Graphene via large N I: Renormalization

Abstract

We analyze the competing effects of moderate to strong Coulomb electron-electron interactions and weak quenched disorder in graphene. Using a one-loop renormalization group calculation controlled within the large-N approximation, we demonstrate that, at successively lower energy (temperature or chemical potential) scales, a type of non-Abelian vector potential disorder always asserts itself as the dominant elastic scattering mechanism for generic short-ranged microscopic defect distributions. Vector potential disorder is tied to both elastic lattice deformations ("ripples") and topological lattice defects. We identify several well-defined scaling regimes, for which we provide scaling predictions for the electrical conductivity and thermopower, valid when the inelastic lifetime due to interactions exceeds the elastic lifetime due to disorder. Coulomb interaction effects should figure strongly into the physics of suspended graphene films, where rs > 1; we expect vector potential disorder to play an important role in the description of transport in such films.

25 pages, 21 figures

References in corpus (45)

• 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
• The structure of suspended graphene sheets
• Intrinsic ripples in graphene
• Electronic Properties of Disordered Two-Dimensional Carbon
• Carrier transport in 2D graphene layers
• A self-consistent theory for graphene transport
• Strong suppression of weak (anti)localization in graphene
• Quantum Hall Ferromagnetism in Graphene
• Quantum transport of massless Dirac fermions in graphene
• Riemannian symmetric superspaces and their origin in random matrix theory
• Electron transport in disordered graphene
• Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• Effect of Disorder on Transport in Graphene
• Demonstration of one-parameter scaling at the Dirac point in graphene
• The Electronic Spectrum of Fullerenes from the Dirac Equation
• Topological delocalization of two-dimensional massless Dirac fermions
• Electron-electron interactions in graphene sheets
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Disorder Effects in Two-Dimensional d-wave Superconductors
• Interaction effects and phase relaxation in disordered systems
• Quasiparticle localization in superconductors with spin-orbit scattering
• Random resistor network model of minimal conductivity in graphene
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Topological Phases in Graphitic Cones
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Disorder and interaction effects in two dimensional graphene sheets
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Coulomb interactions at quantum Hall critical points of systems in a periodic potential
• Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling
• A Classification of random Dirac fermions
• Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions
• Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories
• The effects of weak disorders on Quantum Hall critical points
• Interaction effects on 2D fermions with random hopping
• An Exactly Solvable Model of Fermions with Disorder
• Singular Density of States of Disordered Dirac Fermions in the Chiral Models
• Interactions, disorder and local defects in graphite

Cited by in corpus (123)

