2007/01/31 by D. Son, D. T. Son · 9 citations
Materials Science · Physics and Astronomy · #Coulomb #Dirac fermion #Electron #Fermion #Graphene #Graphene research and applications #Massless particle #Mathematical physics #Momentum (technical analysis) #Physics #Quantum and electron transport phenomena #Quantum mechanics #Scale invariance #Topological Materials and Phenomena #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.75.235423
published as Phys.Rev. B75 (2007) 235423 · 14 pages, 5 figures; added an Appendix with technical details
arxiv created 2007/06/18 · openalex publication_date 2007/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 three dimensional 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 \ensuremathω\ensuremath∼pz, where the dynamic critical exponent z depends on N. In the limit of large N, we find z=1\ensuremath-4∕(\ensuremathπ2N)+O(N^\ensuremath-2). We argue that due to the numerically large Coulomb coupling, graphene (freely suspended) in a 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.