Harnessing acoustic topology for dynamic control of liquid crystal defects

Abstract

Topological soft matter systems rely on controllable defect structures to encode functionality, yet robust, large-scale, and reconfigurable manipulation strategies remain elusive. Here we present a versatile acoustic platform for dynamic control of liquid crystal defect arrays via engineered topological wavefields. By coherently superimposing surface acoustic waves, we generate spatially structured potential landscapes and acoustic streaming vortices that interact with the molecular orientation field of liquid crystals, enabling dynamic reconfiguration of topological defects. Tuning the acoustic parameter space allows precise modulation of defect density, symmetry, morphology, and spatial positioning. A theoretical framework based on Ginzburg-Landau modeling and free energy minimization captures the formation of vortex-induced instabilities and associated topological textures. The platform operates across diverse liquid crystal compositions, demonstrating material generality. This acoustically driven approach offers a scalable strategy for programmable topological structure in soft matter, with potential applications in reconfigurable photonic devices and active material systems.

Introduction

Topological soft matter defines a new paradigm in material science, where topological defects are reimagined as design elements stabilized by topological invariants within ordered media¹. These structures can modulate elasticity^2,3, guide hierarchical self-assembly^4,5, and encode functional responses⁶, making them indispensable in the design of reconfigurable materials⁷. Unraveling their formation, dynamics, and external control is central to advancing both fundamental soft matter physics and emerging material technologies.

Liquid crystals (LCs) offer a uniquely responsive platform for engineering defect-mediated functionalities⁸. Their long-range orientational order and sensitivity to external fields make them ideally suitable for constructing programmable topological textures⁹. Singular topological defects in LCs arise from local frustrations in molecular alignment, typically induced by symmetry-breaking phase transitions^10,11. These defects exhibit rich real-space topology and spatially varying director fields that can be harnessed for tunable optics^12,13,14, microscale templating^15,16,17, and dynamic sensing^18,19. Despite this promise, achieving scalable and reconfigurable control over such defects remains a major challenge. One widely adopted strategy involves interfacial engineering, such as colloidal inclusion^20,21 or patterned substrates^{22,23,24,25,26,27}, to induce desired defect textures. However, once formed, these textures are often locked by boundary conditions, making them static and irreversible. As a more dynamic alternative, external field-based approaches employing electric^28,29, magnetic³⁰, or optical fields^31,32,33,34 have enabled reversible control over defect formation. Since relying on the electrical or optical responsiveness of materials to enable electromagnetic interaction with external fields, these approaches exclude broader applications in many soft materials. Additionally, large-scale external field coupling and modulation in LCs still suffers from limitation in tunability and costs. As a result, there leaves a key mechanical actuation mechanism overlooked in current strategies for controlling topological structures in soft matter.

Among alternative physical stimuli, acoustic fields represent a promising yet underexplored approach for dynamically sculpting topological structures in soft matter^35,36. While traditionally regarded as scalar excitations, acoustic waves have recently been shown to support structured fields with rich vectorial features, such as phase singularities³⁷ and skyrmion-like textures³⁸, when multiple coherent wavefronts interfere. These patterns are not only topologically robust but also dynamically tunable by modulating wave parameters. In LCs, acoustic energy couples to molecular alignment through flow-mediated momentum transfer^39,40,41, reorienting the director field and enabling mechanically driven manipulation⁴². Previous demonstrations using bulk acoustic waves (BAWs) have achieved macroscopic alignment effects through such mechanisms^43,44, but their limited spatial resolution restricts access to defect-level control. Alternatively, surface acoustic waves (SAWs) offer a fundamentally different approach⁴⁵. By confining energy to the substrate surface, SAWs generate highly localized fields with structured pressure and velocity gradients that align naturally with the planar geometry of LC films. Although SAW-based strategies offer a promising route for manipulating LCs, the dynamic and scalable engineering of topological defect architectures remains largely unexplored.

Here, we experimentally demonstrate and theoretically elucidate the coupling between acoustic topological structures carried by SAWs and topological defect textures in LCs, enabling the large-scale generation and dynamic control of defect arrays. By modulating intrinsic acoustic parameters, including amplitude, frequency, phase, and wavevector, we achieve precise modulation of acoustic field and streaming field, that consequently control over key characteristics of the defect textures, including domain size, morphology, lattice symmetry, and spatial distribution. Additionally, we demonstrate dynamic translation of defect arrays along defined direction, revealing a previously inaccessible way of topological matter transport. More broadly, these findings establish a versatile acoustically driven platform for dynamic and programmed control in topological soft matter, opening avenues for mesoscopic material design guided by reconfigurable topological interactions.

Result

Concept of the acoustic-actuated topological defect

To generate a structured acoustic field, multiple SAW beams with rotational symmetry (4 or 6 beams) are designed. Conceptually, the device consists of two orthogonal pairs of interdigital transducers (IDTs) on a 128° Y-cut lithium niobate (LN) piezoelectric substrate oriented at 45° to the x-axis (Fig. 1a). This configuration allows orthogonal SAWs to interfere and form a standing surface acoustic wave (SSAW), generating a spatially structured acoustic field that supports nontrivial topologies and induces steady acoustic streaming. (Fig. 1b, c).

