Fig. 4: Experimental verification of spin-momentum locking and one-way edge waves in an auxetic Maxwell lattice.

a The self-dual twisted kagome lattice⁵⁶. The red star marks the actuation point. Red and green solid circles denote the triangles' centroids, which are used for image tracking. The 2D lattice has primitive basis vectors (a₁, a₂) with a lattice constant of a = 5.71 cm. Insets: (left) circular actuator (with a radius of 5 mm), and linear actuator; and (right) unit-cell geometry (gray: triangles with ideal pin-joint; blue: triangles with beam-like elastic connectors) and assembly diagram. b Super-cell band structures simulated in FEM for the elastic lattice in (a) with edge bands marked in red. c \(\left\vert {C}_{-{{{\bf{k}}}}}/{C}_{{{{\bf{k}}}}}\right\vert\) of the lowest edge band. Shaded area indicates \(\left\vert {C}_{-{{{\bf{k}}}}}/{C}_{{{{\bf{k}}}}}\right\vert \, < \, 0.1\). Dashed line marks k_y = 0.28π/a. d Two simulated edge mode profiles at k_y = 0.28π/a, also showing the geometry simulated in (b). e–g Time domain FEM simulations and h–j experimental results. Black circles and arrows indicate the location and the direction of the excitation, respectively. Solid circle sizes are proportional to velocity magnitudes, and black lines indicate velocity vector directions. Orange (light blue) color indicates the sign of the rotation of the triangle centroids' velocity vector, corresponding to counterclockwise (clockwise) spins. E_L/E_R indicates the energy ratio between left (L) and right (R) propagating modes.