Scattering on an ultralow potential in an armchair graphene nanoribbon is studied. Using the continuous Dirac model and including a couple of artificial waves in the scattering process, described by an augmented scattering matrix, a condition is derived for the existence of a trapped mode. Threshold energies, where the multiplicity of the continuous spectrum changes, are considered, and it is shown that a trapped mode may appear for energies slightly less than a threshold and its multiplicity does not exceed one. For energies that are higher than a threshold, there are no trapped modes, provided that the potential is sufficiently small.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 483, 2019, pp. 85–115.
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Kozlov, V.A., Nazarov, S.A. & Orlof, A. Trapped Modes in Armchair Graphene Nanoribbons. J Math Sci 252, 624–645 (2021). https://doi.org/10.1007/s10958-021-05186-9
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DOI: https://doi.org/10.1007/s10958-021-05186-9