  Precise control of elastic waves in modes and coherences is of great use in
reinforcing nowadays elastic energy harvesting/storage, nondestructive testing,
wave-mater interaction, high sensitivity sensing and information processing,
etc. All these implementations are expected to have elastic transmission with
lower transmission losses and higher degree of freedom in transmission path.
Inspired by topological states of quantum matters, especially quantum spin Hall
effects (QSHEs) providing passive solutions of unique disorder-immune surface
states protected by underlying nontrivial topological invariants of the bulk,
thus solving severe performance trade-offs in experimentally realizable
topologically ordered states. Here, we demonstrate experimentally the first
elastic analogue of QSHE, by a concise phononic crystal plate with only
perforated holes. Strong elastic spin-orbit coupling is realized accompanied by
the first topologically-protected phononic circuits with both robustness and
negligible propagation loss overcoming many circuit- and system-level
performance limits induced by scattering. This elegant approach in a monolithic
substrate opens up the possibility of realizing topological materials for
phonons in both static and time-dependent regimes, can be immediately applied
to multifarious chip-scale devices with both topological protection and massive
integration, such as on-chip elastic wave-guiding, elastic splitter, elastic
resonator with high quality factor, and even (pseudo-)spin filter.
