# Trapped modes in armchair graphene nanoribbons

## TL;DR

This paper investigates the conditions under which trapped electronic modes occur in armchair graphene nanoribbons, using a Dirac model and augmented scattering matrix analysis to identify energy thresholds for trapped mode existence.

## Contribution

It introduces a new analytical condition for trapped mode existence in graphene nanoribbons considering threshold energies and potential size effects.

## Key findings

- Trapped modes can occur slightly below threshold energies.
- No trapped modes exist above threshold energies if potential is small.
- The multiplicity of trapped modes does not exceed one.

## Abstract

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 the the 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.