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.

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

References in corpus (16)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Temperature dependent transport in suspended graphene
• The optical conductivity of graphene in the visible region of the spectrum
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Is graphene in vacuum an insulator?
• 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?
• Quantum Critical Behaviour in a Graphene-like Model
• 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
• Numerical study of the conductivity of graphene monolayer within the effective field theory approach
• First-order chiral transition in the compact lattice theory of graphene and the case for improved actions

Cited by in corpus (23)

• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• Magnetism and interaction-induced gap opening in graphene with vacancies or hydrogen adatoms: Quantum Monte Carlo study
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Metal-insulator transition and phase separation in doped AA-stacked graphene bilayers
• Stability of Dirac Liquids with Strong Coulomb Interaction
• Critical behaviour of reduced QED${}_{4,3}$ and dynamical fermion gap generation in graphene
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Mott insulating state and $d+id$ superconductivity in an ABC graphene trilayer
• Quantum Monte Carlo study of static potential in graphene
• Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model
• A density of states approach to the hexagonal Hubbard model at finite density
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Dynamical gap generation in 2D Dirac semimetal with deformed Dirac cone
• First-principle quantum Monte-Carlo study of charge carrier mobility in organic molecular semiconductors
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• Coulomb center instability in bilayer graphene
• Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Hydrodynamics of particle-hole symmetric systems: a quantum Monte Carlo study
• Effects of electron-electron interactions in suspended graphene
• Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point
• On the semimetal-insulator transition and Lifshitz transition in simulations of mono-layer graphene
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo