Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2007-01-21
Phys.Rev. B75 (2007) 235423
Physics
Condensed Matter
Strongly Correlated Electrons
14 pages, 5 figures; added an Appendix with technical details
Scientific paper
10.1103/PhysRevB.75.235423
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/(\pi^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.
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