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Zeitschrift für angewandte Mathematik und Physik

, 68:78

First Online: 14 June 2017Received: 06 December 2016Revised: 24 May 2017DOI: 10.1007-s00033-017-0823-7

Cite this article as: Kozlov, V.A., Nazarov, S.A. & Orlof, A. Z. Angew. Math. Phys. 2017 68: 78. doi:10.1007-s00033-017-0823-7


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.

Mathematics Subject Classification35P30 47A10 47A40 Download to read the full article text

Author: V. A. Kozlov - S. A. Nazarov - A. Orlof



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