Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model

Abstract

We study the effect of Coulomb interaction between charge carriers on the properties of graphene monolayer, assuming that the strength of the interaction is controlled by the dielectric permittivity of the substrate on which the graphene layer is placed. To this end we consider the tight-binding model on the hexagonal lattice coupled to the non-compact gauge field. The action of the latter is also discretized on the hexagonal lattice. Equilibrium ensembles of gauge field configurations are obtained using the Hybrid Monte-Carlo algorithm. Our numerical results indicate that at sufficiently strong coupling, that is, at sufficiently small substrate dielectric permittivities e<4, and at sufficiently small temperatures T<10^4 K the symmetry between simple sublattices of hexagonal lattice breaks down spontaneously and the low-frequency conductivity gradually decreases down to 20-30% of its weak-coupling value. On the other hand, in the weak-coupling regime (with e>4) the conductivity practically does not depend on e and is close to the universal value s=1/4.

arXiv comment27 pages, 14 figures, RevTeX; v2: new data for larger lattices added and discussed; v3: matches published version

References in corpus (42)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Renormalization Group Approach to Interacting Fermions
• Temperature dependent transport in suspended graphene
• The optical conductivity of graphene in the visible region of the spectrum
• Dirac cones reshaped by interaction effects in suspended graphene
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Strength of effective Coulomb interactions in graphene and graphite
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• Magnetic field driven metal-insulator phase transition in planar systems
• Is graphene in vacuum an insulator?
• A Portable High-Quality Random Number Generator for Lattice Field Theory Simulations
• Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Lattice field theory simulations of graphene
• How close can one approach the Dirac point in graphene experimentally?
• Melting of graphene: from two to one dimension
• Quantum Critical Behaviour in a Graphene-like Model
• Excitonic instability in two-dimensional degenerate semimetals
• Gap generation and semimetal-insulator phase transition in graphene
• Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• First-principles Theory of Nonlocal Screening in Graphene
• Chiral Symmetry Breaking in Graphene
• Chiral anomalies and rooted staggered fermions
• Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-N limits
• Dynamical Mean Field Study of The Dirac Liquid
• Chiral Gap and Collective Excitations in Monolayer Graphene from Strong Coupling Expansion of Lattice Gauge Theory
• Panel discussion on chiral extrapolation of physical observables
• Numerical study of the conductivity of graphene monolayer within the effective field theory approach
• Monte Carlo simulation of monolayer graphene at non-zero temperature
• Chiral anomaly and strength of the electron-electron interaction in graphene
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories
• Topological Aspects of Fermions on a Honeycomb Lattice
• Effects of flavor-symmetry violation from staggered fermion lattice simulations of graphene
• Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice
• First-order chiral transition in the compact lattice theory of graphene and the case for improved actions

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