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

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.

Localisation 2020 conference paper (review); 51 pages, 23 figures

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Cited by in corpus (13)

• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Invariants of disordered semimetals via the spectral localizer
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Anomalous Transport Signatures in Weyl Semimetals with Point Defects
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Disorder effects on triple-point fermions
• The low energy excitation spectrum of magic-angle semimetals
• Anomalous Hall effect in disordered Weyl semimetals
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Localization by particle-hole symmetry breaking: a loop expansion
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals
• Electron transport in a weakly disordered Weyl semimetal