Keldysh functional renormalization group for electronic properties of graphene

TL;DR

This paper develops a nonperturbative nonequilibrium functional renormalization group approach combined with the Keldysh formalism to analyze Coulomb interactions in graphene, deriving quantum kinetic equations and calculating key electronic properties.

Contribution

It introduces a novel nonperturbative framework for graphene electron interactions using combined FRG and Keldysh formalisms, extending previous zero-temperature results.

Findings

Calculated renormalized Fermi velocity at finite temperature.

Determined static dielectric function incorporating Coulomb interactions.

Extended zero-temperature results to finite temperature conditions.

Abstract

We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible non-zero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer~\textit{et~al.}, Phys.\ Rev.\ B {\bf 92}, 121409 (2015).