▎ 摘　　要

Using non-equilibrium Green's function method and maintaining the zigzag carbon chains unchanged, we investigate the transmission rate of acoustic phonon and the reduced thermal conductance through multi-frame graphene nanoribbons (GNRs). The results show that the reduced thermal conductance approaches pi(2)kappa(2)(B) T/3h in the limit T -> 0 K. Due to the fact that only long wavelength acoustic phonons with zero cutoff frequency are excited at such low temperatures, the scattering influence on the long wavelength acoustic phonons by the multi-frame in GNRs can be ignored and these phonons can go through the scattering region perfectly. As the temperature goes up, the reduced thermal conductance decreases. This is because the high-frequency phonons are excited and these high-frequency phonons are scattered easily by the scattering structures. With the further rise in temperature, acoustic phonon modes with the cutoff frequency greater than zero are excited, which leads to a rapid increase of the reduced thermal conductance. This study shows that changing the frame structure by a small length can lead to a significant change of transmission probability. In the higher frequency region, the transmission spectra display complex peak-dip structures, which results from the fact that in higher frequency region more phonon modes are excited and scattered in the middle scattering region with multi-frames, and the scattering phonons are coupled with the incident phonons, with the increase of the length of frame structure, the scattering of the phonon is also enhanced, which leads to the decrease in the phonon transmission; by changing the frame structure, the parameters can effectively adjust the position of low-frequency phonon transmission valley. The frame structure can induce high-frequency phonon blocking effect and the blocking effect depending on the structure parameter of the frame. When the single frame and double frame GNRs are narrowest, the scattering from low-frequency phonons by the scattering structure is largest, which leads to the fact that the reduced thermal conductance is smallest at low temperatures; however, at high temperature, the reduced thermal conductance is biggest when the single frame and double frame GNRs are narrowest. This is because the scattering from high-frequency phonons by the scattering structure is the smallest. When the length of the frame structure is unchanged, a graphite chain is inserted in which the reduced thermal conductance is always reduced. These results provide an effective theoretical basis for designing the thermal transport quantum devices based on GNRs.