Unconventional localisation transition in high dimensions

Abstract

We study non-interacting systems with a power-law quasiparticle dispersion ${\xi }_{\mathbf{k}}\propto k^{\alpha }$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a critical disorder strength (set by the band width), at which the system exhibits a disorder-driven quantum phase transition at the bottom of the band, that lies in a universality class distinct from the Anderson transition. In contrast to the conventional wisdom, it manifests itself in, e.g., the disorder-averaged density of states. For systems in symmetry classes that permit localisation, the striking signature of this transition is a non-analytic behaviour of the mobility edge, that is pinned to the bottom of the band for subcritical disorder and grows for disorder exceeding a critical strength. Focussing on the density of states, we calculate the critical behaviour (exponents and scaling functions) at this novel transition, using a renormalisation group, controlled by an $\epsilon =2\alpha -d$ expansion. We also apply our analysis to Dirac materials, e.g., Weyl semimetal, where this transition takes place in physically interesting three dimensions.

17 pages, 9 figures

References in corpus (25)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Weyl Semimetal in a Topological Insulator Multilayer
• Observation of a topological 3D Dirac semimetal phase in high-mobility Cd3As2
• Experimental Realization of a Three-Dimensional Dirac Semimetal
• Landau Quantization and Quasiparticle Interference in the Three-Dimensional Dirac Semimetal Cd3As2
• Experimental observation of the Anderson transition with atomic matter waves
• Electron transport in disordered graphene
• Effect of Disorder on Transport in Graphene
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Disorder Effects in Two-Dimensional d-wave Superconductors
• Quantum transport of disordered Weyl semimetals at the nodal point
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Random resistor network model of minimal conductivity in graphene
• Rare region effects dominate weakly disordered 3D Dirac points
• Dirty Weyl fermions: rare region effects near 3D Dirac points
• Quantum transport in three-dimensional Weyl electron system
• Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Coulomb disorder in three-dimensional Dirac systems
• Dimensional dependence of the metal-insulator transition
• Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
• Strong quantum interference in strongly disordered bosonic insulators
• Fermionic and bosonic ac conductivities at strong disorder

Cited by in corpus (72)

• Negative longitudinal magnetoresistance in Dirac and Weyl metals
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Critical transport in weakly disordered semiconductors and semimetals
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals
• Phase diagrams of disordered Weyl semimetals
• Effective field theory of the disordered Weyl semimetal
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• Transversal magnetoresistance in Weyl semimetals
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Theory of the strongly disordered Weyl semimetal
• Disorder driven itinerant quantum criticality of three dimensional massless Dirac fermions
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal
• Single particle excitations in disordered Weyl fluids
• Uncovering the hidden quantum critical point in disordered massless Dirac and Weyl semi-metals
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Conductivity of a Weyl semimetal with donor and acceptor impurities
• Vanishing density of states in weakly disordered Weyl semimetals
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• Emergent Weyl excitations in systems of polar particles
• 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
• Transversal magnetoresistance and Shubnikov-de Haas oscillations in Weyl semimetals
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Disordered double Weyl node: Comparison of transport and density-of-states calculations
• Disordered double Weyl node
• Disorder-driven transition in a chain with power-law hopping
• Density of states and magnetotransport in Weyl semimetals with long-range disorder
• 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
• Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
• Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Quantum Multicriticality in Disordered Weyl Semimetal
• Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
• Modulated Helical Metals at Magnetic Domain Walls of Pyrochlore Iridium Oxides
• Instanton Calculus of Lifshitz Tails
• PT invariant Weyl semimetals in gauge symmetric systems
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Effects of anisotropy and disorder on the conductivity of Weyl semimetals
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• 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
• An attractive critical point from weak antilocalization on fractals
• Symmetry Enforced Stability of Interacting Weyl and Dirac Semimetals
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Unconventional scaling theory in disorder-driven quantum phase transition
• Ballistic transport in disordered Dirac and Weyl semimetals
• Non-Anderson critical scaling of the Thouless conductance in 1D
• Duality between disordered nodal semimetals and systems with power-law hopping
• Strange metal state near quantum superconductor-metal transition in thin films
• BCS-like disorder-driven instabilities and ultraviolet effects in nodal-line semimetals
• Renormalization group analysis of Dirac fermions with random mass
• Chiral anomaly without Landau levels: From the quantum to the classical regime
• Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems
• Neutron scattering off Weyl semimetals
• 3D Network Model for Strong Topological Insulator Transitions
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• Tail states and unusual localization transition in low-dimensional Anderson model with power-law hopping
• Disorder Driven Non-Anderson Transition in a Weyl Semimetal
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media
• Coexistence of localized and extended states in the Anderson model with long-range hopping
• Information Bounds on phase transitions in disordered systems
• Electron transport in a weakly disordered Weyl semimetal