Anomalous behavior in an effective model of graphene with Coulomb interactions

Abstract

We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a three-dimensional quantum electromagnetic field. The fermionic correlation functions are written as series in the running coupling constants, with finite coefficients that admit explicit bounds at all orders. The implementation of Ward Identities in the RG scheme implies that the effective charges tend to a line of fixed points. At small momenta, the quasi-particle weight tends to zero and the effective Fermi velocity tends to a finite value. These limits are approached with a power law behavior characterized by non-universal critical exponents.

42 pages, 7 figures; minor corrections, one appendix added (Appendix A). To appear in Ann. Henri Poincare

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• Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• Geometrical and topological aspects of graphene and related materials
• Lattice quantum electrodynamics for graphene
• The scaling limit of the energy correlations in non integrable Ising models
• Phase structure of 2-dimensional topological insulators by lattice strong coupling expansion
• Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice
• Ground state properties of graphene in Hartree-Fock theory
• Conductivity between Luttinger liquids: coupled chains and bilayer graphene
• Dirac cones for a mean-field model of graphene
• Universal conductivity and dimensional crossover in multi-layer graphene