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Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

Departamento de Matemática, Faculdade de Motricidade Humana, Universidade de Lisboa, Portugal

Group of Mathematical Physics, Universidade de Lisboa, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

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and

Petr Siegl

Group of Mathematical Physics, Universidade de Lisboa, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

On leave from the Nuclear Physics Institute ASCR, 25068 Rez, Czech Republic.

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https://doi.org/10.1142/S0129055X14500184Cited by:13 (Source: Crossref)

Abstract

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Keywords:

AMSC: 47F05, 47B25, 47A75, 82D80

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