Quantum capacitance and compressibility of graphene: The role of Coulomb interactions

Many-body effects on quantum capacitance, compressibility, renormalized Fermi velocity, and kinetic and interaction energies of massless Dirac electrons in graphene, induced by Coulomb interactions, are analyzed theoretically in the first-order, Hartree-Fock, and random-phase approximations. Recent experimental data on quantum capacitance and renormalized Fermi velocity are analyzed and compared with the theory. The bare Fermi velocity and the effective dielectric constants are obtained from the experimental data. A combined effect of Coulomb interactions and Gaussian fluctuations of the disorder potential is considered.