Theory of the strongly disordered Weyl semimetal

TL;DR

This paper develops an effective field theory to describe unconventional electromagnetic responses in strongly disordered Weyl semimetals, revealing a novel transport regime with scale-dependent diffusion and ballistic behavior.

Contribution

It introduces a Chern-Simons type effective field theory for strongly disordered Weyl semimetals, extending understanding beyond perturbation theory and uncovering new transport regimes.

Findings

Identification of a scale-dependent drift/diffusion transport regime

Demonstration of a transition from diffusion to ballistic dynamics and back

Analysis of magnetoresponse phenomena in disordered Weyl systems

Abstract

In disordered Weyl semimetals, mechanisms of topological origin lead to novel mechanisms of transport, which manifest themselves in unconventional types of electromagnetic response. Prominent examples of transport phenomena particular to the Weyl context include the anomalous Hall effect, the chiral magnetic effect, and the formation of totally field dominated regimes of transport in which the longitudinal conductance is proportional to an external magnetic field. In this paper, we discuss the manifestations of these phenomena at large length scales including the cases of strong disorder and/or magnetic field which are beyond the scope of diagrammatic perturbation theory. Our perhaps most striking finding is the identification of a novel regime of drift/diffusion transport where diffusion at short scales gives way to effectively ballistic dynamics at large scales, before a re-entrance to diffusion takes place at yet larger scales. We will show that this regime plays a key role in understanding the interplay of the various types of magnetoresponse of the system. Our results are obtained by describing the strongly disordered system in terms of an effective field theory of Chern-Simons type. The paper contains a self-contained derivation of this theory, and a discussion of both equilibrium and non-equilibrium (noise) transport phenomena following from it.