Lattice gauge theory for graphene

Abstract

We propose a lattice gauge model for graphene, described in terms of tight binding electrons hopping on the honeycomb lattice interacting with a three-dimensional quantum U(1) gauge field. The infrared fixed point of the theory is analyzed by exact Renormalization Group methods. We find that the interacting response functions have a large distance decay described by anomalous critical exponents, which vary continuously with the strength of the electron-photon interaction. The dominant excitations at low energies turn out to be the Kekulé distortion, the charge density wave and the staggered magnetization. External fields coupled to the corresponding local order parameters are dramatically enhanced by the interactions. We also derive a non-BCS gap equation, suggesting that spontaneous emergence of Kekulé, staggered density or magnetization can arise at intermediate values of the electromagnetic coupling.