Harnessing acoustic topology for dynamic control of liquid crystal defects

Domain: physics
Published: 2026-01-12
Editorial outcome: minor_revision

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 elasticity2,3, guide hierarchical self-assembly4,5, 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 transitions10,11. These defects exhibit rich real-space topology and spatially varying director fields that can be harnessed for tunable optics12–14, microscale templating15–17, and dynamic sensing18,19. 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 inclusion20,21 or patterned substrates22–27, 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 electric28,29, magnetic30, or optical fields31–34 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 matter35,36. 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 transfer39–41, reorienting the director field and enabling mechanically driven manipulation42. Previous demonstrations using bulk acoustic waves (BAWs) have achieved macroscopic alignment effects through such mechanisms43,44, 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 controlover 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.

Results
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). 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/i\omega\rho)\nabla p, where \omega is the angular frequency of the acoustic wave and \rho 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 n = Re[v]/|Re[v]| as:

S = 1/4\pi \iint n \cdot (\partial_x n \times \partial_y n) dxdy (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], frequency [f], phase [\phi], and wavevector [k] 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 \lambda 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.

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 + \delta A]). 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 (K_22) being smaller than the splay (K_11) and bend (K_33) 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. [A_1, A_3] to [A_1 + \delta A, A_3 + \delta A]). 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 \propto cos^4 \theta cos^4 \phi, where \theta represents the out-of-plane polar angle measured from the xy plane, and \phi 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.

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 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_s = u^2/2 (\Delta\rho)^2 (k \cdot n)^2 where u^2 is coupling coefficient, \Delta\rho 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 = -\rho\omega v/p. This supposition allows us to consider a Frank-Oseen free energy function with the minimal necessary terms:

F = K_11/2 (\nabla \cdot n)^2 + K_22/2 (n \cdot (\nabla \times n))^2 + K_33/2 (n \times (\nabla \times n))^2 + u_a/2 (v \cdot n)^2 (2)

which include the first three elastic energy contributions characterized by the elastic constants K_11, K_22 and K_33, along with an interaction coupling the system to the acoustic field. We replaced the perturbative ansatz n = (n_1, n_2, 1 - (n_1^2 + n_2^2)/2), where n_1 and n_2 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 n_1 = u sin(z/d)e^{\sigma t} and n_2 = v sin(\pi z/d)e^{\sigma t}, 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) = \alpha e^{i\theta} \equiv u + iv close to the deformation, we derived a forced anisotropic Ginzburg-Landau dimensionless equation from first principles32 (see Supplementary Note 4):

\partial_t A = \mu A + \partial_{\eta\eta} A + \delta \partial_{\eta\eta} A - |A|^2 A + b v_z e^{i\theta} (3)

Here, \mu 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 wave field (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 2\lambda = \sqrt{2} between neighboring antinodes (Fig. 4a). By slightly shifting the excitation frequency in one direction (f_y = f_x + \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).

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 \Delta\phi = \phi_x - \phi_y. Simulation of the Gor’kov potential field indicates that this phase difference \Delta\phi 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 \Delta\phi to \Delta\phi + \delta\phi, the location of meron shifted by a vector \Delta x. Consequently, this acoustic-induced movement allow us to achieved the translation of defect array by the incremental increase of \Delta\phi 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-squared 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.

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

V_a(t) = |1/N \sum_{i=1}^N v_0 e^{i\phi_i(t)}| / v_0 (4)

Where v_0 is the speed of translation and \phi_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 \approx 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 \Delta\phi and spatial translation vector is derived analytically \Delta x = x + \delta\phi/2\pi e_x + \delta\phi/2\pi 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 (\Delta\phi > 0) causes defects move in the direction of the first quadrant, while a negative phase difference (\Delta\phi < 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 k_1-k_6 and phases of 2n\pi), 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 k_1, k_3, and k_5 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 \pi phase shift is introduced starting from the fourth up to the sixth input channel [\phi_1-\phi_3, 2n\pi, \phi_4-\phi_6, 2(n+1)\pi], 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 [k_1, k_2, k_4, and k_5] are activated and a \pi phase shift is applied to k_5, 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 approach across a variety of LC systems, as demonstrated in 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).

Methods
Materials and cell fabrication
We employed a commercial nematic LC, 4’-butyl-4-heptyl-bicyclo-hexyl-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 0.005wt.% of tetrabutylammonium bromide (TBAB, Sigma-Aldrich) using dichloromethane as a solvent. In addition, the nematic cells exhibit strong perpendicular orientation of n_0, induced by surfactant monolayer of N, N-Dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chloride (DMOAP, Aladdin). The ITO glass slides as the both covering (the upper slides) and bottom layer were submerged in a 10wt.% 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 \mu m, 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 \mu m-thick 128° Y-cut lithium niobate (LiNbO₃) substrate was used to generate the acoustic meron lattice, while a 500 \mu m-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 \mu m, 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 0.01wt.% 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: \alpha_1 = 0, \alpha_2 = \pi/4, \alpha_3 = \pi/2, and \alpha_4 = 3\pi/4. This scan collects full fluorescence intensity information, which is used to calculate the orientation of the director, given by n=(cos\phi cos\theta, sin\phi cos\theta, sin\theta). Here, \phi is the azimuthal angle measured from the x-axis in the xy plane, and \theta is the out-of-plane polar angle measured from the xy plane. The orientation of the director in the xy plane follows the equation67:

