Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of “zigzag type” and those of “armchair type,” generalizing the classical zigzag and armchair edges. We prove that zero-energy/flat-band edge states arise for edges of zigzag type, but never for those of armchair type. We exhibit explicit formulae for flat-band edge states when they exist. We produce strong evidence for the existence of dispersive (nonflat) edge state curves of nonzero energy for most l.
|Original language||English (US)|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Nov 22 2022|
All Science Journal Classification (ASJC) codes
- edge state
- tight binding