Eliashberg theory of excitonic insulating transition in graphene

TL;DR

This paper develops an Eliashberg theoretical framework for understanding the excitonic insulator transition in graphene, highlighting how self-consistent coupling of the fermion gap and polarization enhances the dynamical gap without altering the critical point.

Contribution

It introduces a self-consistent Eliashberg approach to excitonic transitions in graphene, accounting for gap effects on Coulomb screening and validating the theory at large N.

Findings

Fermion gap increases due to reduced screening effects.

The critical point remains unchanged despite gap inclusion.

Vertex corrections are suppressed at large N, supporting the theory's validity.

Abstract

A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semimetal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of vacuum polarization function. Including the fermion gap into polarization function increases the effective strength of Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enhancement of the dynamical fermion gap in the excitonic insulating phase. The validity of the Eliashberg theory is justified by showing that the vertex corrections are suppressed at large $N$ limit.