Lattice generalization of the Dirac equation to general spin and the role of the flat band
Abstract
We provide a setup for generalizing the twodimensional pseudospin S=1/2 Dirac equation, arising in graphene’s honeycomb lattice, to general pseudospin S. We engineer these band structures as a nearestneighbor hopping Hamiltonian involving stacked triangular lattices. We obtain multilayered lowenergy excitations around halffilling described by a twodimensional Dirac equation of the form H=v_{F}S·p, where S represents an arbitrary spin S (integer or halfinteger). 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 zeroenergy Landaulevel degeneracy. By changing the stacking pattern, the topological properties are altered significantly, with no obvious analog in multilayer graphene stacks.
 Publication:

Physical Review B
 Pub Date:
 November 2011
 DOI:
 10.1103/PhysRevB.84.195422
 arXiv:
 arXiv:1104.0416
 Bibcode:
 2011PhRvB..84s5422D
 Keywords:

 05.30.Fk;
 81.05.ue;
 71.10.Fd;
 73.21.Ac;
 Fermion systems and electron gas;
 Lattice fermion models;
 Multilayers;
 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 14 pages, 6 figures, 1 table, revised version with a new section on experimental possibilities