Dirty Weyl semimetals: Stability, phase transition and quantum criticality

TL;DR

This paper investigates how disorder affects three-dimensional Weyl semimetals, revealing stability under weak disorder, a transition to a metallic phase at stronger disorder, and critical behavior characterized by scaling laws.

Contribution

It provides a comprehensive analysis of disorder-induced phase transitions in Weyl semimetals, including numerical determination of critical exponents and phase diagrams.

Findings

Weak disorder preserves Weyl semimetal phase.

Strong disorder induces a quantum phase transition to a metallic phase.

Critical exponents are insensitive to the number of Weyl pairs.

Abstract

We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetal and the phase diagram of dirty double Weyl semimetal at finite energies.