Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals

Abstract

We numerically study the effect of short ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed quantum critical point separating the semimetal and diffusive metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian ($H$) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on $H^2$ and the kernel polynomial method on $H$. We establish the existence of two distinct types of low energy eigenstates contributing to the disordered density of states in the weak disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states, and (ii) nonperturbative rare eigenstates that are weakly-dispersive and quasi-localized in the real space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two types of eigenstates. We find that the Dirac states contribute low energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasi-localized eigenstates contribute a nonzero background DOS which is only weakly energy-dependent near zero energy and is exponentially small at weak disorder. We find that the expected semimetal to diffusive metal quantum critical point is converted to an {\it avoided} quantum criticality that is "rounded out" by nonperturbative effects, with no signs of any singular behavior in the DOS near the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of the rare region effects.

20 pages, 19 figures, replaced with published version

References in corpus (17)

• Localization of interacting fermions at high temperature
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• The Kernel Polynomial Method
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Chiral anomaly and transport in Weyl metals
• 3D Dirac semimetals: current materials, design principles and predictions of new materials
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Topological-Metal to Band-Insulator Transition in (Bi1-xInx)2Se3 Thin Films
• Rare region effects dominate weakly disordered 3D Dirac points
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Unconventional localisation transition in high dimensions
• Effective field theory of the disordered Weyl semimetal
• Theory of the strongly disordered Weyl semimetal
• Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal
• Diamagnetism of nodal fermions
• Note on "Diffusive quantum criticality in three-dimensional disordered Dirac semimetals"

Cited by in corpus (91)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Amorphous Metals
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Triple point fermions in a minimal symmorphic model
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Single particle excitations in disordered Weyl fluids
• Uncovering the hidden quantum critical point in disordered massless Dirac and Weyl semi-metals
• Do the surface Fermi arcs in Weyl semimetals survive disorder?
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• High Surface Conductivity of Fermi Arc Electrons in Weyl semimetals
• Pseudospin 3/2 Fermions, Type-II Weyl Semimetals and Critical Weyl Semimetals in Tricolor Cubic Lattice
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Vanishing density of states in weakly disordered Weyl semimetals
• Magic-Angle Semimetals with Chiral Symmetry
• Global phase diagram of a three dimensional dirty topological superconductor
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Delocalization Transition of Disordered Axion Insulator
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Quantitative analytical theory for disordered nodal points [Article and Erratum]
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Fermi arc reconstruction at the interface of twisted Weyl semimetals
• Disorder driven multifractality transition in Weyl nodal loops
• Disorder-induced exceptional and hybrid rings in Weyl/Dirac semimetals
• Weyl node with random vector potential
• Quantum Transport in Weyl Semimetal Thin Films in the Presence of Spin-Orbit Coupled Impurities
• Electronic properties of disordered Weyl semimetals at charge neutrality
• The theory of avoided criticality in quantum motion in a random potential in high dimensions
• Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Quasicrystalline second-order topological semimetals
• Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions
• Quantum criticality in Ising chains with random hyperuniform couplings
• Quantum Multicriticality in Disordered Weyl Semimetal
• Breakdown of universality in three-dimensional Dirac semimetals with random impurities
• Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Disorder in tilted Weyl semimetals from a renormalization group perspective
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Anomalous Transport Signatures in Weyl Semimetals with Point Defects
• Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Direct link between disorder, mobility and magnetoresistance in topological semimetals
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Stability of Weyl semimetals with quasiperiodic disorder
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• Short note on the density of states in 3D Weyl semimetals
• Time-reversal-broken Weyl semimetal in the Hofstadter regime
• Topological Anomalous Skin Effect in Weyl Superconductors
• Fermi arcs and surface criticality in dirty Dirac materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Competition between disorder and interaction effects in 3D Weyl semimetals
• Symmetry Enforced Stability of Interacting Weyl and Dirac Semimetals
• Diluted magnetic Dirac-Weyl materials: Susceptibility and ferromagnetism in three-dimensional chiral gapless semimetals
• Interplay of disorder and interactions in subcritically tilted and anisotropic three-dimensional Weyl fermions
• Ballistic transport in disordered Dirac and Weyl semimetals
• Duality between disordered nodal semimetals and systems with power-law hopping
• Delocalization of topological surface states by diagonal disorder in nodal loop semimetals
• Surface quantum critical phenomena in disordered Dirac semimetals
• Chiral anomaly without Landau levels: From the quantum to the classical regime
• Disordered Weyl semimetal as an array of coupled Hubbard chains
• Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems
• Stability of Weyl node merging processes under symmetry constraints
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• 3D Network Model for Strong Topological Insulator Transitions
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Connecting the avoided quantum critical point to the magic-angle transition in three-dimensional Weyl semimetals
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Absence of localization in Weyl semimetals
• Real-time evolution and quantized charge pumping in magnetic Weyl semimetals
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Mass fluctuations and absorption rates in Dirac materials sensors
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Electron transport in a weakly disordered Weyl semimetal
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals
• Information Bounds on phase transitions in disordered systems
• Fermi energy sensitive universal conductance fluctuations in anisotropic materials
• Quantum geometric contribution to the diffusion constant
• Markov Inequality as a Tool for Linear-Scaling Estimation of Local Observables
• Chiral charge conservation and ballistic magnetotransport in a disordered Weyl semimetal
• Impact of spin-orbit coupling on electron correlation corrections to the density of states in anisotropic conductors