Quantum Spin of Elastic Wave

Unveiling intrinsic spins of propagating waves usually offers people a fundamental understanding of the geometrical and topological properties of waves from classical to quantum aspects. A great variety of research has shown that transverse waves can possess non-trivial quantum spins and topology without help of strong wave-matter interaction. However, until now we still lack essential physical insights about the spin and topological nature of longitudinal waves. Here, demonstrated by elastic waves we uncover unique quantum spins for longitudinal waves and the mixed longitudinal-transverse waves that play essential roles in topological spin-momentum locking. Based on this quantum spin perspective, several abnormal phenomena beyond pure transverse waves are attributed to the hybrid spin induced by mixed longitudinal-transverse waves. The intrinsic hybrid spin reveals the complex spin essence in elastic waves and advances our understanding about their fundamental topological properties. We also show these spin-dependent phenomena can be exploited to control the wave propagation, such as non-symmetric elastic wave excitation by spin pairs, uni-directional Rayleigh wave and spin-selected elastic wave routing. These findings are generally applicable for arbitrary waves with longitudinal and transverse components.