Gamayun O. Electron-electron interaction and gap generation in graphene

Critical constant of electron-electron interaction which corresponds to the excitonic condensation in graphene leading to gap generation in quasiparticles spectrum is found. It is shown deep connection between gap generation phenomenon and fall into supercritical charged center. Gap behaviour with momentum is obtained numerically. With an additional four-fermion interaction the phase diagram is obtained and critical indices of excitonic phase transition are calculated. It is shown that at the presence of magnetic field critical value of the coupling constant tends to zero. For bilayer graphene analytical expression for the 1-loop polarization function, screened Coulomb potential and plasmon dispersion are calculated.