Fig. 1: Essential concept of the acoustic-actuated topological defect.

a Schematic of the acoustic device with two orthogonal pairs of interdigital transducers (IDTs) generating standing surface acoustic wave (SSAWs), enabling precise control over the defect array. b Schematic of the mechanism of interaction between the acoustic wave and the fluid medium, illustrating the generation of acoustic streaming. The inset depicts LC molecular reorientation induced by streaming-driven forces. c Illustration of parameter modulation (amplitude, frequency, and phase) of acoustic waves, allowing the generation of various soft lattice structures for manipulating topological defects. d Spin vector field of the acoustic velocity exhibiting meron-type topological textures. Shown are the intensity distribution of the acoustic pressure field (bottom) and the corresponding acoustic spin orientation distribution at the pressure antinode center (top). e Acoustic velocity spin component distribution along the z-axis, and f in the xy plane. g LC director configuration at the core of a topological defect viewed along the z-axis and h corresponding director distribution in the xy plane.

This SSAW system can be described by two spatially varying fields: a scalar pressure field p and a vector velocity field v. The spatial gradient of the acoustic pressure gives rise to an oscillatory first-order velocity component³⁸, v = (1/iωρ)∇p, where ω is the angular frequency of the acoustic wave and ρ is the mass density of the medium (see details in Supplementary Note 1). Through nonlinear and dissipative effects, these first-order fields generate a time-averaged acoustic force that drives the steady streaming flow. This formulation is analogous to reconstructing a three-dimensional (3D) surface plasmon polariton field from the gradient of a vertical electric field⁴⁶, or to deriving a gravity water-wave field from surface elevation gradients⁴⁷. The real-space topology of the acoustic field is characterized by the skyrmion number S, computed from the normalized real velocity field ${{{\bf{n}}}}_{{\mbox{v}}}={\mbox{Re}}\{{{\bf{v}}}\}/\left|{\mbox{Re}}\{{{\bf{v}}}\}\right|$ as:

$${{\mbox{S}}}=\frac{1}{4{{\rm{\pi }}}}\iint {{{\bf{n}}}}_{{\mbox{v}}}\cdot (\frac{\partial {{{\bf{n}}}}_{{\mbox{v}}}}{\partial x}\times \frac{\partial {{{\bf{n}}}}_{{\mbox{v}}}}{\partial y}){{\mbox{d}}}x{{\mbox{d}}}y$$

(1)

This topological structure appears in the antinode region, where the velocity field exhibits a rotationally symmetric meron pattern, characterized by a gradual transition of vector orientation from vertical at the core to horizontal at the periphery. (Fig. 1d and Supplementary Fig. 1). Within this structured velocity field, the acoustic pressure gradients generate oscillatory motions that, through nonlinear viscous and thermal dissipation, transfer momentum to the medium and establish a steady acoustic streaming flow. The resulting streaming vortices produce spatially varying shear, which exerts viscous torques on the nematic director. These torques realign the LC molecules along the local flow direction, leading to defect configurations that inherit the symmetry and topology of the underlying acoustic meron lattice (Fig. 1e-h). Owing to the topological robustness of the meron lattice, the system ensures uniform defect formation across large areas. Beyond this intrinsic spatial stability, it also offers a high degree of tunability: the amplitude [A_i], frequency [f_i], phase [φ_i], and wave vector [k_i] of each intrinsic component in the acoustic lattice can be controlled independently or in combination (Fig. 1c). This programmability enables dynamic reconfiguration of the acoustic topological field, offering multiple degrees of freedom for dynamic manipulation of LC topological defects (see Supplementary Table 1).

Reconfigurable formation of defect array

The inherent periodicity of the acoustic meron lattice offers a unique opportunity to simultaneously generate reconfigurable topological defect arrays over large areas (Fig. 2a). As shown in Fig. 2a–h, the formation of a defect array texture follows a generic process, where increasing the amplitude of the acoustic field plays a key role. Polarizing optical microscopy (POM) reveals that independent umbilic defects are spontaneously formed at each meron location (i.e. antipode pressure node) across the entire superimposed region of the SSAW when the acoustic field amplitude exceeds the threshold. These defects form a highly ordered square array, ensuring a uniform and periodic structure across the entire region. Magnified images with the corresponding Fourier transform patterns (leftmost image in Fig. 2a) confirm that the formation of these structures is uniform over several cm² under our experimental conditions (Supplementary Fig. 2). By inserting a λ wave plate, the variation of the interference color allows us to investigate the local orientation of the director qualitatively. As shown in Fig. 2e–h, the color in the first and third quadrants of each umbilic defect shifts to green, except near the center, indicating an increase in optical retardation. In contrast, the color in the second and fourth quadrants changes to yellow, suggesting a decrease in optical retardation. Rotating one of the polarizers away from the cross-polarized state causes the umbilic defect to rotate in the same direction (Supplementary Fig. 3). This information suggests the existence of a ‘+ 1’ strength topological defect of the radial type, rather than the spiral type. In the present type of soft acoustic field, the center of the node and antipode lines always hosts a hyperbolic hedgehog defect with ‘−1’ strength due to the topological constraint of the director field. It is noted that nearly hundreds of these defects are packed with regular spacing, and it takes an average of 0.45 seconds to completely fill the area (Supplementary Fig. 4). This response time is much lower than the several tens to hundreds seconds through electrically-induced nematic flows²⁸.

