Trapped modes in zigzag graphene nanoribbons

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.

References in corpus (3)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Electronic States of Graphene Nanoribbons

Cited by in corpus (1)

• Trapped modes in armchair graphene nanoribbons