Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities

TL;DR

This paper develops a gauge-invariant semiclassical kinetic theory for multi-band systems, incorporating quantum geometric effects, and demonstrates its ability to derive key phenomena like the chiral anomaly and anomalous Hall effect.

Contribution

It introduces a general, gauge-invariant semiclassical framework for multi-band quantum systems, including all first-order quantum corrections, unifying various physical effects.

Findings

Derived a generalized Berry curvature tensor controlling spectral weight redistribution.

Established limits of previous density of states corrections.

Unified derivation of chiral anomaly, anomalous Hall conductivity, and chiral magnetic effect.

Abstract

Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\smash{U(1) \times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown to control a redistribution of spectral weights. New expressions for certain physical quantities ensue, establishing the limits of a previously proposed correction to the density of states. In the two-band case, we derive a completely general semiclassical kinetic theory including all $O(\hbar)$ quantum corrections. As an application, we show how one can recover, out of a single simple calculation, the chiral anomaly, intrinsic anomalous Hall conductivity and chiral magnetic effect, in all generality. The demonstrated flexibility and efficiency of our formalism derives from the insulation it provides from the underlying complexity of the quantum kinetics, notwithstanding its rigorous connection to this deeper level.