Vibrational Tamm states at the edges of graphene nanoribbons

TL;DR

This paper investigates vibrational edge states in graphene nanoribbons, identifying localized phonon modes analogous to electronic Tamm states, including nonlinear surface breather solitons in armchair configurations.

Contribution

It introduces the concept of vibrational Tamm states in graphene nanoribbons and analyzes their properties, including in-plane, out-of-plane, and nonlinear localized modes.

Findings

Edge vibrational modes are localized at the nanoribbon edges.

Surface modes include both in-plane and out-of-plane phonons.

Nonlinear surface breather solitons can form in armchair nanoribbons.

Abstract

We study vibrational states localized at the edges of graphene nanoribbons. Such surface oscillations can be considered as a phonon analog of Tamm states well known in the electronic theory. We consider both armchair and zigzag graphene stripes and demonstrate that surface modes correspond to phonons localized at the edges of the graphene nanoribbon, and they can be classified as in-plane and out-of-plane modes. In addition, in armchair nanoribbons anharmonic edge modes can experience longitudinal localization in the form of self-localized nonlinear modes, or surface breather solitons.