Trapped modes in zigzag graphene nanoribbons

We study the scattering on an ultra-low potential in zigzag graphene nanoribbon. Using a mathematical framework based on the continuous Dirac model and the augmented scattering matrix, we derive a condition for the existence of a trapped mode. We consider the threshold energies where the continuous...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2017-08, Vol.68 (4), p.1-31, Article 78
Main Authors: Kozlov, V. A., Nazarov, S. A., Orlof, A.
Format: Article
Language:English
Subjects:
Engineering
Graphene
Mathematical analysis
Mathematical Methods in Physics
Mathematical models
Matrices (mathematics)
Matrix methods
Nanoribbons
Nanostructure
Scattering
Theoretical and Applied Mechanics
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Summary:We study the scattering on an ultra-low potential in zigzag graphene nanoribbon. Using a mathematical framework based on the continuous Dirac model and the augmented scattering matrix, we derive a condition for the existence of a trapped mode. We consider the threshold energies where the continuous spectrum changes its multiplicity and show that the trapped modes may appear for energies slightly less than a threshold and that its multiplicity does not exceeds one. We prove that trapped modes do not appear outside the threshold, provided the potential is sufficiently small.
ISSN:0044-2275
1420-9039
1420-9039
DOI:10.1007/s00033-017-0823-7