DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES

Charles L. Fefferman, Sonia Fliss and M Weinstein
submitted
Publication type:
Paper in peer-reviewed journals
arXiv:
assets/images/icons/icon_arxiv.png 2203.03775
Keywords :
tight binding model; edge states; honeycomb structure; discrete operator on a graph;
Abstract:
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 formulas for flat band edge states when they exist. We produce strong evidence for the existence of dispersive (non flat) edge state curves of nonzero energy for most l.
BibTeX:
@article{Fef-Fli-Wei-2200,
    author={Charles L. Fefferman and Sonia Fliss and M Weinstein },
    title={DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES },
    year={submitted },
    month={3},
}