1211.1748 (Bitan Roy)
Bitan Roy
We here classify of all the possible gapped massive and gapless nematic phases in bilayer graphene. We review the derivation of effective low energy Hamiltonian for AB-stacked bilayer graphene. Various discrete and continuous symmetries of the non-interacting theory is discussed. Response of the gapped insulating orders for the spinless fermions to the quantizing magnetic field is addressed. A precise definition of the quantum anomalous Hall state is given. We show, even though there are three time-reversal symmetry breaking orders for spinless fermions, only one of them corresponds to anomalous Hall state. Upon constructing a particle-hole doubled 16 component Nambu-Dirac spinor, we recognize all the possible mass orders, leading to gaps for the quasi-particle excitations as well as the nematic orders, which on the other hand, splits the parabolic dispersion into two anisotropic Dirac like conical ones. Transformation of the order parameters under various continuous and/or discrete symmetries is reported. We show there are altogether 16 and 12 fermionic bilinears, respectively defining all the gapped insulating and superconducting orders, yielding only 8 insulating and 4 superconducting phases. Among the gapped superconductors, three are spin-singlet, which include uniform s-wave and two spatially inhomogeneous, translational symmetry breaking Kekule superconductors. The triplet pairing exhibits an f-wave symmetry. Besides the gapped phases, there are altogether 56 fermionic bilinears, describing all the nematic orders in bilayer graphene. 32 of them corresponds to semi-metallic and 24 to superconducting order parameters, leading to 16 semimetallic and 8 superconducting states. Some of the nematic superconducting phases break the translational symmetry, named as nematic-FFLO superconductors. A brief review over the role of electron-electron interactions is presented.
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http://arxiv.org/abs/1211.1748
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