DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Communications on Pure and Applied Mathematics Year : 2023

DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES

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.
Fichier principal
Vignette du fichier
ffw-arXiv1.pdf (6.47 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03606004 , version 1 (11-03-2022)

Identifiers

Cite

Charles Louis Fefferman, Sonia Fliss, Michael Weinstein. DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES. Communications on Pure and Applied Mathematics, In press, ⟨10.1002/cpa.22141⟩. ⟨hal-03606004⟩
116 View
96 Download

Altmetric

Share

More