Authors: Alessandro Giuliani, Vieri Mastropietro, Marcello Porta

Title: A lattice gauge theory model for graphene: critical exponents and anomalous gap
 
Abstract: The effects of the electromagnetic (e.m.) electron-electron interaction in half-filled graphene are investigated in terms of a lattice gauge theory model where tight binding electrons hopping on a honeycomb lattice are coupled to a three-dimensional quantum e.m. field. By using exact Renormalization Group methods and lattice Ward Identities, we show that the quasi-particle weight vanishes at the Fermi points and the effective Fermi velocity tends to the speed of light as power laws with non-universal critical exponents. The analysis of the response functions indicates a tendency towards excitonic pairing. By a variational argument on the ground state energy, we derive exact non-BCS self-consistence equations for the excitonic gap, admitting a non-trivial solution if its critical exponent exceeds a critical value.

Keywords: Graphene, Dirac fermions, Coulomb interactions, Ward identities, Renormalization Group, lattice gauge theory

Alessandro Giuliani
Dipartimento di Matematica
Università di Roma Tre
L.go S. Leonardo Murialdo 1, 00146 Roma - Italy
e-mail: giuliani AT mat DOT uniroma3 DOT it

Vieri Mastropietro
Dipartimento di Matematica
Università di Roma Tor Vergata
V.le della Ricerca Scientifica 1, 00133 Roma - Italy
e-mail: mastropi AT mat DOT uniroma2 DOT it

Marcello Porta
Dipartimento di Fisica
Università di Roma Sapienza
P.le A. Moro, 00185 Roma - Italy
e-mail: marcello DOT porta AT roma1 DOT infn DOT it