  We present a first-principles study of the temperature- and density-dependent
intrinsic electrical resistivity of graphene. We use density-functional theory
and density-functional perturbation theory together with very accurate Wannier
interpolations to compute all electronic and vibrational properties and
electron-phonon coupling matrix elements; the phonon-limited resistivity is
then calculated within a Boltzmann-transport approach. An effective
tight-binding model, validated against first-principles results, is also used
to study the role of electron-electron interactions at the level of many-body
perturbation theory. The results found are in excellent agreement with recent
experimental data on graphene samples at high carrier densities and elucidate
the role of the different phonon modes in limiting electron mobility. Moreover,
we find that the resistivity arising from scattering with transverse acoustic
phonons is 2.5 times higher than that from longitudinal acoustic phonons. Last,
high-energy, optical, and zone-boundary phonons contribute as much as acoustic
phonons to the intrinsic electrical resistivity even at room temperature and
become dominant at higher temperatures.
