Chemical-potential flow equations for graphene with Coulomb interactions

TL;DR

This paper develops a nonperturbative method using flow equations to study how the Fermi velocity and dielectric function in graphene change with chemical potential, confirming minimal density dependence.

Contribution

It introduces a novel flow equation approach for chemical potential dependence in graphene, extending the functional renormalization group framework with a nontrivial initial condition.

Findings

Charge carrier density has negligible effect on Fermi velocity.

Results agree with previous zero-density fRG calculations.

Validation against experimental data confirms theoretical predictions.

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 confirm that the charge carrier density dependence of the Fermi velocity is negligible, validating the comparison of the fRG calculation at zero density of Bauer et al., Phys. Rev. B 92, 121409 (2015) with the experiment of Elias et al., Nat. Phys. 7, 701 (2011).