Hao Wang, Jin-Hua Gao, Fu-Chun Zhang
Multilayer graphene systems with a rhombohedral stacking order harbor nearly flat bands in their single-particle spectrum. Ansatz states have been proposed to describe the edge-localized states of flat band electrons. The absence of kinetic dispersion near the fermi surface leaves the interaction as a dominate mechanism to govern the low energy physics of the electron system. We build up an effective interaction lattice model under a basis of flat-band Wannier functions, which contains long-range and off-diagonal portions of the Coulomb interaction in addition to the common onsite Hubbard term. The constructed orthonormal Wannier basis enables us to directly calculate the interaction matrix coefficients. We then present a protocol for flat-band projection that yields an interaction-only lattice model of flat band electrons. We argue that, at low density, this model might energetically favor a ferromagnetic quantum crystal.
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http://arxiv.org/abs/1210.7590
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