Fig. 2: Reconfigurable formation of defect array.

a–d Crossed polarizing optical microscopy (POM) images and (e–h) POM images with a 530 nm phase retardation plate showing the evolution of a highly ordered defect array controlled by amplitude. Insets display the corresponding Fourier-transformed images. Scale bar, 200 μm. i Illustration of chiral symmetry breaking under amplitude control and the j corresponding optical intensity measured along the defect diagonal. k Simulated plot of the acoustic pressure distribution in the LC layer on the xz plane. l–m Comparison of pattern features at lower (l) and higher (m) amplitudes, each after 30 cycles. n, o Heat maps showing cross-correlation values from 30 patterns at the same amplitude. Each pattern calculation was conducted between single defect images (n) and defect array images (o). The color bar represents the similarity index, where values along the diagonal represent correlations within the same image set, and off-diagonal values represent correlations between different images.

The micrographic appearance of defects changes dramatically with a further increase in amplitude. We first explored the effects of simultaneously increasing the amplitude of two pairs of IDTs (e.g. [A_i] to [A_i + δA]). These topological defects display the spontaneous breaking of chiral symmetry corresponding to the pinwheel configuration and expand their domain size (Fig. 2i, j). It is clearly seen that the coexistence of the two types of opposite handedness. The observed chiral symmetry breaking arises from twist distortions, which are favored due to the twist elastic constant (K₂₂) being smaller than the splay (K₁₁) and bend (K₃₃) elastic constants⁴⁸. To contextualize the experimental results further, we simulated the corresponding acoustic pressure with various amplitude using finite element simulation method. The computational result demonstrates the acoustic pressure increase in depth dimension and expand the region in the xy plane, which agree with the experimental result (Fig. 2k). This indicates that the soft acoustic lattice region expands in the xy plane, leading to an increase in defect size. To further examine the effect of targeted acoustic modulation, we selectively activated a single pair of IDTs (i.e. [A₁, A₃] to [A₁ + δA, A₃ + δA]). This selective modulation introduced distinct asymmetries in the defect structures, suggesting that directional change in shape of meron significantly impact both defect size and shape. By isolating the effect of a single pair of IDTs, we observed the defects gradually elongating from a pinwheel shape into an olive-like form along the diagonal, ultimately leading to the formation of new defect structures at junction points (Supplementary Fig. 5 and Supplementary Movie 1).

To evaluate the reconfigurability and stability of the defect arrays, we quantified their topographical feature similarity using the feature similarity (FSIM), as detailed in Supplementary Note 2. Robustness under varying acoustic conditions was then tested by selecting representative high and low acoustic field amplitudes, both with and without actuation. In all cases, the defect arrays maintained consistently high FSIM values over 30 reconfiguration cycles, indicating excellent repeatability (Fig. 2l, m). We further analyzed the spatial consistency of defect configurations by computing both defect-to-defect and array-to-array similarity across cycles. As shown in Fig. 2n, o, the cross-correlation map exhibits typical diagonal pattern. This diagonal structure not only reflects high self-consistency within individual defect patterns, with all intra-pattern correlation coefficients exceeding 0.9803, but also indicates high similarity between distinct configurations across different cycles, with all inter-pattern correlations above 0.9817. Together, these results demonstrate that the acoustic-induced topological defect array exhibits uniform characteristics across the entire region, confirming its high reconfigurable capability.

Three-dimensional defect structures formed in acoustic field

To gain deeper insight into the mechanism behind defect formation, we conducted a detailed investigation of their internal structures. Notably, the defects did not reach extinction under crossed polarizers, particularly at the center, with the extent of extinction regions increasing with amplitude (Fig. 2j). This observation suggests that these defects can be identified as 3D point defects, exhibiting a spontaneous “escape” along the depth direction, which leads to optical rotation effects. Further optical micrographs obtained at different focal depths reveal lens-like effects due to deformation in the z-direction (Supplementary Fig. 6). The escape direction may be upward or downward with equal probability, as both orientations have equivalent free energy⁴⁹. Thus, this chiral symmetry breaking results in four distinct topological configurations of ‘+1’ strength, as shown in Supplementary Fig. 7. To characterize the precise structure, we utilized fluorescence confocal polarizing microscopy (FCPM) to reconstruct the 3D director field orientation (see Methods for details). For FCPM measurements, a commercial chromophore was mixed with the LCs, with the chromophores aligning parallel to the local director. The chromophores emit their strongest fluorescent signal when the excitation optical field polarization has the largest projection onto their orientation, following the relationship I ∝cos⁴θcos⁴φ, where θ represents the out-of-plane polar angle measured from the xy plane, and φ is the azimuthal angle measured from the x-axis in the xy plane. By capturing FCPM images with varying laser light polarizations, we reconstructed the director field, revealing point defects and the localized director field configuration around them (Fig. 3a–d and Supplementary Fig. 8). The reconstructed director field was then used to simulate FCPM signal images and compute the free-energy density distribution, as shown in Fig. 3e, f. The agreement between simulated and experimental images confirms the accuracy of the director field reconstruction, showing that the director field undergoes a nontrivial out-of-plane rotation rather than a simple in-plane twist (Fig. 3g). This validates that the defects driven by the acoustic field exhibit a cylindrical shape with curvatures and an upward escape symmetry breaking configuration.

