Lattice generalization of the Dirac equation to general spin and the role of the flat band

@article{Dora2011LatticeGO,
  title={Lattice generalization of the Dirac equation to general spin and the role of the flat band},
  author={Bal'azs D'ora and Janik Kailasvuori and Roderich Moessner},
  journal={Physical Review B},
  year={2011},
  volume={84},
  pages={195422}
}
We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian involving stacked triangular lattices. We obtain multi-layered low energy excitations around half-filling described by a two-dimensional Dirac equation of the form H=v_F S\cdot p, where S represents an arbitrary spin-S (integer or half-integer). For integer-S, a… 

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