Phononic higher-order topology has been discovered in several crystalline materials in recent years. However, studies on the properties related to applications of phonon higher-order topological states, especially their transport characteristics, remain scarce. In this work, we demonstrate the existence of phononic higher-order topological phases characterized by fractional quadrupole topological numbers in AB-stacked bilayer $2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$ ($\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$) and AB-stacked bilayer $2\mathrm{H}\text{−}{\mathrm{WTe}}_2$ ($\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{WTe}}_2$). Phononic topological corner states are found in nanodisks of $\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$ and $\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{WTe}}_2$. Using the nonequilibrium Green's function method, we calculate the phonon transmission spectra near the frequencies of corner states and reveal that transmission peaks emerge when the frequencies between incident phonons and corner states match, indicating that the phonon topological corner states can serve as efficient transmission channels. Our work deepens the understanding of phononic higher-order topology and provides theoretical support for future applications of higher-order topological phases.

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• Ballistic transport
• Bosons
• Optical phonons
• Phonons
• Symmetry protected topological states
• Topological order
• Topological phases of matter