Fermi velocity renormalization and dynamical gap generation in graphene

TL;DR

This paper investigates how Coulomb interactions in graphene affect the Fermi velocity and the conditions for gap formation, revealing that velocity renormalization raises the critical coupling needed for insulating states.

Contribution

It provides a detailed analysis of Fermi velocity renormalization and its impact on the critical coupling for gap generation using Dyson-Schwinger equations in graphene.

Findings

Fermi velocity renormalization increases the critical coupling for gap formation.

Long-range Coulomb interactions significantly influence the semimetal-insulator transition.

Velocity renormalization effects are crucial for understanding electronic phase transitions in graphene.

Abstract

We study the renormalization of the Fermi velocity by the long-range Coulomb interactions between the charge carriers in the Dirac-cone approximation for the effective low-energy description of the electronic excitations in graphene at half filling. Solving the coupled system of Dyson-Schwinger equations for the dressing functions in the corresponding fermion propagator with various approximations for the particle-hole polarization we observe that Fermi velocity renormalization effects generally lead to a considerable increase of the critical coupling for dynamical gap generation and charge-density wave formation at the semimetal-insulator transition.