Quantum kinetic equation in phase-space textured multiband systems

Understand

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.