Excitonic Instabilities and Insulating States in Bilayer Graphene

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 $\mathbf{K}$, ${\mathbf{K}}^{\prime }$, 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 $\mathbf{Q}=\mathbf{K}-{\mathbf{K}}^{\prime }$, 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

References in corpus (13)

• The electronic properties of graphene
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Topological Mott Insulators
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Pseudospin Magnetism in Graphene
• Quantum Anomalous Hall State in Bilayer Graphene
• Cyclotron resonance in bilayer graphene
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Electronic multicriticality in bilayer graphene
• Spin excitations in the excitonic spin-density-wave state of the iron pnictides
• Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly
• Renormalization group aspects of graphene