Quantum kinetic equation in phase-space textured multiband systems

TL;DR

This paper derives a semiclassical kinetic equation for two-band systems, incorporating quantum corrections and interband effects, and applies it to Dirac and Weyl fermions to analyze their electromagnetic responses.

Contribution

It introduces a systematic derivation of a quantum kinetic equation including second-order quantum corrections and interband effects for multiband systems.

Findings

Reproduces known anomalous currents such as the parity and Adler-Bell-Jackiw anomaly.

Highlights the role of phase-space Berry curvature and interband terms in electron dynamics.

Provides a framework applicable to inhomogeneous and dynamical spin textures.

Abstract

Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time gradients. We find, in addition to band-projected corrections to the single-particle equation of motion due to phase-space Berry curvature, interband terms that we attribute to the nonorthorgonality of the projected Hilbert spaces. As examples, we apply our kinetic equation to electronic systems in the presence of spatially inhomogeneous and dynamical spin textures stemming from electromagnetic gauge potentials. Specifically, we consider the electromagnetic response of massive two-dimensional Dirac fermions and three-dimensional Weyl fermions, and reproduce the anomalous currents known as the parity and the Adler-Bell-Jackiw anomaly in particle physics.