Quantum capacitance and Landau parameters of massless Dirac fermions in graphene

Extensive numerical results for the thermodynamic density of states (i.e. quantum capacitance) of a two-dimensional massless Dirac fermion fluid in a doped graphene sheet are presented. In particular, by employing the random phase approximation, the impact of screening exerted by a metal gate located nearby a graphene flake is quantified. Finally, the spin- and circularly-symmetric Landau parameter, which can be experimentally extracted from independent measurements on the same setup of the quantum capacitance and quasiparticle velocity, is calculated.