Vertex renormalization in dc conductivity of doped chiral graphene

The remarkable transport properties of graphene follow not only from the Dirac-type energy dispersion, but also from the chiral nature of its excitations, which makes unclear the limits of applicability of the standard semiclassical Boltzmann approach. In this paper we provide a quantum derivation of the transport scattering time in graphene in the case of electron-phonon interaction. By using the Kubo formalism, we compute explicitly the vertex corrections to the dc conductivity by retaining the full chiral matrix structure of graphene. We show that at least in the regime of large chemical potential the Boltzmann picture is justified. This result is also robust against a small sublattice inequivalence, which partly spoils the role of chirality and leads to a doping dependence of the resistivity that can be relevant to recent transport experiments in doped graphene samples