Chiral anomaly without Landau levels*

We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielson and Ninomiya’s mechanism. In the weak disorder regime, there exists rare regions of the random potential where the disorder strength is locally strong, this gives rise to quasi-localized resonances. These rare states are non-perturbative and thus their effect on the chiral anomaly is unknown. We numerically show that rare states do not affect the chiral anomaly only in the case of a single Weyl node, but weakens the anomaly in a quantized way when there are two nodes without inter-node scattering. When the disorder strength is strong and the system is deep in the diffusive regime, the chiral Landau level itself is not well defined. In this limit, we analytically use the supersymmetry method and find an additional Chern-Simons (CS) term in the effective action which is not present in non-topological systems. This CS term results in a non-zero average level velocity: using numerical calculations we show that this as an indicator of the chiral anomaly in the presence of strong disorder when the system can no longer be described using band theory.