Quantum criticality and minimal conductivity in graphene with long-range disorder

Abstract

We consider the conductivity ${\sigma }_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $\sigma$-model including a topological term with $\theta =\pi$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and ${\sigma }_{xx}$ acquires the value characteristic for the quantum Hall transition.

4 pages, 1 figure

References in corpus (26)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• The structure of suspended graphene sheets
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Weak localisation magnetoresistance and valley symmetry in graphene
• Strong suppression of weak (anti)localization in graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Quantum transport of massless Dirac fermions in graphene
• Electron transport in disordered graphene
• Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
• Effect of Disorder on Transport in Graphene
• Nondissipative Spin Hall Effect via Quantized Edge Transport
• Low energy theory of disordered graphene
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Localization in a quantum spin Hall system
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions
• Conductance fluctuations at the integer quantum Hall plateau transition
• Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates
• Integrable sigma models with theta=pi
• Quantum Electron Transport in Disordered Wires with Symplectic Symmetry
• Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems
• Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry

Cited by in corpus (134)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Anderson Transitions
• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Charge Transport in Disordered Graphene-Based Low Dimensional Materials
• Demonstration of one-parameter scaling at the Dirac point in graphene
• Topological delocalization of two-dimensional massless Dirac fermions
• Slow imbalance relaxation and thermoelectric transport in graphene
• Topological surface states in three-dimensional magnetic insulators
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Disorder and Electronic Transport in Graphene
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Interaction-induced criticality in Z_2 topological insulators
• Graphene via large N I: Renormalization
• Smooth electron waveguides in graphene
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Theory of Anomalous Quantum Hall Effects in Graphene
• Conductivity and Fano factor in disordered graphene
• Topological states in two-dimensional optical lattices
• Collective cyclotron motion of the relativistic plasma in graphene
• Two-dimensional Graphene with Structural Defects: Elastic Mean Free Path, Minimum Conductivity and Anderson Transition
• Linear Scaling Quantum Transport Methodologies
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• The dependence of topological Anderson insulator on the type of disorder
• Diffusion and criticality in undoped graphene with resonant scatterers
• Observation of Anderson localization in ultrathin films of three-dimensional topological insulators
• Charge transport in graphene with resonant scatterers
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Coulomb interaction in graphene: Relaxation rates and transport
• Anomalous Hall effect with massive Dirac fermions
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Anderson localization of electron states in graphene in different types of disorder
• Ballistic transport in disordered graphene
• Impurity-assisted tunneling in graphene
• Electronic transport in normal-conductor/graphene/normal-conductor junctions and conditions for insulating behavior at a finite charge-carrier density
• Finite difference method for transport properties of massless Dirac fermions
• Conductivity of suspended graphene at the Dirac point
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Coulomb drag in graphene near the Dirac point
• Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Quantum Hall effect in polycrystalline graphene: The role of grain boundaries
• Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects
• Universal scaling of current fluctuations in disordered graphene
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons
• Multiple Quantum Phases in Graphene with Enhanced Spin-Orbit Coupling: From the Quantum Spin Hall Regime to the Spin Hall Effect and a Robust Metallic State
• Disorder enabled band structure engineering of a topological insulator surface
• Interaction-mediated surface state instability in disordered three-dimensional topological superconductors with spin SU(2) symmetry
• Metal-Insulator Transition in Graphene on Boron Nitride
• Sensitivity of anomalous Hall effect to disorder correlations
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• Relativistic Gurzhi effect in channels of Dirac materials
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Anderson Transition in Disordered Graphene
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Disordered Weyl semimetals and their topological family
• Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
• Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
• Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry
• Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder
• Weak momentum scattering and the conductivity of graphene
• Holographic Conductivity in Disordered Systems
• Valley polarization effects on the localization in graphene Landau levels
• Localised zero-energy modes in the Kitaev model with vacancy-disorder
• Metal-insulator transition in hydrogenated graphene as manifestation of quasiparticle spectrum rearrangement of anomalous type
• Large Diamagnetism and Electromagnetic Duality in Two-dimensional Dirac Electron System
• Emergence of integer quantum Hall effect from chaos
• Interaction and disorder effects in 3D topological insulator thin films
• The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Multifractality and electron-electron interaction at Anderson transitions
• Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point
• Lévy flights due to anisotropic disorder in graphene
• Surface transport coefficients for three-dimensional topological superconductors
• Disorder-driven splitting of the conductance peak at the Dirac point in graphene
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Demonstration of a New Transport Regime of Photon in Two-dimensional Photonic Crystal
• The Z2-anomaly and boundaries of topological insulators
• Gate tunable quantum transport in double layer graphene
• Anderson Transitions: Criticality, Symmetries, and Topologies
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Topological Effects on the Magnetoconductivity in Topological Insulators
• Delocalization of boundary states in disordered topological insulators
• Sputtering induced re-emergence of the topological surface state in Bi${}_2$Se${}_3$
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Field theory of non-Hermitian disordered systems
• Critical Percolation Without Fine Tuning on the Surface of a Topological Superconductor
• Electronic and transport properties in geometrically disordered graphene antidot lattices
• Fragility of surface states in non-Wigner Dyson topological insulators
• Dirac fermions in a power-law-correlated random vector potential
• Interacting lattice electrons with disorder in two dimensions: Numerical evidence for a metal-insulator transition with a universal critical conductivity
• Effect of weak impurities on electronic properties of graphene: functional renormalization-group analysis
• Enhanced quantum metric due to vacancies in graphene
• Topological quantum criticality of the disordered Chern insulator
• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Floquet simulators for topological surface states in isolation
• Universality of Anderson transition in two-dimensional systems of symplectic symmetry class
• Majorana zero modes in graphene with trigonal warping
• Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion
• Doping-dependent metal-insulator transition in a disordered Hubbard model
• Scale-dependent theory of the disordered electron liquid
• Transport in topological insulator nanowires
• Keldysh functional renormalization group for electronic properties of graphene
• Bulk effects on topological conduction on the surface of 3-D topological insulators
• The phase diagram of a two-dimensional dirty tilted Dirac semimetal
• Composite Fermion Nonlinear Sigma Models
• Transport of Dirac electrons in a random magnetic field in topological heterostructures
• Two-parameter scaling theory of transport near a spectral node
• Metallic proximity effect in ballistic graphene with resonant scatterers
• Dynamics of impurity in the environment of Dirac fermions
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Half-Quantized Hall Metal and Marginal Metal in Disordered Magnetic Topological Insulators
• Parity Anomalous Semimetal with Minimal Conductivity Induced by an In-Plane Magnetic Field
• Strong localization in a suspended monolayer graphene by intervalley scattering
• Quantum Restored Symmetry Protected Topological Phases
• Quantum Hall Effect without Chern Bands
• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators
• Random Magnetic Field and the Dirac Fermi Surface
• Inhomogeneous Fixed Point Ensembles Revisited
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Conductivity scaling and absence of localization in disordered nodal line semimetals
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals
• Transport scaling and critical tilt effects in disordered two-dimensional Dirac fermions
• Disordered Parity Anomalous Semimetal