Fig. 3: Three-dimensional defect structures formed in acoustic field.

a 3D visualization of the director field structures in umbilic defect filaments. b Reconstruction of the director field around the defect center in the xy plane at the midplane of the cell. c POM image of a left-handed twist defect. Scale bar, 50 μm. d Experimental and e simulated XY cross-sectional FCPM images in the midplane of the cell. f Free energy density distribution, with background colors representing its magnitude. The calculations are based on reconstructed director fields obtained from fluorescence confocal polarizing microscopy (FCPM) data. g The director distribution around defect in yz plane. The background color denotes the angle θ between the LC director and the z-axis, with red and blue indicating regions where the director tilts in opposite directions. h, i Simulated pressure distribution (h) and streaming patterns (i) in the xz plane, generated by vertical and horizontal vibrations. In (h), the white arrow indicates the direction of the acoustic streaming. Streaming lines rotate clockwise or counterclockwise from displacement nodes to neighboring displacement antinodes, with arrows indicating rotation directions. j The simulated defect behavior driven by the acoustic field is solved using the anisotropic force Ginzburg-Landau equation. The left and right figures correspond to configurations under low and high acoustic field intensities, respectively.

To identify the dominant mechanism responsible for the acoustic-induced generation of topological defects, we consider three main factors: (i) acoustic radiation force, (ii) thermal effects due to wave attenuation, and (iii) acoustic-induced flow (Supplementary Discussion 1, Supplementary Fig. 9 and Fig. 10). These findings collectively suggest that flow-induced mechanisms are primarily responsible for the generation of topological defects under acoustic excitation. Our numerical results reveal periodic acoustic streaming in the yz plane, forming vortex flows reminiscent of Rayleigh-Bénard convection rolls (Fig. 3h, i and Supplementary Note 3). These flows originate from a pressure node, rotate clockwise or counterclockwise toward adjacent antinodes, and then return to the original node. The strongest flow occurs at the junction between two convection vortices, where LC molecules are effectively realigned, leading to the formation of topological defects.

To gain the insight into the mechanism about acoustic driven defect, we constructed an analytical model based on the minimization of free energy. Earlier studies have described the interaction between the acoustic field and LCs, which can be represented by the following functions⁵⁰: ${F}_{{\mbox{s}}}\,=\,\frac{{u}_{2}}{2}{(\Delta \rho )}^{2}{\left({{\bf{k}}}\cdot {{\bf{n}}}\right)}^{2}$ where u₂ is coupling coefficient, ∆ρ is the local density. The mathematical form of the acoustic interaction is analogous to the interaction of a director with the electric or magnetic field, suggesting that the acoustic interaction may have similar aligning effects. Through the Euler equation, we can obtain k = −ρωv/p. This supposition allows us to consider a Frank-Oseen free energy function with the minimal necessary terms:

$${F}_{{\mbox{el}}}=\frac{{K}_{11}}{2}{(\nabla \cdot {{\bf{n}}})}^{2}+\frac{{K}_{22}}{2}{({{\bf{n}}}\cdot (\nabla \times {{\bf{n}}}))}^{2}+\frac{{K}_{33}}{2}{({{\bf{n}}}\times (\nabla \times {{\bf{n}}}))}^{2}+\frac{{{\mbox{u}}}_{2}{\mbox{a}}}{2}{\left({{\bf{v}}}\cdot {{\bf{n}}}\right)}^{2}$$

(2)

which includes the first three elastic energy contributions characterized by the elastic constants K₁₁, K₂₂ and K₃₃, along with an interaction coupling the system to the acoustic field. We replaced the perturbative ansatz ${{{\bf{n}}}}\,=\,({n}_{1},{n}_{2},1{-}({{n}_{1}}^{2}+{{n}_{2}}^{2})/2)$, where n₁ and n₂ are small perturbations. The next step is to find the condition at which the first unstable distorted mode grows, that is, we consider an ansatz of the form n₁ = usin(z/d)e^σt and n₂ = vsin(πz/d)e^σt, where these components satisfy the homeotropic boundary conditions at z = 0 and z = d (d is the cell thickness).

By introducing the complex order parameter A(x, y, t) = αe^iθ ≡ u + iv close to the deformation, we derived a forced anisotropic Ginzburg-Landau dimensionless equation from first principles³² (see Supplementary Note 4):

$${\partial }_{{\mbox{t}}}{{\mbox{A}}}=\mu {{\mbox{A}}}+{\partial }_{{{\rm{\eta }}}\bar{{{\rm{\eta }}}}}{{\mbox{A}}}+{{\rm{\delta }}}{\partial }_{{{\rm{\eta }}}{{\rm{\eta }}}}\bar{{{\rm{A}}}}{{-}}{{\mbox{A}}}{|{\mbox{A}}|}^{2}+{{\mbox{b}}}\frac{{{\bf{v}}}\left(z\right)}{z}{{{\boldsymbol{\nu }}}}_{z}{{\mbox{e}}}^{{\mbox{i}}\theta }$$

(3)

Here, μ is the bifurcation parameter, accounting for the competition between elastic and acoustic forces. The second term represents diffusion arising from elastic coupling, the third term embodies the anisotropic correction due to the differing energetic costs of various deformations, the fourth term corresponds to nonlinear saturation, and the final term represents the forcing produced by the topological distribution of the acoustic field within the valve. We solved this equation using a variational method, which ultimately yields a stable solution by minimizing the free energy function (Supplementary Movie 2 and 3). Beginning from an unstable uniform state with noise, numerous +1 and −1 vortices spontaneously emerge. These vortices then collide and annihilate, eventually leaving only a single positive vortex. As shown in Fig. 3j, at low forcing, the defect exhibits fourfold symmetry; however, as the forcing gradually increase, spontaneous symmetry breaking occurs. These results agree with experimental observations, suggesting that acoustic forcing may be the underlying mechanism behind the formation of topological defects.

