On the universal ac optical background in graphene

Latest experiments have confirmed the theoretically expected universal value pi e(2/)2h of the ac conductivity of graphene and have revealed departures of the quasi-particle dynamics from predictions for the Dirac fermions in idealized graphene. We present analytical expressions for the ac conductivity in graphene that allow one to study how it is affected by interactions, temperature, external magnetic field and the opening of a gap in the quasi-particle spectrum. We show that the ac conductivity of graphene does not necessarily give a metrologically accurate value of the von Klitzing constant h/e(2), because it is depleted by the electron-phonon interaction. In a weak magnetic field, the ac conductivity oscillates around the universal value and the Drude peak evolves into a peak at the cyclotron frequency.