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

Understand

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 flat band appears, whose presence modifies qualitatively the response of the system.