Higher-order renormalization of graphene many-body theory

Abstract

We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior of the electron system beyond the simple logarithmic dependence of electronic correlators on the high-energy cutoff, which is characteristic of the large-N approximation. We show that the graphene many-body theory is perfectly renormalizable in the ladder approximation, as all higher powers in the cutoff dependence can be absorbed into the redefinition of a finite number of parameters (namely, the Fermi velocity and the weight of the fields) that remain free of infrared divergences even at the charge neutrality point. We illustrate this fact in the case of the vertex for the current density, where a complete cancellation between the cutoff dependences of vertex and electron self-energy corrections becomes crucial for the preservation of the gauge invariance of the theory. The other potentially divergent vertex corresponds to the staggered (sublattice odd) charge density, which is made cutoff independent by a redefinition in the scale of the density operator. This allows to compute a well-defined, scale invariant anomalous dimension to all orders in the ladder series, which becomes singular at a value of the interaction strength marking the onset of chiral symmetry breaking (and gap opening) in the Dirac field theory. The critical coupling we obtain in this way matches with great accuracy the value found with a quite different method, based on the resolution of the gap equation, thus reassuring the predictability of our renormalization approach.

27 pages, 7 figures, references added

References in corpus (16)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Is graphene in vacuum an insulator?
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Screening of a hypercritical charge in graphene
• Quantum Critical Behaviour in a Graphene-like Model
• Supercritical Coulomb center and excitonic instability in graphene
• Charge response function and a novel plasmon mode in graphene
• Screening of Coulomb Impurities in Graphene
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-N limits
• Variational approach to the excitonic phase transition in graphene
• Renormalization group approach to chiral symmetry breaking in graphene
• Power law Kohn anomalies and the excitonic transition in graphene

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• Is graphene on the edge of being a topological insulator?
• Impurity effects and bandgap-closing in massive Dirac systems
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Massless Dirac cones in graphene: experiments and theory
• A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene