Resonant splitting of phonon transport in periodic T-shaped graphene nanoribbons

By using the nonequilibrium Green's function method, we study the phonon transport properties in periodic T-shaped graphene nanoribbons (GNRs). An interesting resonant phenomenon is found in the phonon transmission of the out-of-plane mode. When the T-shaped GNR includes n constrictions, there are (n−1)-fold resonant splitting peaks in the low-frequency region of the transmission spectrum. The peaks are induced by low quasibound states in which phonons are intensively localized in the stubs. While (n−2)-fold resonant splitting rule occurs at frequency slightly higher than the first threshold frequency. These resonant peaks are originated from high quasibound states in which phonons are mainly localized in the constrictions. To the high quasibound states the constriction acts as a potential well rather than a potential barrier, which is the inverse of the case of the low quasibound states. These resonant splitting peaks in the spectrum of the out-of-plane mode can also be found in the total transmission