Abstract
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.
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Kozlov, V.A., Nazarov, S.A. & Orlof, A. Trapped modes in zigzag graphene nanoribbons. Z. Angew. Math. Phys. 68, 78 (2017). https://doi.org/10.1007/s00033-017-0823-7
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DOI: https://doi.org/10.1007/s00033-017-0823-7