Reversible transformation of defect patterning

The frequency-controlled acoustic meron lattice enables precise and versatile spatial patterning in a fully reversible and programmable manner. Theoretical calculations of the Gor’kov potential field indicate that frequency mismatch between orthogonal SSAW pairs alters the periodicity and symmetry of the resulting acoustic wavefield (Fig. 4a, d). Specifically, when both orthogonal SSAW pairs are driven at the same frequency (f_x = f_y), a well-defined meron dot array form with a periodicity of $\sqrt{2}\lambda /2$ between neighboring antinodes (Fig. 4a). By slightly shifting the excitation frequency in one direction (f_x = f_y + $\delta$f), the spacing between adjacent antinodes changes to $\lambda /2$ (Fig. 4d) producing a denser and more uniform lattice. This frequency-driven tuning enables fine control over the spacing and geometry of the defect lattice, highlighting the programmability and responsiveness of the acoustic meron platform (Supplementary Note 5).

Fig. 4: Reversible transformation of topological patterning.

a Simulated Gor’kov potential fields with identical excitation frequencies [f_x = f_y], yellow regions represent antinodes, with the distance between neighboring nodes equal to $\sqrt{2}/2$ of the wavelength. b,c Lattice of umbilic defects with topological charge +1 located at the center of each square formed by antinodes, shown in POM images without (b) and with (c) a 530 nm phase retardation plate, scale bar 100 μm. This lattice is generated by identical frequency excitation. d Simulated Gor’kov potential fields with different excitation frequencies [f_y = f_x + δf], where the distance between neighboring nodes is half the wavelength. e,f POM images of a lattice of umbilic defects with topological charge +1, located at the center of each antinode square; e shows the lattice without a wave plate, and f with an inserted wave plate. This configuration is generated by different frequency excitation. g Topological analysis of the different excitation states with the basic unit length set at half the wavelength. h The radial distribution function g(r) for different excitation states, indicating the spatial distribution of defects across the two frequency excitation conditions.

The topological defect patterning differs between identical and mismatched excitation frequencies (Fig. 4b, c and Fig. 4e, f, respectively). Under identical-frequency conditions, each +1 defect is consistently located at an acoustic antinode, centered within a square formed by four neighboring pressure nodes that host –1 defects. This arrangement forms a checkerboard lattice of alternating +1 and –1 defects, with a unit cell dimension matching that of the meron array (Fig. 4g). When different excitation frequencies are applied, the acoustic lattice not only positions +1 defects at square centers but also introduces additional defects between adjacent antinodes, as reflected in the shorter-range positional correlations observed in the radial distribution function g(r) (Fig. 4h). Notably, under unequal-frequency conditions, not all +1 defects originate from antinodes. Some +1 defects also form at pressure nodes, driven by the emergence of symmetric convection flows. As a result, the overall defect density nearly doubles compared to the structures formed under equal-frequency excitation. At equal excitation frequencies, the higher lattice energy imposes a greater free energy cost for defect formation, thereby minimizing defect density and promoting more ordered structures.

Ordered collective locomotion of defect array

Time-variant phase control allows for precise manipulation of meron lattice propagating in multiple directions within a two-dimensional (2D) plane, thereby enabling highly ordered manipulation of collective defect translations with enhanced flexibility. With the capability to adjust the phases of SAWs both simultaneously and independently, the orthogonal pair of SSAWs can generate a phase difference between the x and y direction SAWs, which is denoted as Δφ = φ_x − φ_y. Simulation of the Gor’kov potential field indicates that this phase difference Δφ can induce gradual in-plane translation of the entire SSAWs field, as illustrated in Supplementary Fig. 11. As previously described, defects can be nucleated and formed at the antinodes of SSAW field. When the phase differences change from Δφ to Δφ + δφ, the location of meron shifted by a vector Δx. Consequently, this acoustic-induced movement allow us to achieved the translation of defect array by the incremental increase of Δφ in the modulated excitation signals. The trajectory of this translation and the morphological evolution of the defect arrays on a rectangular lattice are depicted in Fig. 5a–i and Supplementary Movie 4, respectively. During the phase transition, the moving meron lattice induces shear flow, causing morphological distortion in the defects (Fig. 5m–q). Once the modulation phase control is turned off, the defects gradually revert to their pinwheel structure due to elastic relaxation. In addition, the mean-square displacement (MSD) is scales quadratically with time at modulation of phase when modulated phase difference is applied, but average to zero at no phase modulation (Fig. 5j). The discrete differences in the x and y coordinates exhibit normal distributions, as shown in Fig. 5k. This indicates that the variations in both dimensions exhibit a Gaussian distribution, with discrete differences centered around the mean and symmetrically declining in probability with increasing deviation.

Fig. 5: Ordered collective locomotion of defect array.

a Trajectories of defects driven by the phase shifting from Δφ to Δφ + δφ, with colors representing elapsed time. The defects net displacement Δr(t) is shown as a function of time according to the color scale with red and blue. b–i Successive crossed POM images showing the motion of the defect array induced by phase differences, scale bar 150 μm. j Mean square distance (MSD) plotted as average over time of net displacement (Δr²) and as separate displacements along the x- and y-axis (Δx² + Δy²). (k) Distribution of displacements along the x- and y-axis. l Displacement as a function of phase difference, characterizing the relationship between phase modulation and defect movement. m–q Visualizations of south pole preimages (light red) and locations of point defects (yellow) for a single umbilic defect (m) and a square lattice of defect arrays (n), displayed in both the xy plane and in 3D perspectives (o–q). Red arrows indicate the direction of shearing and movement caused by phase shifts.

