  We calculate the ground-state energy of Dirac electrons in graphene in the
presence of disorder. We take randomly distributed charged impurities at a
fixed distance from the graphene sheet and surface fluctuations (ripples) as
the main scattering mechanisms. Mode-coupling approach to scattering rate and
random-phase approximation for ground-state energy incorporating the many-body
interactions and the disorder effects yields good agreement with experimental
inverse compressibility.
