Weyl systems: anomalous transport normally explained

Abstract

The chiral kinetic theory is derived from exact spinor mean field equations without symmetrybreaking 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 ∼ EB 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. 75.76.+j, 05.60.Gg. 47.70.Nd,51.10.+y,

Quantum Uncertainty and Energy Flux in Extended Electrodynamics

“…From the asymmetry of F µν it follows that ∂ µ (j µ + i µ ) = 0, i.e., the current j µ + i µ is conserved. This is analogous to what happens with the chiral anomaly in Weyl systems, where the anomalous term can be rewritten as a current that satisfies the classical balance equation [13,14].…”

Exploring Anomalies by Many‐Body Correlations

“…and experimentally interpreted [ 11,15,16 ] as having observed a chiral anomaly. This has led to an enormous theoretical activity [ 17–19 ] describing, for example, anomalous transport, [ 20–25 ] the relation of chiral anomaly, and quantized Hall effects [ 26,27 ] up to chiral heat effect. [ 28 ]…”

“…[44] it has been shown that a proper subtraction scheme of the infrared divergences shows that corresponding extra terms do not appear. Actually, the Lorentz‐invariant chiral kinetic theory can be derived from the quantum kinetic approach [ 25,45–50 ] leading to the chiral anomaly by many‐body correlations. A hint that the anomalies can be possibly explained by many‐body effects is also the relation of 2D conformal anomalies and virial expansions [ 51 ] and that the Dirac sea [ 52,53 ] can describe the Schwinger anomaly.…”

“…Correspondingly, the quantum kinetic derivation of this result without any non‐conserving assumptions can be found. [ 25 ]…”

“…One cannot conclude backward from the observed term (3) to a symmetry‐breaking field‐theoretical assumption since (5) appears also by a conserving theory without the described field‐theoretical assumptions. [ 25 ]…”