# From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation

## TL;DR

This paper provides a comprehensive theoretical analysis of Weyl semimetals' conductivity across all disorder strengths using the self-consistent Born approximation, revealing critical regimes and universal behaviors.

## Contribution

It introduces a detailed functional analysis of observables in disordered Weyl semimetals, highlighting the importance of vertex corrections and the critical behavior at intermediate disorder levels.

## Key findings

- Identification of a critical regime separating semimetal and diffusion phases.
- Vertex corrections cause saturation of dc conductivity in strong disorder.
- Analysis of optical conductivity evolution and scaling near criticality.

## Abstract

We analyze theoretically the conductivity of Weyl semimetals within the self-consistent Born approximation (SCBA) in the full range of disorder strength, from weak to strong disorder. In the range of intermediate disorder, we find a critical regime which separates the semimetal and diffusion regimes. While the numerical values of the critical exponents are not expected to be exact within the SCBA, the approach allows us to calculate functional dependences of various observables (density of states, quasiparticle broadening, conductivity) in a closed form. This sheds more light on the qualitative behavior of the conductivity and its universal features in disordered Weyl semimetals. In particular, we have found that the vertex corrections in the Kubo formula are of crucial importance in the regime of strong disorder and lead to saturation of the dc conductivity with increasing disorder strength. We have also analyzed the evolution of the optical conductivity with increasing disorder strength, including its scaling properties in the critical regime.