1/N Expansion in Correlated Graphene

Details 1/N Expansion in Correlated Graphene 1/N Expansion in Correlated Graphene

2009-03-11

arxiv.org/abs/0903.2046v3

Phys.Rev.B80:165424,2009

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, 2 figures; expanded presentation, references added

Scientific paper

10.1103/PhysRevB.80.165424

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.

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