Nodal points of Weyl semimetals survive the presence of moderate disorder

TL;DR

This paper investigates how Weyl semimetals' nodal points remain robust against moderate disorder by analyzing rare fluctuation effects and demonstrating the persistence of zero-energy spectral density suppression.

Contribution

It reconciles previous theories by showing rare fluctuations create resonances that preserve the spectral density gap at zero energy despite disorder.

Findings

Rare fluctuations generate resonances near zero energy.

Vanishing density of states at the Weyl node persists with moderate disorder.

Protection of the nodal density of states is hard to observe in finite-size simulations.

Abstract

In this work we address the physics of individual three dimensional Weyl nodes subject to a moderate concentration of disorder. Previous analysis indicates the presence of a quantum phase transition below which disorder becomes irrelevant and the integrity of sharp nodal points of vanishing spectral density is preserved in this system. This statement appears to be at variance with the inevitable presence of statistically rare fluctuations which cannot be considered as weak and must have strong influence on the system's spectrum, no matter how small the average concentration. We here reconcile the two pictures by demonstrating that rare fluctuation potentials in the Weyl system generate a peculiar type of resonances which carry spectral density in any neighborhood of zero energy, but never at zero. In this way, the vanishing of the DoS for weak disorder survives the inclusion of rare events. We demonstrate this feature by considering three different models of disorder, each emphasizing specific aspects of the problem: a simplistic box potential model, a model with Gaussian distributed disorder, and one with a finite number of $s$-wave scatterers. Our analysis also explains why the protection of the nodal DoS may be difficult to see in simulations of finite size lattices.