Effect of disorder on the transverse magnetoresistance of Weyl semimetals

TL;DR

This paper investigates how different types of impurity potentials affect the transverse magnetoresistance in Weyl semimetals under various magnetic field regimes, revealing deviations from linear behavior due to long-range disorder effects.

Contribution

It provides a detailed analysis of the impact of impurity potential range on magnetoresistance in Weyl semimetals using a formal diagrammatic approach in different magnetic field limits.

Findings

Long-range impurity potentials alter magnetoresistance behavior.

Magnetoresistance can deviate from linearity due to impurity effects.

Different impurity types significantly influence magnetotransport properties.

Abstract

We study the effect of random potential created by different types of impurities on the transverse magnetoresistance of Weyl semimetals. It is shown that the magnetic field and temperature dependence of magnetoresistance is strongly affected by the type of impurity potential. Two limiting cases are analyzed in detail: ($i$) the ultra-quantum limit, when the applied magnetic field is so high that only the zeroth and first Landau levels contribute to the magnetotransport, and ($ii$) the semiclassical situation, for which a large number of Landau levels comes into play. A formal diagrammatic approach allowed us to obtain expressions for the components of the electrical conductivity tensor in both limits. In contrast to the oversimplified case of the $\delta$-correlated disorder, the long-range impurity potential (including that of Coulomb impurities) introduces an additional length scale, which changes the geometry and physics of the problem. It is shown that the magnetoresistance can deviate from the linear behavior as a function of magnetic field for a certain class of impurity potentials.