Discrete honeycombs, rational edges, and edge states

Charles L. Fefferman, Sonia Fliss, Michael I. Weinstein

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1575-1634
Number of pages60
JournalCommunications on Pure and Applied Mathematics
Volume77
Issue number3
DOIs
StatePublished - Mar 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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