Fig. 4
From: Elastic pseudospin transport for integratable topological phononic circuits
Pure pseudospin current of elastic waves. a Experimental configuration for investigating pure pseudospin current of elastic helical edge states. Two (orange) identical elastic sources (ultrasonic transducers) working at same power and frequency (111 kHz) are placed in two different places of a straight TI–OI interface, dividing the interface into three regions (top, middle, and bottom). In the top (red) region, there only exists upward-traveling pseudospin+ , superimposed from two individual pseudospins+ , each originated from one of the two sources. Similar situation in the bottom (blue) region, instead there only exists downward-traveling pseudospin−. Remarkably, pseudospin+ and pseudospin− coexist in the middle (green) region. b Physical image of the pseudospin current can be well exhibited by the vector sum of the pseudospin+ and the pseudospin− in their (S/A) spin space at time-domain. Because the anti-clockwise pseudospin+ (red arrows, S + iA) and the clockwise pseudospin− (blue arrows, S − iA) are with the same amplitude and velocity (that is, rotation speed in spin space), thus in any location along the TI–OI interface, like seven representative locations from #1 to #7, the vector sum of these two elastic pseudospins will inevitably presents a single polarization feature in the spin space all over time, e.g., ∓S ↔ ±S (position #1 and #7) or +A ↔ −A (position #4) as illustrated by the (violet-green) double-headed arrows. Meanwhile, along the interface (kII), the vector sum of these two elastic pseudospins (that is, the single polarization in spin space) will evolve in a one-way spiral fashion, shown as the (violet-green) double helix, owning to the spin-momentum locking. c Experimentally measured elastic field distribution of the out-of-plane displacement along the TI–OI interface conforming the pure pseudospin current. Particularly, at the three representative locations marked by black hexagons, the elastic displacements verify single polarization normal modes −S ↔ +S (position #1), +A ↔ −A (position #4) and +S ↔ −S (position #7), all only oscillates harmonically with time as shown in the right-most panel. This is a clear indication of the formation of a standing-wave with one-way spiral in the real space
