Edge states in rationally terminated honeycomb structures

C. L. Fefferman, S. Fliss, M. I. Weinstein

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Article numbere2212310119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number47
StatePublished - Nov 22 2022

All Science Journal Classification (ASJC) codes

  • General


  • edge state
  • graphene
  • spectrum
  • tight binding


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