Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

Freitas, Pedro; Siegl, Petr (2014). Spectra of graphene nanoribbons with armchair and zigzag boundary conditions. Reviews in mathematical physics, 26(10), 1450018, 32. World Scientific 10.1142/S0129055X14500184

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Siegl, Petr

Subjects:

500 Science > 510 Mathematics

ISSN:

0129-055X

Publisher:

World Scientific

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:43

Last Modified:

07 Oct 2015 10:25

Publisher DOI:

10.1142/S0129055X14500184

URI:

https://boris.unibe.ch/id/eprint/66710

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