Effect of Holstein phonons on the electronic properties of graphene

Abstract

We obtain the self-energy of the electronic propagator due to the presence of Holstein polarons within the first Born approximation. This leads to a renormalization of the Fermi velocity of one percent. We further compute the optical conductivity of the system at the Dirac point and at finite doping within the Kubo-formula. We argue that the effects due to Holstein phonons are negligible and that the Boltzmann approach which does not include inter-band transition and can thus not treat optical phonons due to their high energy of $\hslash {\omega }_0\sim 0.1-0.2$eV, remains valid.

arXiv comment13 pages, 4 figures

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