Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors

TL;DR

This paper reviews how disorder affects Weyl semimetals and superconductors, highlighting the role of rare regions in destabilizing phases and altering transitions, with new results confirming the fragility of the Weyl phase under disorder.

Contribution

It presents new findings on a bipartite random hopping model, showing particle-hole symmetry does not stabilize the Weyl phase against disorder, and discusses the nature of avoided transitions in continuum models.

Findings

Rare regions destabilize the Weyl semimetal phase.

Disorder rounds the semimetal-to-metal transition into a crossover.

Particle-hole symmetry alone does not stabilize the Weyl phase.

Abstract

Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disorder on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting nature of excitations, transport, and topology are reviewed. New results on a bipartite random hopping model are presented that confirm previous results in a $p+ip$ Weyl superconductor, demonstrating that particle-hole symmetry is insufficient to help stabilize the Weyl semimetal phase in the presence of disorder. The nature of the avoided transition in a model for a single Weyl cone in the continuum is discussed. We close with a discussion of open questions and future directions.