Variational approach to the excitonic phase transition in graphene

TL;DR

This paper investigates the excitonic phase transition in undoped graphene by employing a variational approach, revealing how exchange interactions and Fermi velocity renormalization influence the critical coupling for instability.

Contribution

It introduces a comprehensive variational method that accounts for exchange effects and Fermi velocity renormalization in analyzing graphene's excitonic transition.

Findings

Exchange interactions increase the critical coupling needed for the phase transition.

Fermi velocity renormalization suppresses the excitonic instability.

The derived gap equation extends previous theoretical results.

Abstract

We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchange term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.