Twisted multilayer moiré water waves topologically robust to disorder

Abstract

Moiré patterns, stacking and twisting multilayer periodic lattices into superlattices, have become cornerstones of many physical systems from condensed matter to wave phenomena, but have never been properly studied in water waves. Here, we demonstrate twisted multilayer moiré water surface waves carrying robust skyrmionic topologies. Using a custom water tank of circular multi-channel phased array, we precisely generate water-wave skyrmion lattices and superimpose them into moiré superlattices with higher-order topological textures, e.g., skyrmion bags and clusters, programmed via the twist angle. We also quantitatively compare the topological robustness of bilayer and trilayer configurations under spatiotemporal perturbations. The trilayer moiré superlattices exhibit more enhanced stability, stronger field localization and energy concentration than the bilayer. Our work establishes water waves as a macroscopic, tunable, and visually accessible platform for moiré physics, towards robust particle manipulation and classical analogues of topological quantum phenomena.

Figures (5)

• Figure 1: Moiré skyrmion superlattices in water waves.(a) Conceptual illustration of a skyrmion lattice formed in the three-dimensional displacement field $\mathbfcal{R}(x,y,t)$ via interference of six plane waves in a hexagonal arrangement (orange arrows). (b) Experimental scheme. Multiple acoustic sources in a ring-shaped cavity excite water waves, forming two twisted hexagonal skyrmion lattices (orange, green arrows). Their superposition creates the moiré superlattice. (c) Measured vertical displacement field of two skyrmion lattices (orange, green) with a relative twist angle $\varphi=13.17^\circ$. Their moiré superlattice (blue) is obtained by simultaneously exciting both skyrmion lattices. Following this principle, trilayer superlattices can be constructed by adding a third twisted skyrmion lattice. (d) The topological robustness is probed by introducing a controlled perturbation to the moiré skyrmion superlattice.
• Figure 2: Bilayer moiré skyrmion superlattices in water waves.(a) Measured displacement field $\mathcal{Z}(x,y,t=0)$ for different interlayer twist angles $\varphi$. (b-d) Magnified view of the red-boxed region in (a). (b) Vertical field $\mathcal{Z}$ with reconstructed in-plane displacement vectors $(\mathcal{X},\mathcal{Y})$ indicated by arrows. (c) 3D vector field distribution $\mathbfcal{R}(x,y,t=0)$ encoded by color (in-plane orientation) and brightness (out-of-plane amplitude). (d) Skyrmion density distribution. Integration using the boundaries of the skyrmion cluster (green) and the total skyrmion bag (black) yields topological charges of $S_\text{cluster} \simeq 18.83$ and $S_\text{bag} \simeq 17.82$.
• Figure 3: Trilayer moiré skyrmion superlattices in water waves.(a) Measured vertical displacement field $\mathcal{Z}(x,y,t=0)$ for trilayer moiré superlattices with twist angles $\varphi_{12} = \varphi_{23}.$(b-d) Magnified view of the red-boxed region in (a). (b) Vertical field $\mathcal{Z}$ with reconstructed in-plane displacement fields $(\mathcal{X},\mathcal{Y})$ indicated by arrows. (c) 3D vector field distribution $\mathbfcal{R}(x,y,t=0)$ encoded by color (in-plane orientation) and brightness (out-of-plane amplitude). (d) Skyrmion density distribution. Contours denote integration boundaries yielding topological charges $S_\text{cluster} \simeq 6.98$ and $S_\text{bag} \simeq 6.01$.
• Figure 4: Enhanced topological robustness in moiré skyrmion superlattices under perturbation.(a) A skyrmion bag in an unperturbed trilayer superlattice ($S_\text{bag} \simeq 5.99$). (b) Response to perturbation ($p=1$): a stable texture with topological charge ($S_\text{bag} \simeq 6.01$, left) and a distorted case yielding a non-integer charge ($S_\text{bag} \simeq 6.75$, right). (c) Layer-dependent robustness. Statistical robustness of unit-charge skyrmions ($S=1$) under fixed perturbation ($p=1$). The monolayer lattice (black) exhibits minimal robustness. Bilayer (blue, $\varphi_{12}=14.75^\circ$) and trilayer (red, $\varphi_{12}=\varphi_{23}=9.75^\circ$) configurations achieve near-perfect robustness, with trilayers consistently superior. (d) Robustness versus perturbation strength. Measured (dashed) and simulated (solid) robustness $\mathscr{R}(p)$. Trilayer superlattices (red) exhibit superior stability across all $p$.
• Figure 5: Enhanced energy localization in moiré skyrmion superlattices.(a) Spatial distribution of vertical energy density $W_z$ reveals localized hotspots. (b) Cross-sectional profiles show the trilayer’s peak intensity exceeds the bilayer’s by more than a factor of two. (c) Dynamics of $E_{\text{spots}}$, $E_{\text{bag}}$, and $\eta(t)$ under sustained perturbation ($p=1$). The trilayer (red) maintains a higher $\eta(t)$ than the bilayer (blue), demonstrating stronger energy localization in the hotspots.