Trapped modes in armchair graphene nanoribbons

We study scattering on an ultra-low potential in armchair graphene nanoribbon. Using the continuous Dirac model and including a couple of artificial waves in the scattering process, described by an augumented scattering matrix, we derive a condition for the existence of a trapped mode. We consider the threshold energies, where multiplicity of the continuous spectrum changes and show that a trapped mode may appear for energies slightly less than a threshold and its multiplicity does not exceed one. For energies which are higher than a threshold, there are no trapped modes, provided that the potential is sufficiently small.