Disorder driven itinerant quantum criticality of three dimensional massless Dirac fermions

Abstract

Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder driven semimetal to metal quantum phase transition of three dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent ($z$) and correlation length exponent ($\nu$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field theoretical analysis.

18 pages, 9 figures, replaced with published version

References in corpus (13)

• The Kernel Polynomial Method
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Bose-Einstein Condensation in Magnetic Insulators
• Heavy Fermions and Quantum Phase Transitions
• 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
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Unconventional localisation transition in high dimensions
• Effective field theory of the disordered Weyl semimetal
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Charge transport in gapless chiral electron systems with arbitrary band dispersion

Cited by in corpus (52)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Disorder-induced zero-bias peaks in Majorana nanowires
• Linear Scaling Quantum Transport Methodologies
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals
• Phase diagrams of disordered Weyl semimetals
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Universal optical conductivity of a disordered Weyl semimetal
• 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
• 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
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Global phase diagram of a three dimensional dirty topological superconductor
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Note on "Diffusive quantum criticality in three-dimensional disordered Dirac semimetals"
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Disorder driven multifractality transition in Weyl nodal loops
• 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
• 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
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Breakdown of universality in three-dimensional Dirac semimetals with random impurities
• Disorder in tilted Weyl semimetals from a renormalization group perspective
• Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders
• Role of boundary conditions, topology and disorder in the chiral magnetic effect in Weyl semimetals
• Anomalous Transport Signatures in Weyl Semimetals with Point Defects
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Disorder and magnetic transport in tilted Weyl semimetals
• Disorder and magnetoconductivity in tilted Weyl semimetals
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Short note on the density of states in 3D Weyl semimetals
• Topological diffusive metal in amorphous transition metal monosilicides
• Effects of random potentials in three-dimensional quantum electrodynamics
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Ballistic transport in disordered Dirac and Weyl semimetals
• On the nature of the magnetic phase transition in a Weyl semimetal
• Chiral anomaly without Landau levels: From the quantum to the classical regime
• Direct topological insulator transitions in three dimensions are destabilized by non-perturbative effects of disorder
• 3D Network Model for Strong Topological Insulator Transitions
• Disorder Driven Non-Anderson Transition in a Weyl Semimetal
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Electron transport in a weakly disordered Weyl semimetal