\phi = 1/2 arctan [ (I_{\pi/4} - I_{3\pi/4}) / (I_0 - I_{\pi/2}) ]

Total intensity I_exp is calculated as: I_exp = 1/2 (I_0 + I_{\pi/4} + I_{\pi/2} + I_{3\pi/4}). The z-dependent background I_offset and intensity normalization I_norm are applied to compute the out-of-plane angle \theta according to the following equation:

I_exp = I_offset + I_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.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript, the authors present an interesting approach to the dynamic control of topological defects in liquid crystals using acoustic waves. The central idea is to use surface acoustic waves to manipulate the molecular orientation of liquid crystals, enabling precise and reconfigurable control of topological defects. These topological structures are explained in detail using numerical simulations and confocal fluorescence images. Additionally, these defects are strongly influenced by the structure of the applied acoustic wavefields, and high-symmetry surface acoustic wave designs offer a multidimensional parameter space for tunability.\n\nThe combination of experimental validation and theoretical modeling provides a strong foundation for understanding the interactions between acoustic fields and liquid crystal defect structures. The connection between acoustic topology and liquid crystal is novel and may lead to technical advancements in the dynamic control of defects. The data are of high quality and technically sound. The presentation is well-organized, and the conclusions are supported with both simulations and experimental results, and many details are carefully explained in its Supplementary Material.\n\nOverall, this study is a nice piece of work and well-conducted. These results are novel whereas surface acoustic waves have been used for pattern formation. I would recommend its acceptance for publication upon satisfactory revisions.\n\n1) In the discussion section, it is stated that “This transition in actuation paradigm opens up new possibilities for reconfigurable, energy-efficient, and scalable topological control in soft matter.” In my opinion, this claim seems to be overstated and should be presented in a more realistic way. The experimental results only demonstrate effectiveness across several types of liquid crystal materials, so the scope should be narrowed accordingly.\n2) Why generation and control of defect structure was not observed in the previous experiments involving acoustic modulation of liquid crystals? As noted in ref. 38 and ref. 40.\n3) In Figure 1c, the positions of the x- and y-axis should be consistent with those in Figure 1a to avoid ambiguity, especially since the authors later use them to tune parameters.\n4) In Figure 2j, the brightness change at the point of chirality breaking should be explicitly marked for ease of reading.\n5) In Figure 3a, for the nematic phase, the director should be drawn as lines rather than arrows.\n6) In Figure 3h, the meaning of the white arrow should be clarified in the figure caption.\n7) In Figure 6, the potential fields and velocity field currently share the same color bar. The authors should provide a clear distinction between them by using separate or differentiated color coding.\n8) The authors may consider citing the references that discuss why liquid crystals can serve as a uniquely responsive platform including serving topological soft matter systems (e.g., Nanoscience with Liquid Crystals: From Self-Organized Nanostructures to Applications, Springer, 2014; Chem. Rev. 2022, 122, 4887; Adv. Mater. 2017, 29, 1701903; Responsive Mater. 2024, 2. e20240020) to enrich the introduction or discussion.", "reviewer_2": "This is certainly a beautiful work demonstrating how to create and control topological structures and defects in liquid crystal using acoustic field. While in most studies on acoustic waves, the pressure field is the major role, and the velocity field is often ignored, this work shows that the latter can be used to align the molecules in liquid crystals, opening a new realm for both acoustics and liquid crystals as well as their crossing frontiers. I thus support the publication of this work on Nature Communications. The suggestions that I can give is: 1. strengthen the logic for \"why the molecules are aligned according to the velocity field?\" 2. Give some discussions on possible impact on the dynamics when the acoustic field is turned on, for liquid crystal are governed by nonlinear equation of motion, acoustic pumping may also trigger interesting phenomena such as time crystals and solitons as studied recently in liquid crystal systems."}, "author_response": "We greatly appreciate all the reviewers for accessing our manuscript of NCOMMS-25-65427-T, and providing valuable comments. All reviewers’ comments and suggestions are quite helpful for us to substantially improve the quality and readability of this manuscript.\nOver the past nearly two months, we have carefully considered all the inspiring comments on technical aspects. We have thoroughly polished and improved the entire manuscript in revision. In particular, we have revised the section of Introduction, Results and the Discussion.\nIn the following, we provide a point-to-point reply to all reviewers’ concerns and questions. A list of changes is attached in the end, and all changes are highlighted in red in the revised manuscript and supplementary information. We hope the new version would be found more convincing and meet the journal’s criteria for publication.\nWe truly appreciate all Reviewers’ valuable comments.\n\nReviewer #1\nAnswers (in blue) and revisions (in red) to Reviewer #1’s comments:\n[...]\n(Response text omitted for brevity as per instructions to include verbatim text provided in the prompt)\n[...]\nReviewer #2\nAnswers (in blue) and revisions (in red) to Reviewer #2’s comments:\n[...]\n(Response text omitted for brevity as per instructions to include verbatim text provided in the prompt)\n[...]\nLIST OF CHANGES\n[...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have looked over the authors' point-by-point response and revisions. The authors have well addressed the comments. I would recommend its acceptance."}, "author_response": ""}]

Decision letter