  We demonstrate experimentally that graphene quantum capacitance
$C_{\mathrm{q}}$ can have a strong impact on transport spectroscopy through the
interplay with nearby charge reservoirs. The effect is elucidated in a
field-effect-gated epitaxial graphene device, in which interface states serve
as charge reservoirs. The Fermi-level dependence of $C_{\mathrm{q}}$ is
manifested as an unusual parabolic gate voltage ($V_{\mathrm{g}}$) dependence
of the carrier density, centered on the Dirac point. Consequently, in high
magnetic fields $B$, the spectroscopy of longitudinal resistance ($R_{xx}$) vs.
$V_{\mathrm{g}}$ represents the structure of the unequally spaced relativistic
graphene Landau levels (LLs). $R_{xx}$ mapping vs. $V_{\mathrm{g}}$ and $B$
thus reveals the vital role of the zero-energy LL on the development of the
anomalously wide $\nu=2$ quantum Hall state.

Mesoscale and Nanoscale Physics;Disordered Systems and Neural Networks;Materials Science;Other Condensed Matter