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Title: Discrete honeycombs, rational edges, and edge states
Abstract

Consider the tight binding model of graphene, sharply terminated along an edgelparallel to a direction of translational symmetry of the underlying period lattice. We classify such edgeslinto 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 mostl.

 
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PAR ID:
10486406
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
77
Issue:
3
ISSN:
0010-3640
Format(s):
Medium: X Size: p. 1575-1634
Size(s):
p. 1575-1634
Sponsoring Org:
National Science Foundation
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