Two-parameter scaling theory of the longitudinal magnetoconductivity in a Weyl metal phase: Chiral anomaly, weak disorder, and finite temperature

TL;DR

This paper develops a two-parameter scaling theory for the longitudinal magnetoconductivity in Weyl metals, revealing how disorder and temperature influence the chiral anomaly-induced transport, and demonstrating a breakdown of simple $B/T$ scaling.

Contribution

It introduces a novel two-parameter scaling framework combining renormalization group and Boltzmann theory to analyze disorder effects on topological transport in Weyl metals at finite temperature.

Findings

Disorder renormalizes the Weyl point separation.

Finite temperature modifies the topological transport coefficient.

The $B/T$ scaling breaks down to $B/T^{1 + ext{"eta"}}$ with $0< ext{"eta"}<1$.

Abstract

It is at the heart of modern condensed matter physics to investigate the role of a topological structure in anomalous transport phenomena. In particular, chiral anomaly turns out to be the underlying mechanism for the negative longitudinal magnetoresistivity in a Weyl metal phase. Existence of a dissipationless current channel causes enhancement of electric currents along the direction of a pair of Weyl points or applied magnetic fields ($B$). However, temperature ($T$) dependence of the negative longitudinal magnetoresistivity has not been understood yet in the presence of disorder scattering since it is not clear at all how to introduce effects of disorder scattering into the "topological-in-origin" transport coefficient at finite temperatures. The calculation based on the Kubo formula of the current-current correlation function is simply not known for this anomalous transport coefficient. Combining the renormalization group analysis with the Boltzmann transport theory to encode the chiral anomaly, we reveal how disorder scattering renormalizes the distance between a pair of Weyl points and such a renormalization effect modifies the topological-in-origin transport coefficient at finite temperatures. As a result, we find breakdown of $B/T$ scaling, given by $B/T^{1 + \eta}$ with $0 < \eta < 1$. This breakdown may be regarded to be a fingerprint of the interplay between disorder scattering and topological structure in a Weyl metal phase.