Abstract
We present 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. In particular, by employing the random phase approximation, we quantify the impact of screening exerted by a metal gate located nearby a graphene flake. Finally, we calculate 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.
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