Is graphene on the edge of being a topological insulator?
arXiv:1211.3905 · doi:10.1007/JHEP07(2013)175
Abstract
We show that, at sufficiently large strength of the long-range Coulomb interaction, a mass term breaking parity (so-called Haldane mass) is dynamically generated in the many-body theory of Dirac fermions describing the graphene layer. While the tendency towards chiral symmetry breaking is stronger than for the dynamical breakdown of parity at spatial dimension D > 2, we find that the situation is reversed at D = 2. The need to regularize the many-body theory in a gauge-invariant manner (taking the limit D = 2 - ε) is what leads to the dominance of the parity-breaking pattern in graphene. We compute the critical coupling for the generation of a parity-breaking mass from the finite radius of convergence of the ladder series supplemented with electron self-energy corrections, finding a value quite close to the effective interaction strength for graphene in vacuum after including Fermi velocity renormalization and static RPA screening of the Coulomb interaction.
12 pages, 3 figures
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- Topological phase transitions and universality in the Haldane-Hubbard model
- Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
- Lattice Field Theory Study of Magnetic Catalysis in Graphene
- Half vortex and fractional electrical charge in two dimensions
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