Symmetry properties of vibrational modes in graphene nanoribbons

TL;DR

This paper analyzes the symmetry and vibrational properties of graphene nanoribbons with armchair and zigzag edges, identifying Raman-active modes and their potential for experimental characterization.

Contribution

It provides a detailed symmetry analysis and predicts vibrational modes, including Raman-active modes, specific to armchair and zigzag graphene nanoribbons, using density functional theory.

Findings

Phonon modes at the Brillouin zone edge are degenerate in non-symmorphic nanoribbons.

Number of Raman-active modes depends on nanoribbon type and size.

A breathing-like mode frequency inversely relates to nanoribbon width.

Abstract

We present symmetry properties of the lattice vibrations of graphene nanoribbons with pure armchair (AGNR) and zigzag edges (ZGNR). In non-symmorphic nanoribbons the phonon modes at the edge of the Brillouin zone are twofold degenerate, whereas the phonon modes in symmorphic nanoribbons are non-degenerate. We identified the Raman-active and infrared-active modes. We predict 3N and 3(N+1) Raman-active modes for N-ZGNRs and N-AGNRs, respectively (N is the number of dimers per unit cell). These modes can be used for the experimental characterization of graphene nanoribbons. Calculations based on density functional theory suggest that the frequency splitting of the LO and TO in AGNRs (corresponding to the E2g mode in graphene) exhibits characteristic width and family dependence. Further, all graphene nanoribbons have a Raman-active breathing-like mode, the frequency of which is inversely proportional to the nanoribbon width and thus might be used for experimental determination of the width of graphene nanoribbons.