@article{88a374ea7de24941ba50887524b6007d,
title = "Edge states in rationally terminated honeycomb structures",
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 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.",
keywords = "edge state, graphene, spectrum, tight binding",
author = "Fefferman, {C. L.} and S. Fliss and Weinstein, {M. I.}",
note = "Funding Information: ACKNOWLEDGMENTS. This research was initiated at a working group on “irrational edges” at the American Institute of Mathematics (AIM) Workshop on the Mathematics of Topological Insulators, December 7–11, 2020, which was supported by AIM, the US NSF, the Simons Foundation, and Columbia University. C.L.F. was supported, in part, by NSF Grant DMS-1700180. M.I.W. was supported, inpart,byNSFGrantsDMS-1620418andDMS-1908657,aswellasSimonsFoun-dation Math + X Investigator Award 376319. We warmly thank the participants of the AIM working group, as well as Pierre Delplace, David Gontier, and Mikael Rechtsman for stimulating discussions. Funding Information: This research was initiated at a working group on “irrational edges” at the American Institute of Mathematics (AIM) Workshop on the Mathematics of Topological Insulators, December 7–11, 2020, which was supported by AIM, the US NSF, the Simons Foundation, and Columbia University. C.L.F. was supported, in part, by NSF Grant DMS-1700180. M.I.W. was supported, in part, by NSF Grants DMS-1620418 and DMS-1908657, as well as Simons Foundation Math + X Investigator Award 376319. We warmly thank the participants of the AIM working group, as well as Pierre Delplace, David Gontier, and Mikael Rechtsman for stimulating discussions. Publisher Copyright: Copyright {\textcopyright} 2022 the Author(s).",
year = "2022",
month = nov,
day = "22",
doi = "10.1073/pnas.2212310119",
language = "English (US)",
volume = "119",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
publisher = "National Academy of Sciences",
number = "47",
}