(color online) (a), (d) Phonon transmission function of out-of-plane modes and horizontally polarized SH mode calculate by force-constant model and dielectric continuum model, respectively. The different curve represent the 14-ZGNR without defect (solid line), with double-cavity defect (dashed line), and the 8-ZGNR without defect (dotted line), with double-cavity defect (dash-dotted line), respectively. (b), (e) The phonon dispersion relation of 14-ZGNR (solid curve) and 8-ZGNR (dotted curve) without double cavity. (c), (f) The corresponding total thermal conductance divided by temperature K/T. Reprinted with permission from Ref. [47]. Copyright (2011) by AIP Publishing LLC.