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 $ u=2$ quantum Hall state.
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