To quantitatively examine the ordering and directionality of defect collective translation, we measured the instantaneous velocity order parameter:

$${{\mbox{V}}}_{{\mbox{a}}}\left({{t}}\right)=\frac{\left|{\sum }_{{i}=1}^{{N}}{{{\bf{v}}}}_{0}{{\mbox{e}}}^{{{\mbox{i}}}{{{\rm{\varphi }}}}_{{i}}({t})}\right|}{{N}{{{\bf{v}}}}_{0}}$$

(4)

Where v₀ is the speed of translation and φ_i is an instantaneous angle between the direction of motion of the i-th defect and the average velocity vector. In our experiments, all the defects move in one direction with a high order of V_a ≈ 0.94, indicating the acoustic field is highly effective for order movement of defects, as shown in Supplementary Fig. 12. For two orthogonal pairs of IDTs, the relationship between phase change Δφ and spatial translation vector is derived analytically $\Delta {{\bf{x}}}={{\bf{x}}}+\left(\updelta \varphi/2{{\rm{\pi }}}\right){{{\bf{e}}}}_{x}+\left(\updelta \varphi /2{{\rm{\pi }}}\right){{{\bf{e}}}}_{y}$ (see details in Supplementary Note 6). The displacement values measured in the experiment closely match those predicted by theoretical calculations, as demonstrated in the corresponding Fig. 5l. This alignment between the experimentally measured displacements and the theoretical predictions validates the theoretical model used to control and predict defect translation movements within the acoustic field. It is noteworthy that the velocity of the defect moving along the desired path is primarily determined by the rate of change in the phase difference. Additionally, the translated direction of topological defects in 2D plane can be easily tuned by changing the phase difference of the applied SSAWs. As illustrated in Supplementary Movie 5, a positive phase difference (Δφ > 0) causes defects move in the direction of the first quadrant, while a negative phase difference (Δφ < 0) results in motion towards the third quadrant. With this capability for precise array translation, we can further use this acoustic manipulation to explore fundamental physics in dynamics of defect behind the translation.

Expand to high rotational symmetry modulation

By engineering IDTs with sixfold symmetry, the system accesses an expanded acoustic parameter space, allowing for finer, more versatile manipulation of topological defect networks (Fig. 6a). As a conceptual validation, we present a hexagonal configuration that generates a sixfold symmetric skyrmion lattice (Supplementary Fig. 13), where both the density and morphology of defects can be dynamically programmed. For instance, when all six IDTs are driven coherently with identical wavevectors and zero phase offsets (wavevectors k₁–k₆ and phases of 2nπ), the resulting pressure antinodes self-organize into a pristine hexagonal lattice with a periodicity of $2\lambda /\sqrt{3}$. This induces a transition from a conventional quadrilateral geometry to a highly ordered hexagonal geometry, as shown in Fig. 6b–d. In contrast, selective activation of only three non-adjacent IDTs k₁, k₃, and k₅ rotates the entire lattice by 30 degrees and compresses the lattice constant to one-third of the wavelength, effectively enabling angular and spatial reconfiguration of the defect configuration (Fig. 6e–g). More strikingly, by modulating both the wavevectors and relative phases of the input signals, we unlock shape transformation at the single-defect level, with topological shape morphing from squares into triangles or rectangles in real time. Specifically, when all six IDTs are activated, a π phase shift is introduced starting from the fourth up to the sixth input channel [φ₁–φ₃, 2nπ, φ₄–φ₆, 2(n + 1)π], breaking the inherent sixfold rotational symmetry of the interference field. This controlled symmetry breaking leads to a deformation of the Gor’kov potential field and velocity field landscape, transitioning the originally circular or hexagonal acoustic potential wells into anisotropic shapes, such as triangles (Figs. 6h and 6i). Both simulations and experiments confirm that this transformation precisely reshapes the associated defect geometry, demonstrating dynamic control over individual topological morphologies (Fig. 6h–j). Furthermore, when only four IDTs [k₁, k₂, k₄, and k₅] are activated and a π phase shift is applied to k₅, the interference field exhibits a pronounced symmetry distortion. This results in elongated potential contours along specific axes, reshaping the original defect into rectangular configurations (Fig. 6k–m). Additionally, this high degree of spatial and morphological control is not limited to a single LC material. We confirmed the generality of the method across multiple LC systems, underscoring the robustness and adaptability of our high-symmetry acoustic design (Supplementary Fig. 14 and Supplementary Movie 6). Notably, both the global field configuration and the resulting defect morphologies are dynamically reconfigurable in real time, further highlighting the programmability of our approach (Supplementary Movie 7).

