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We calculate $\partial\mu/\partial n$ in extrinsic graphene as a function ofcarrier density $n$ at zero temperature by obtaining the electronic self-energywithin the Hartree-Fock approximation. The exchange-driven Dirac-pointlogarithmic singularity in the quasiparticle velocity of intrinsic graphenedisappears in the extrinsic case. The calculated renormalized$\partial\mu/\partial n$ in extrinsic graphene has the same qualitative$n^{-\frac12}$ density dependence as the inverse bare density of states with a20% enhancement from the corresponding bare value, a relatively weak effectcompared to the corresponding parabolic-band case.Comment: 4 pages, 3 figure

physical review letters

Density Dependent Exchange Contribution to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>∂</mml:mo><mml:mi>μ</mml:mi><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>n</mml:mi></mml:math>and Compressibility in Graphene

Density Dependent Exchange Contribution to∂μ/∂nand Compressibility in Graphene