Chemical-potential flow equations for graphene with Coulomb interactions

Abstract

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results are consistent with a charge carrier-independent Fermi velocity v(k) for small densities n≲k2/π, supporting the comparison of the zero-density fRG calculation of Bauer et al. [Phys. Rev. B 92, 121409 (2015)], with the experiment of Elias et al. [Nat. Phys. 7, 701 (2011)].