Quantum kinetic equation in phase-space textured multiband systems

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.