The robust transport of quantized particles in gap systems through adiabatic cyclic evolution corresponds to dynamical versions of topological insulators, which have recently emerged as a thriving topic. Until now, these connections were thought to be limited to gap systems. Here, we report a mechanism for corner state transfer in a gapless system, which arises as a synthetic higher-order Weyl semimetal. This is realized in the phononic version of a breathing kagome lattice, which is stacked layer by layer with weak interlayer couplings in the $z$ direction, mimicking the time axis. We observed the corner state transfer, which hosts Weyl points and hinge states in synthetic three-dimensional (two-dimensional lattice$+$one-dimensional time) space. Our proposed corner states periodically undergo two topologically nontrivial phases along the time axis, resulting in the transport of the corner states, which corresponds to the switching of the two hinge states. Moreover, we experimentally demonstrated that the transport process is robust against defects. Our results provide insight into studying topological phases in synthetic space as well as an effective approach for manipulating acoustic waves.

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• Phononic crystals
• Topological insulators
• Topological phase transition
• Topological materials
• Weyl semimetal
• Acoustic techniques