Pyatkovskiy P. Dynamics of quasiparticle excitations in graphene

The dynamical screening of Coulomb interaction in graphene and its dependence on temperature, external magnetic field, impurity scattering rate, band gap and a chemical potential are studied. In the framework of Dirac model for quasiparticles in graphene, the exact analytical expressions for the one-loop polarization function are derived, which are then employed to find the plasmon spectrum and to analyze the behaviour of the screened static Coulomb potential of a point charge. The exact form of the vertex function is obtained in the simplified Lorentz invariant model of graphene, which is equivalent to (2+1)-dimensional quantum electrodynamics in the first order of 1/N expansion.