Dynamical gap generation in graphene with frequency dependent renormalization effects

TL;DR

This paper investigates how frequency-dependent renormalization effects influence the dynamical gap formation in graphene by solving Dyson-Schwinger equations within an effective QED framework, highlighting the importance of screening and retardation.

Contribution

It introduces a self-consistent approach to analyze frequency-dependent renormalization effects on gap generation in graphene using Dyson-Schwinger equations.

Findings

Frequency dependence significantly affects gap formation.

Retardation effects alter the fermion Green's function.

Screening modifies the effective interaction strength.

Abstract

We study the frequency dependencies in the renormalization of the fermion Greens function for the $\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.