2009/03/31 by Valeri N. Kotov, Bruno Uchoa, A. H. Castro Neto
Materials Science · Physics and Astronomy · #Condensed matter physics #Coulomb #Coupling (piping) #Coupling constant #Electric field #Graphene #Graphene research and applications #Materials science #Mathematical physics #Physics #Quantum Electrodynamics and Casimir Effect #Quantum and electron transport phenomena #Quantum mechanics #Quasiparticle #Superconductivity #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.80.165424
published as Phys. Rev. B 80, 165424 (2009) · 7 pages, 2 figures; expanded presentation, references added
arxiv created 2009/06/17 · openalex publication_date 2009/10/23 · openalex created_date 2016/06/24 · arxiv updated 2022/03/07 · openalex updated_date 2026/08/05
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 Δ= 2 m. We find that for Nα≫1, where α is graphene's "fine structure constant", there is a crossover as a function of distance r from the usual 3D Coulomb law, V(r) ∼ 1/r, to a 2D Coulomb interaction, V(r) ∼ ln(Nα/mr), for m-1 ≪ r ≪ m-1 N α/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.