Eur. Phys. J. B (2013) 86: 344
https://doi.org/10.1140/epjb/e2013-40068-5

Regular Article

Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects^*

¹ MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Shaanxi 710049, P.R. China
² Center on Experimental Physics, School of Science, Xi’an Jiaotong University, Shaanxi 710049, P.R. China
³ Department of Applied Physics, School of Science, Xi’an Jiaotong University, Shaanxi 710049, P.R. China
⁴ Centre for Computational Science and Engineering, Graphene Research Center, and Department of Physics, National University of Singapore, 117456 Singapore, Republic of Singapore
⁵ NUS-Tongji Center for Phononics and Thermal Energy Science, Department of Physics, Tongji University, Shanghai 200092, P.R. China

^a e-mail: xiamg@mail.xjtu.edu.cn

Received: 28 January 2013
Received in final form: 12 June 2013
Published online: 5 August 2013

Abstract

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm^-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.