We calculate $\partial \mu /\partial n$ (where $\mu =\mathrm{\text{chemical}}$ potential and $n=\mathrm{\text{electron}}$ density), which is associated with the compressibility, in graphene as a function of $n$, within the Hartree-Fock approximation. The exchange-driven Dirac-point logarithmic singularity in the quasiparticle velocity of intrinsic graphene disappears in the extrinsic case. The calculated renormalized $\partial \mu /\partial n$ in extrinsic graphene on ${\mathrm{SiO}}_2$ has the same $n^{-(1/2)}$ density dependence but is 20% larger than the inverse bare density of states, a relatively weak effect compared to the corresponding parabolic-band case. We predict that the renormalization effect can be enhanced to about 50% by changing the graphene substrate.

• Received 19 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.226801