Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction

Abstract

Motivated by the physics of graphene, we consider a model of N species of 2+1 dimensional four-component massless Dirac fermions interacting through a 3D instantaneous Coulomb interaction. We show that in the limit of infinitely strong Coulomb interaction the system approaches a quantum critical point, at least for sufficiently large fermion degeneracy. In this regime the system exhibits invariance under scale transformations in which time and space scale by different factors. The elementary excitations are fermions with dispersion relation omega ~ p^z, where the dynamic critical exponent z depends on N. In the limit of large N we find z=1-4/(π^2 N). We argue that due to the numerically large Coulomb coupling, graphene (freely suspended) in vacuum stays near the scale-invariant regime in a large momentum window, before eventually flowing to the trivial fixed point at very low momentum scales.

arXiv comment14 pages, 5 figures; added an Appendix with technical details

References in corpus (15)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Two Dimensional Atomic Crystals
• The structure of suspended graphene sheets
• Unconventional Integer Quantum Hall effect in graphene
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Interactions and phase transitions on graphene's honeycomb lattice
• Magnetic field driven metal-insulator phase transition in planar systems
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene
• Electron-electron interactions and the phase diagram of a graphene bilayer
• Excitonic instability in two-dimensional degenerate semimetals
• Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
• Coulomb interactions at quantum Hall critical points of systems in a periodic potential
• Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

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