Trapped modes in zigzag graphene nanoribbons
Mathematical Physics
2017-06-28 v1 math.MP
Spectral Theory
Abstract
We study a scattering on an ultra-low potential in zigzag graphene nanoribbon. Using mathematical framework based on the continuous Dirac model and augumented 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 its multiplicity does not exceeds one. We prove that trapped modes do not appear outside the threshold, provided the potential is sufficiently small.
Keywords
Cite
@article{arxiv.1701.05795,
title = {Trapped modes in zigzag graphene nanoribbons},
author = {V. A. Kozlov and S. A. Nazarov and A. Orlof},
journal= {arXiv preprint arXiv:1701.05795},
year = {2017}
}