous derivation of interband and intraband coherence effects from the density matrix equation of motion, enhancing the Boltzmann transport framework.

Findings

Interband coherence terms are derived systematically from density matrix analysis.

Disorder-induced off-diagonal equilibrium density matrix elements are crucial for anomalous responses.

Intraband coherence contributes similarly to interband coherence in Hall conductivities.

Abstract

To account for the anomalous/spin Hall conductivities and spin-orbit torque in the zeroth order of electron scattering time in strongly spin-orbit coupled systems, the Boltzmann transport theory in the case of weak disorder-potentials has been augmented by adding some interband coherence effects by hand. In this work these interband coherence terms are derived systematically from analyzing the equation of motion of the single-particle density matrix in the Bloch representation. Interband elements of the out-of-equilibrium density matrix are related to only one part of interband-coherence responses. Disorder-induced off-diagonal elements of the equilibrium density matrix are shown to be vital in producing the coordinate-shift anomalous driving term in the modified Boltzmann equation. Moreover, intraband coherence is inherent in the Boltzmann equation, whose contribution to anomalous/spin Hall conductivities is parametrically the same as the interband coherence.