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.

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

References in corpus (111)

• The electronic properties of graphene
• Topological Insulators
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Anderson Transitions
• Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd${}_3$As${}_2$
• Observation of a topological 3D Dirac semimetal phase in high-mobility Cd3As2
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Correlated quantum phenomena in the strong spin-orbit regime
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Experimental Realization of a Three-Dimensional Dirac Semimetal
• The Kernel Polynomial Method
• Observation of the chiral magnetic effect in ZrTe5
• Dirac materials
• The missing atom as a source of carbon magnetism
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Quantized circular photogalvanic effect in Weyl semimetals
• Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+delta
• Three-Dimensional Topological Insulators
• Evidence for Magnetic Weyl Fermions in a Correlated Metal
• Electromagnetic Response of Weyl Semimetals
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
• Experimental discovery of a topological Weyl semimetal state in TaP
• Anomalous Hall Effect in Weyl Metals
• Dirac vs. Weyl in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena
• Direct optical detection of Weyl fermion chirality in a topological semimetal
• Double Dirac Semimetals in Three Dimensions
• Spatial Fluctuations of Helical Dirac Fermions on the Surface of Topological Insulators
• Observation of Weyl nodes and Fermi arcs in TaP
• Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids
• Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals
• A sudden collapse in the transport lifetime across the topological phase transition in $(B{i}_{1-x}I{n}_x{)}_{2}S{e}_3$
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Topological-Metal to Band-Insulator Transition in (Bi1-xInx)2Se3 Thin Films
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Quasiparticle localization in superconductors with spin-orbit scattering
• Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal
• Topological surface states in nodal superconductors
• Axial anomaly and longitudinal magnetoresistance of a generic three dimensional metal
• Quantum transport of disordered Weyl semimetals at the nodal point
• Two-dimensional higher-order topology in monolayer graphdiyne
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Weyl-Kondo Semimetal in Heavy Fermion Systems
• Rare region effects dominate weakly disordered 3D Dirac points
• Tantalum Monoarsenide: an Exotic Compensated Semimetal
• Electron scattering in tantalum monoarsenide
• Dirty Weyl fermions: rare region effects near 3D Dirac points
• Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals
• The chiral anomaly factory: Creating Weyl fermions with a magnetic field
• Quantum transport in three-dimensional Weyl electron system
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal
• Critical transport in weakly disordered semiconductors and semimetals
• Photogalvanic effect in Weyl semimetals
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• Phase diagrams of disordered Weyl semimetals
• Random phase vector for calculating the trace of a large matrix
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Unconventional localisation transition in high dimensions
• Optical gyrotropy as a test for dynamic chiral magnetic effect of Weyl semimetals
• Evidence for Weyl fermions in a canonical heavy-fermion semimetal YbPtBi
• Origin of dissipative Fermi arc transport in Weyl semimetals
• Universal optical conductivity of a disordered Weyl semimetal
• Effective field theory of the disordered Weyl semimetal
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Coulomb disorder in three-dimensional Dirac systems
• Quasiparticle Interference Evidence of the Topological Fermi Arc States in Chiral Fermionic Semimetal CoSi
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Disorder driven itinerant quantum criticality of three dimensional massless Dirac fermions
• Competing orders and topology in the global phase diagram of pyrochlore iridates
• Theory of the strongly disordered Weyl semimetal
• Statistics of random voltage fluctuations and the low-density residual conductivity of graphene
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal
• Uncovering the hidden quantum critical point in disordered massless Dirac and Weyl semi-metals
• Single particle excitations in disordered Weyl fluids
• Do the surface Fermi arcs in Weyl semimetals survive disorder?
• Diamagnetism of nodal fermions
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Vanishing density of states in weakly disordered Weyl semimetals
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Disorder-driven transition in a chain with power-law hopping
• Weyl node with random vector potential
• Electronic properties of disordered Weyl semimetals at charge neutrality
• The theory of avoided criticality in quantum motion in a random potential in high dimensions
• Parity-violating hybridization in heavy Weyl semimetals
• Robustness and Universality of Surface States in Dirac Materials
• Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
• Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Quantum Multicriticality in Disordered Weyl Semimetal
• Instanton Calculus of Lifshitz Tails
• Breakdown of universality in three-dimensional Dirac semimetals with random impurities
• Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation
• Stability of Weyl semimetals with quasiperiodic disorder
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Short note on the density of states in 3D Weyl semimetals
• Strong disorder in nodal semimetals: Schwinger-Dyson--Ward approach
• Fermi arcs and surface criticality in dirty Dirac materials
• Dynamical density response and optical conductivity in topological metals
• Unconventional scaling theory in disorder-driven quantum phase transition
• Corrections to the self-consistent Born approximation for Weyl fermions
• Non-Anderson critical scaling of the Thouless conductance in 1D
• Chiral anomaly without Landau levels: From the quantum to the classical regime

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• 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