Excitonic Instabilities and Insulating States in Bilayer Graphene
arXiv:1208.1339 · doi:10.1103/PhysRevB.86.205418
Abstract
The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta , , where the conduction band and valence band touch each other, yielding a semi-metal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if inter-band interactions are present. Using a perturbative renormalization group analysis up to the one-loop level, we find different competing ordered ground states, including ferromagnetism, superconductivity, spin and charge density wave states with ordering vector , and excitonic insulator states. In addition, two states with valley symmetry breaking are found in the excitonic insulating and ferromagnetic phases. This analysis strongly suggests that the ground state of bilayer graphene should be gapped, and with the exception of superconductivity, all other possible ground states are insulating.
17 pages, 6 figures, 2 Tables, Added references
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- Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
- Realization of graphene logics in an exciton-enhanced insulating phase
- Electrically controllable magnetic order in the bilayer Hubbard model on honeycomb lattice --- a determinant quantum Monte Carlo study
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- Applied electric and magnetic field effects on the bandgap formation and antiferromagnetic ordering in AA-stacked Bilayer Graphene