Chiral anomaly without Landau levels: From the quantum to the classical regime

TL;DR

This paper investigates the persistence of the chiral anomaly in disordered Weyl semimetals across quantum and classical regimes, revealing that topological effects survive strong disorder and are detectable via average level velocity.

Contribution

It demonstrates that the chiral anomaly persists in disordered Weyl semimetals beyond the quantum regime, using numerical and analytical methods to identify topological signatures in diffusive conditions.

Findings

Resonant states do not affect the anomaly in single Weyl nodes.

Nonzero average level velocity indicates the chiral anomaly in diffusive regimes.

Chiral Landau levels are ill-defined at high disorder, but topological effects remain.

Abstract

We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielsen and Ninomiya's mechanism and disorder is strong enough that quantum effects are important. In the weak disorder regime, there exist rare regions of the random potential where the disorder strength is locally strong, which gives rise to quasilocalized resonances and their effect on the chiral anomaly is unknown. We numerically show that these resonant states do not affect the chiral anomaly only in the case of a single Weyl node. At energies away from the Weyl point, or with strong disorder where one is deep in the diffusive regime, the chiral Landau level itself is not well defined and the semiclassical treatment is not justified. In this limit, we analytically use the supersymmetry method and find that the Chern-Simons term in the effective action which is not present in nontopological systems gives rise to a nonzero average level velocity which implies chiral charge pumping. We numerically establish that the nonzero average level velocity serves as an indicator of the chiral anomaly in the diffusive limit.