• Electronic transport in two dimensional graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Properties of Graphene: A Theoretical Perspective
• Gauge fields in graphene
• Dirac materials
• Dirac cones reshaped by interaction effects in suspended graphene
• Thermoelectric and Magnetothermoelectric Transport Measurements of Graphene
• Magnetic impurities on the surface of a topological insulator
• Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering
• Quantum critical transport in clean graphene
• Colloquium: Graphene spectroscopy
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Adsorbate-limited conductivity of graphene
• Theory of resonant multiphonon Raman scattering in graphene
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Slow imbalance relaxation and thermoelectric transport in graphene
• Theory of thermopower in 2D graphene
• Quantum-critical relativistic magnetotransport in graphene
• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Electron screening and excitonic condensation in double-layer graphene systems
• Gaps tunable by electrostatic gates in strained graphene
• Midgap states in corrugated graphene: Ab-initio calculations and effective field theory
• Theory of charged impurity scattering in two dimensional graphene
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Coulomb interaction in graphene: Relaxation rates and transport
• Gauge fields, ripples and wrinkles in graphene layers
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Ballistic transport in disordered graphene
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Why does graphene behave as a weakly interacting system?
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Coulomb drag in graphene: perturbation theory
• Conductivity of suspended graphene at the Dirac point
• Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• Out-of-bounds hydrodynamics in anisotropic Dirac fluids
• Geometrical and topological aspects of graphene and related materials
• Optical properties of graphene: the Fermi liquid approach
• Density dependent electrical conductivity in suspended graphene: Approaching the Dirac point in transport
• Neutrality point of graphene with coplanar charged impurities
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Making ARPES Measurements on Corrugated Monolayer Crystals: Suspended Exfoliated Single-Crystal Graphene
• Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons
• Excitonic condensation in a double-layer graphene system
• Dynamical Mean Field Study of The Dirac Liquid
• Variational approach to the excitonic phase transition in graphene
• Disorder effects at a nematic quantum critical point in d-wave cuprate superconductor
• Graphene in periodic deformation fields: dielectric screening and plasmons
• Velocity renormalization and anomalous quasiparticle dispersion in extrinsic graphene
• How many-body effects modify the van der Waals interaction between graphene sheets
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Coulomb instabilities of 3D higher-order topological insulators
• Relativistic Gurzhi effect in channels of Dirac materials
• The fate of interaction-driven topological insulators under disorder
• Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene
• Spin g-factor due to electronic interactions in graphene
• Renormalization group aspects of graphene
• Effect of Coulomb interactions on the physical observables of graphene
• QED${}_3$ with quenched disorder: quantum critical states with interactions and disorder
• Thermoelectric effect in high mobility single layer epitaxial graphene
• Novel Type of Superlattices Based on Gapless Graphene with the Alternating Fermi Velocity
• Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder
• Two dimensional metallic phases from disordered QED${}_3$
• 1/N Expansion in Correlated Graphene
• Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions
• Interaction and disorder effects in 3D topological insulator thin films
• Strong magnetoresistance of disordered graphene
• Multilogarithmic velocity renormalization in graphene
• Kinetic theory of Coulomb drag in two monolayers of graphene: from the Dirac point to the Fermi liquid regime
• Topological phase transitions and universality in the Haldane-Hubbard model
• Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials
• Velocity renormalization of nodal quasiparticles in d-wave superconductors
• Graphene, Dirac equation and analogue gravity
• Disordered fermionic quantum critical points
• The influence of a weak magnetic field in the Renormalization-Group functions of (2+1)-dimensional Dirac systems
• Local density of states in disordered graphene
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Valley Order and Loop Currents in Graphene on Hexagonal Boron Nitride
• Effect of Coulomb interaction on the gap in monolayer and bilayer graphene
• Superconductivity in two-dimensional disordered Dirac semimetals
• The effect of vertex corrections on the possibility of chiral symmetry breaking, induced by long-range Coulomb repulsion in graphene
• The effects of disorder and interactions on the Anderson transition in doped Graphene
• Effect of weak impurities on electronic properties of graphene: functional renormalization-group analysis
• Quantum-Critical transport at a semimetal-to-insulator transition on the honeycomb lattice
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Coulomb interactions in systems of generalized semi-Dirac fermions
• Emergent space-time supersymmetry at disorder quantum critical point
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Phases of the excitonic condensate in two-layer graphene
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• Bolometric arrays and infrared sensitivity of VO2 films with varying stoichiometry
• Reduced quantum electrodynamics in curved space
• Corrections to the self-consistent Born approximation for Weyl fermions
• Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors
• Keldysh functional renormalization group for electronic properties of graphene
• Influence of the four-fermion interactions in (2+1)D massive electrons system
• Tunneling spectroscopy of c-axis epitaxial cuprate junctions
• Incommensurate magnetic states induced by ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{N}{\mathrm{a}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene
• Large-$N$ properties of a non-ideal Bose gas
• Graphene as a quantum surface with curvature-strain preserving dynamics
• Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction
• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Quasiparticle renormalization in ABC graphene trilayers
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Gross-Neveu Interaction at finite temperature
• Intrinsic and extrinsic effects on intraband optical conductivity of hot carriers in photoexcited graphene
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Growth of Tall Vertical Carbon Nanotube Forests using Al-Fe Catalysts and Transfer to Flexible Substrates
• Soft pair excitations and double-log divergences due to carrier interactions in graphene
• Scaling and interaction-assisted transport in graphene with one-dimensional defects
• Perturbative renormalization group approach to magic-angle twisted bilayer graphene using topological heavy fermion model
• Aharonov-Bohm magnetism and Landau diamagnetism in semimetals
• Robust non-integer conductance in disordered 2D Dirac semimetals
• Chemical sensing with graphene: A quantum field theory perspective
• Monte-Carlo study of quasiparticle dispersion relation in monolayer graphene
• Resonant optical gating of suspended carbon nanotube transistor
• Renormalization group analysis of weakly interacting van der Waals Fermi system
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals