Edge states in rationally terminated honeycomb structures

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

doi:10.1073/pnas.2212310119

Edge states in rationally terminated honeycomb structures

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

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-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 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	American English
Article number	e2212310119
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	119
Issue number	47
DOIs	https://doi.org/10.1073/pnas.2212310119
State	Published - Nov 22 2022

ASJC Scopus subject areas

General

Keywords

edge state
graphene
spectrum
tight binding

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10.1073/pnas.2212310119

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N2 - 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.

AB - 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.

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KW - graphene

KW - spectrum

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ER -

Edge states in rationally terminated honeycomb structures

Abstract

ASJC Scopus subject areas

Keywords

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