Phonon localization around vacancies in graphene nanoribbons

The transport regime a particular phonon mode is in is dependent on its mean free path relative to the system size of the material. In addition to these “mobile” modes, some modes are localized at defect locations. In this study, phonon localization is investigated in graphene nanoribbons with vacancies and the extent of localization is quantified by the mode participation ratio and the localization contribution coefficient. It is revealed that localization mainly affects long-wavelength and high-frequency modes. Spatial analyses show that localized acoustic modes are concentrated around the vacancy and at edges (structural imperfections), while optical counterparts behave more randomly. Since acoustic modes are the dominant heat-carriers, it partially explains the reduction of thermal conductivity in graphene nanoribbons with vacancies. It is propounded that the dissimilar behavior of the optical modes is due to stronger inelastic scattering, as compared to acoustic modes, hence diminishing the weak localization effect. This work also presents the gradual evolution of localization strength of modes close to 60 cm− 1, 110 cm− 1, and 225 cm− 1, with distance from the vacancy, suggesting that localization strength varies spatially.

► It is shown that localization mainly affects long-wavelength and high-frequency modes. ► Spatial analyses suggest that localized acoustic modes are concentrated around the vacancy and at edges. ► Optical modes encounter stronger inelastic scattering than acoustic modes. ► Some of the acoustic modes exhibit a gradual spatial evolution of localization strength.