  We report capacitors in which a finite electronic compressibility of graphene
dominates the electrostatics, resulting in pronounced changes in capacitance as
a function of magnetic field and carrier concentration. The capacitance
measurements have allowed us to accurately map the density of states D, and
compare it against theoretical predictions. Landau oscillations in D are robust
and zero Landau level (LL) can easily be seen at room temperature in moderate
fields. The broadening of LLs is strongly affected by charge inhomogeneity that
leads to zero LL being broader than other levels.

Mesoscale and Nanoscale Physics;Materials Science