Fig. 6: Modulation of high rotational symmetry.

a Schematic illustration of the high rotational symmetry IDT structure realized by the interference of six coherent acoustic waves, enabling multifunctional control of the defect array. The inset figure depicts the expanded parameter space, including wavevector, amplitude, frequency, and phase. b–g Control over wavevector combinations changes the periodicity of the defect array (right column). Experimental and simulated results show hexagonal defect arrays, their corresponding Gor’kov potential fields (left column), and velocity fields (middle) when six IDTs [k₁–k₆] are simultaneously activated (b–d), compared with the selective activation of three IDTs [k₁, k₃, k₅] (e–g). h–m Combined modulation of wavevector and phase enables transformation of defect configurations from the original arrangement into triangular (h–j) or rectangular (k–m) structures. Shown are simulated results, their corresponding Gor’kov potential field (h,k) and acoustic velocity field (i,l), and the experimentally observed POM image (j,m). The triangular defect structure is generated by activating all six wavevectors [k₁–k₆] with phase settings [φ₁–φ₃, 2nπ, φ₄–φ₆, 2(n + 1)π]. Additionally, a rectangular lattice emerges when only four wavevectors [k₁, k₂, k₄, k₅] are activated, with corresponding phase settings [φ₁, φ₂, φ₄, 2nπ, φ₅, 2(n + 1)π], all scale bars 100 μm.

Discussion

In this study, we introduce an acoustic approach for the dynamic and programmable manipulation of topological defect patterns in liquid crystals. By leveraging a periodic topological acoustic field, this method enables fully reversible control over defect morphology and spatial distribution, including domain size, shape, lattice symmetry, and large-scale translation. The mechanism is driven by acoustic momentum transfer and further enhanced by acoustically induced flow, offering high spatial precision and exceptional thermal stability. Distinct from conventional acoustic approaches that primarily emphasize the pressure field, our results indicate that the velocity field and the accompanying streaming flow play an essential role in governing molecular alignment and topological reconfiguration. This strategy represents a fundamental shift from traditional manipulation techniques based on electromagnetic fields to a mechanically driven framework. Unlike optical or electric field methods, which often rely on specific dielectric properties, require patterned electrodes, or are limited by thermal diffusion, the use of acoustic waves introduces following critical advantages: (i) LC defects empowered by the SSAW field enable the formation of dynamically tunable and reconfigurable topological structures, which enhance spatial uniformity and topological stability. (ii) Acoustic fields operate independently of the optical or dielectric characteristics of the medium, allowing their application in a wide range of LC systems, even in turbid or light-absorbing environments where electromagnetic methods lose effectiveness. (iii) Mechanical energy transmission enables efficient molecular alignment and flow control at low power with minimal heat generation. This transition in actuation paradigm opens up new possibilities for reconfigurable, energy-efficient, and scalable topological control within liquid crystal systems. Furthermore, our findings contribute a crucial mechanical field-based strategy, completing a previously missing component in the broader framework of field-driven manipulation of topological structures in liquid crystals.

Beyond the steady-state configurations demonstrated here, the acoustic field may also induce dynamic evolution of the director and defect structures as the system relaxes toward equilibrium. The nonlinear coupling between flow and director reorientation can give rise to such transient dynamics, which are typically suppressed once the steady state is reached⁵¹. Moreover, under periodically modulated or pulsed acoustic excitation, this nonlinear coupling could potentially lead to richer spatiotemporal behaviors, such as time crystals^52,53, solitonic structure propagation^{54,55,56,57,58}, or soft actuator^59,60 like mechanical responses in liquid crystal architectures. Investigating these dynamic regimes would provide deeper insight into the nonequilibrium physics of acoustically driven soft-matter topologies.

While these advantages mark a significant advance over conventional approaches, certain physical limits inherent to the acoustic system still constrain the ultimate resolution of the technique. The most obvious factor affecting controlled actuation is the absorption attenuation of SAWs at high frequencies during propagation in the LN substrate. Intuitively, using higher-frequency SAWs (e.g., hundreds of MHz) could enhance controlled actuation by creating smaller nodes and antinodes, allowing for more precise alignment of the LC molecules. However, the medium’s viscosity causes internal friction between particles, converting some of the acoustic energy into heat. This heat, combined with thermal conduction, leads to additional energy loss through heat exchange between dense and rarefied regions, resulting in unwanted thermal effects that cause unintended realignment of the LC molecules. Consequently, this absorption attenuation, typically proportional to the square of the acoustic wave frequency, limits the resolution of the actuation in our system. These factors result in a resolution on the scale of tens of micrometers in our acoustic method. Subsequent developments may explore advanced field-shaping techniques, including custom IDTs design⁶¹, harmonic wave synthesis⁶², and holographic acoustic modulation⁶³, to enable the creation of finer and more complex topological textures with improved spatial resolution and minimal hardware overhead.

In summary, we present a versatile and conceptually elegant strategy for sculpting acoustically modulated topological structures in LCs. This approach enables the creation of diverse defect configurations with tunable periodicities through precise control of acoustic parameters. The resulting morphologies and vortex textures are quantitatively described by acoustic interference theory and the Ginzburg-Landau model, offering a solid foundation for the inverse design of reconfigurable topological architectures. Beyond static patterning, controllable array-level translation facilitates dynamic exploration of defect evolution during motion, unlocking regimes inaccessible to conventional electromagnetic manipulation. Such topology-based designs have potential for novel tunable photonic applications, including structured light and micro-cargo transport^64,65. Moreover, the concept of virtual geometric confinement—realized via the soft acoustic lattice—offers a promising framework extendable to other soft material systems, such as synthetic colloids, microrobots, and block copolymers, among others⁶⁶.

