1/N Expansion in Correlated Graphene

TL;DR

This paper analyzes the 1/N expansion in gapped graphene, revealing a crossover from 3D to 2D Coulomb interactions and its effects on quasiparticle properties, with implications for understanding electron interactions in graphene.

Contribution

It introduces a detailed analysis of Coulomb interactions in gapped graphene using the 1/N expansion, highlighting a crossover in potential behavior and its impact on quasiparticle renormalization.

Findings

Crossover from 1/r to logarithmic Coulomb potential in graphene.

Weak confinement of electric field in the graphene plane.

Unusual renormalization of quasiparticle velocity and gap.

Abstract

We examine the 1/N expansion, where N is the number of two-component Dirac fermions, for Coulomb interactions in graphene with a gap of magnitude $\Delta = 2 m$. We find that for $N\alpha\gg1$, where $\alpha$ is graphene's "fine structure constant", there is a crossover as a function of distance $r$ from the usual 3D Coulomb law, $V(r) \sim 1/r$, to a 2D Coulomb interaction, $V(r) \sim \ln(N\alpha/mr)$, for $m^{-1} \ll r \ll m^{-1} N \alpha/6$. This effect reflects the weak "confinement" of the electric field in the graphene plane. The crossover also leads to unusual renormalization of the quasiparticle velocity and gap at low momenta. We also discuss the differences between the interaction potential in gapped graphene and usual QED for different coupling regimes.