Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $\sigma_0$ at large energies.Comment: 22 pages, 19 figures, submitted to PR

On the universal AC optical background in graphene

The 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 quasiparticle dynamics from predictions for the Dirac fermions in idealized graphene. We present analytical expressions for the ac conductivity in graphene which allow one to study how it is affected by interactions, temperature, external magnetic field and the opening of a gap in the quasiparticle 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.Comment: 18 pages, 4 figures; v2: to match New J. Phys. (Focus on Graphene issue