Fig. 4

Phononic spin–orbit interaction in a ring resonator. a Device under test. The pair of IDTs function as the input and output of the circuit and address the clockwise (CW) and counter-clockwise (CCW) love-like mode simultaneously. Focused IDTs and shield structure are used to improve signal to noise ratio. b Orbital angular momentum (OAM) carried by Love-like mode. c Left: Zoomed in mode profile of Love-like mode, with displacements indicated by the black arrows. We observe circular trajectory of displacement. Right: Spin-momentum locking—CW and CCW propagating phonons possess spins of opposite direction. The direction of spin of point A (the purple dot in the left panel) is indicated by either cross (right-hand) or dot (left-hand). Dash line indicates the trajectory of displacement (solid dot). d Phase response difference between CW and CCW modes, when the device is subject to in-plane and out-of-plane rotation. The comparison between Δϕ measured with rotation of different direction is a clear signature of SOI. e Applying an out-of-plane CCW rotation to the system, CW and CCW Modes have resonant frequency shift towards the opposite direction, due to the opposite chiralities that they possess. f Phase response measured at various peak rotation rate