Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response.

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

Magnetism and Interaction-Induced Gap Opening in Graphene with Vacancies or Hydrogen Adatoms: Quantum Monte Carlo Study.

We study the electronic properties of graphene with a finite concentration of vacancies or other resonant scatterers by a straightforward lattice quantum Monte Carlo calculation. Taking into account a realistic long-range Coulomb interaction, we calculate the distribution of the spin density associated with midgap states and demonstrate antiferromagnetic ordering. An energy gap is open due to interaction effects, both in the bare graphene spectrum and in the vacancy or impurity bands. In the case of a 5% concentration of resonant scatterers the latter gap is estimated to be 0.7 eV and 1.1 eV for graphene on boron nitride and freely suspended graphene, respectively.

Monte Carlo study of the semimetal-insulator phase transition in monolayer graphene with a realistic interelectron interaction potential.

We report on the results of the first-principles numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction, which takes into account the screening of Coulomb potential by electrons on σ orbitals. In contrast to the results of previous numerical simulations with unscreened potential, we find that suspended graphene is in the conducting phase with unbroken chiral symmetry. This finding is in agreement with recent experimental results by the Manchester group [D. C. Elias et al., Nat. Phys. 7, 701 (2011); A. S. Mayorov et al., Nano Lett. 12, 4629 (2012)]. Further, by artificially increasing the interaction strength, we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.