Methods

Materials and cell fabrication

We employed a commercial nematic LC, 4’-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47) with negative dielectric and conductive anisotropies (Nematel Gmbh & Co. KG, Germany) for majority of experimental and computational studies. The mixture of NLC was modulated by doping with 0.005 wt.% of tetrabutylammonium bromide (TBAB, Sigma-Aldrich) using dichloromethane as a solvent. In addition, the nematic cells exhibit strong perpendicular orientation of n₀, induced by surfactant monolayer of N, N-Dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chlorid (DMOAP, Aladdin). The ITO glass slides as the both covering (the upper slides) and bottom layer were submerged in a 10 wt.% DMOAP aqueous solution for 30 min at room temperature. Then, the slides were rinsed several times with deionized water to eliminate the unbound DMOAP from the surface. Subsequently, the DMOAP decorated glass slides were dried with nitrogen flow and baked in a 100 °C oven for one hour to permit the cross-linking of DMOAP. In general, the substrates were assembled using double-sided tape, creating a cell gap of ∼20.1 μm, which was measured by the thin film interference method. Finally, the nematic LC mixture was injected into the cell in the isotropic phase at 70 °C due to the capillary effect. The temperature of the sample is maintained using a hot stage with a controller (Linkam, PE94).

Acoustic chip fabrication

The fabricated acoustic chip consists of an ITO-coated glass cover and an array of IDTs patterned on a piezoelectric substrate. A 500 μm-thick 128° Y-cut lithium niobate (LiNbO₃) substrate was used to generate the acoustic meron lattice, while a 500 μm-thick Z-cut LiNbO₃ substrate was used for the skyrmion lattice. To construct the device, two orthogonal pairs of IDTs were deposited on the 128° Y-cut substrate and three pairs on the Z-cut substrate. Each IDT comprises a 5 nm Cr adhesion layer and an 80 nm Au conductive layer, fabricated using standard photolithography, electron-beam evaporation, and lift-off processes. Each pair of IDTs is capable of generating SSAWs with independently controlled modulation. The sample chamber is assembled at the center of the orthogonal IDT pairs, consisting of an ITO-coated glass as the top cover. The cell thickness is maintained at 20 μm, defined by double-sided tape spacers and confirmed by standard interferometry.

Optical microscopy and electric characterization

To analyze the generation and manipulation of topological defects in LCs, the samples were observed using a polarized optical microscope (Leica, DM750P) equipped with a digital camera (Sony, ESISPM20000KPA). The acoustic–optical properties were characterized using a 632.8 nm He–Ne laser (Pacific Lasertec, 05-LHP-991), a linear polarizer (JCOPTIX, OPPF1-VIS), and a Si amplified detector (Thorlabs, PDA100A), enabling detailed measurement of the acoustic response. The videos were recorded using Captura software at a frame rate of 10 fps. The trajectories of the defect array were analyzed using the open-source software ImageJ, employing both the Manual Tracking and TrackMate plugins for manual and automated tracking as needed. The velocity of the defects was determined by calculating the displacement between consecutive time frames. The acoustic chip was powered with a sinusoidal AC signal from a function generator (UNI-Trend Technology Co. Ltd, UTG962) and an amplifier (Minicircuit, LZY-22 + ).

Fluorescence confocal polarizing microscopy

A laser scanning confocal microscope (Zeiss, LSM900) was used to elucidate the director configuration of defects. The NLC samples were doped with 0.01 wt.% of a fluorescent dye, 7-diethylamino-3,4-benzophenoxazine-2-one (Nile Red, Sigma-Aldrich). Due to its shape anisotropy, Nile Red molecules orient along the director field. A laser with a wavelength of 552 nm and linear polarization excites the dye molecules. The detected fluorescence intensity depends on the angle between the polarization direction and the director. A laser confocal xyz scan was performed under four linear polarization angles in the xy plane: α₁ = 0, α₂ = π/4, α₃ = π/2, and α₄ = 3π/4. This scan collects full fluorescence intensity information, which is used to calculate the orientation of the director, given by n = (cosφcosθ, sinφcosθ, sin$\theta$). Here, $\varphi$ is the azimuthal angle measured from the x-axis in the xy plane, and θ is the out-of-plane polar angle measured from the xy plane. The orientation of the director in the xy plane follows the equation⁶⁷:

$${{\varphi }}=\frac{1}{2}\arctan \frac{{{I}}_{{{\rm{\pi }}}/4}{-}{{I}}_{3{{\rm{\pi }}}/4}}{{{I}}_{0}{-}{{I}}_{{{\rm{\pi }}}/2}}$$

Total intensity ${I}_{\exp }$ is calculated as: ${I}_{\exp }$ = 1/2 (${I}_{0}$ + ${I}_{{{\rm{\pi }}}/4}$ + ${I}_{{{\rm{\pi }}}/2}$ + ${I}_{3{{\rm{\pi }}}/4}$). The z-dependent background ${I}_{{\mbox{offset}}}$ and intensity normalization ${I}_{{\mbox{norm}}}$ are applied to compute the out-of-plane angle $\theta$ according to the following equation:

$${I}_{\exp }={I}_{{\mbox{offset}}}+{I}_{{\mbox{norm}}}{\cos }^{4}\theta$$

Numerical modeling and simulation

2D finite element models were constructed using the pressure acoustics module in finite element analysis software to simulate the distribution of pressure fields and acoustic streaming. We also used finite element analysis software to solve the Ginzburg-Landau model. Other data analysis and calculation was performed using homemade MATLAB code. The details of numerical simulation methods were provided in Supplementary Notes 1 to 6.