Is Graphene in Vacuum an Insulator?

Abstract

We present evidence, from Lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at α crit g = 1.11 ± 0.06, where α g ≃ 2.16 in vacuum, and α g ≃ 0.79 on a SiO 2 substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors 4 < N crit f < 6. Our data are consistent with a second-order transition. Graphene, a carbon allotrope with a two-dimensional honeycomb structure, has become an important player at the forefront of condensed matter physics, drawing the attention of theorists and experimentalists alike due to its challenging nature as a many-body problem, its unusual electronic properties and possible technological applications (see Refs. [1, 2] and references therein). Graphene also belongs to a large class of planar condensed-matter systems, which includes other graphite-related materials as well as high-T c superconductors.A distinctive feature of graphene is that its band structure contains two degenerate 'Dirac points', in the vicinity of which the dispersion is linear, as in relativistic theories [3]. The low-energy excitations in graphene are thus Dirac quasiparticles of Fermi velocity v ≃ c/300, where c is the speed of light in vacuum. These are described by the Euclidean actionwhere g 2 = e 2 /ǫ 0 for graphene in vacuum, ψ a is a four-component Dirac field in 2+1 dimensions, A 0 is a Coulomb field in 3+1 dimensions, N f = 2 for real graphene, andwhere the Dirac matrices γ µ satisfy the Euclidean Clifford algebra {γ µ , γ ν } = 2δ µν . The strength of the Coulomb interaction is controlled (as can be shown by rescaling t and A 0 ) by α g = e 2 /(4πvǫ 0 ), which is the graphene analogue of the fine-structure constant α ≃

Artificial honeycomb lattices for electrons, atoms and photons

“…In recent years, several efforts have been made [98][99][100][101] to describe electrons moving in a honeycomb lattice and interacting through the non-relativistic Coulomb force. In this case the strength of interactions is measured by the dimensionless parameter [5,12] α ee ≡ e 2 /( hv F ), where e is the absolute value of the electron's charge, is a suitably-defined dielectric constant, and v F is the Fermi velocity.…”

“…A excitonic insulating phase has been predicted to occur spontaneously [99][100][101] at a critical value of the Coulomb coupling constant α ee 1.1 for N f = 4 fermion flavors. Note that electrons in natural suspended graphene are characterized by α ee ∼ 2.2 (since, in this case, ∼ 1 and v F ∼ 10 6 m/s).…”

Chirald-wave superconductivity in doped graphene

“…[4,5,6,7,8,9,10,11,12,13,14,15,17,16]). There, the predominant ordering tendencies are in the particle-hole channel, and usually superconductivity is not among the leading candidates.…”

Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory

“…González et al 3 performed renormalization-group calculations and showed that the suppression of screening of the long-range Coulomb interaction gives rise to deviations from conventional Fermi-liquid behavior. Lattice field theory simulations 4 indicated a Coulomb driven second-order semimetal-to-insulator transition. Meng et al 5 performed extensive variational quantum Monte Carlo (QMC) simulations for the Hubbard model with varying cluster sizes and identified a spin-liquid phase between the semimetallic state characterized by massless Dirac fermions and an antiferromagnetically ordered Mott insulator.…”