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

Abstract

Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $U(1)\times SU(N)$ 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 $O(\hslash )$ 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.

arXiv commentFinal version, including in particular i) a more pedagogical presentation of the theoretical underpinning of our theory, ii) a revised application section providing a unified derivation of the chiral anomaly, intrinsic anomalous hall effect and chiral magnetic effect for a general two-band Hamiltonian

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Cited by in corpus (3)

• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Nonlocal Electrical Detection of Reciprocal Orbital Edelstein Effect
• Quantum Kinetic Theory of the Linear Response for Weakly Disordered Multiband Systems