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

We provide a 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 multilayered low-energy excitations around half-filling described by a two-dimensional Dirac equation of the form H = v(F) S . p, where S represents an arbitrary spin S (integer or half-integer). For integer S, a flat band appears, the presence of which modifies qualitatively the response of the system. Among physical observables, the density of states, the optical conductivity, and the peculiarities of Klein tunneling are investigated. We also study Chern numbers as well as the zero-energy Landau-level degeneracy. By changing the stacking pattern, the topological properties are altered significantly, with no obvious analog in multilayer graphene stacks.