Finite-temperature screening and the specific heat of doped graphene sheets

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work, we present a semi-analytical expression for the dynamical density-density linear-response function of non-interacting massless Dirac fermions (the so-called 'Lindhard' function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the random phase approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.