Weyl systems: anomalous transport normally explained

TL;DR

This paper derives the chiral kinetic theory from fundamental spinor equations for SU(2) systems, clarifying the origin of anomalous transport terms and challenging their interpretation as signals of anomalies or Lorentz-invariance breaking.

Contribution

It provides a derivation of chiral kinetic theory from mean field equations, elucidating the origin of anomalous terms and their relation to Berry curvature and the Dirac sea.

Findings

The anomalous $oldsymbol{E} oldsymbol{B}$ term arises mainly from Berry curvature divergence.

The Dirac sea contribution is transferred to the Dirac monopole during derivation.

The anomalous term is suppressed by two thirds due to dynamical effects.

Abstract

The chiral kinetic theory is derived from exact spinor mean field equations without symmetry-breaking terms for large classes of SU(2) systems with spin-orbit coupling. The influence of the Wigner function's off-diagonal elements is worked out. The decoupling of the diagonal elements renormalizes the drift according to Berry connection which is found as an expression of the meanfield, spin-orbit coupling and magnetic field. As special limit, Weyl systems are considered. The anomalous term $\sim\V E\V B$ in the balance of the chiral density appears consequently by an underlying conserving theory. The experimental observations of this term and the anomalous magneto-transport in solid-sate physics usually described by chiral kinetic theory are therefore not a unique signal for mixed axial-gravitational or triangle anomaly and no signal for the breaking of Lorentz-invariance. The source of the anomalous term is by two thirds the divergence of Berry curvature at zero momentum which can be seen as Dirac monopole and by one third the Dirac sea at infinite momentum. During the derivation of the chiral kinetic theory this source by the Dirac sea is transferred exclusively to the Dirac monopole due to the projection of the spinor Wigner functions to the chiral basis. The dynamical result is shown to suppress the anomalous term by two thirds.