Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2012-02-02
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
6 pages, to appear in Phys. Rev. B. arXiv admin note: substantial text overlap with arXiv:1103.3650
Scientific paper
We investigate the dynamical breakdown of the chiral symmetry in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for the dynamical gap generation in the ladder approximation, showing that it blows up at a critical value \alpha_c in the graphene fine structure constant which is quite sensitive to many-body corrections. Under static RPA screening of the interaction potential, we find that taking into account electron self-energy corrections to the vertex increases the critical coupling to \alpha_c \approx 4.9, for a number N = 4 of two-component Dirac fermions. When dynamical screening of the interaction is instead considered, the effect of Fermi velocity renormalization in the electron and hole states leads to the value \alpha_c \approx 1.75 for N = 4, substantially larger than that obtained without electron self-energy corrections (\approx 0.99), but still below the nominal value of the interaction coupling in isolated free-standing graphene.
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