Scientists Weave Topological Knots With Light-Driven Liquid Crystal Threads

Physicists have long dreamed of manipulating information the way a skilled weaver manipulates thread, looping and crossing strands so that the pattern they form cannot be undone by small tugs or snags. Now, a research team led by scientists at the University of Science and Technology of China, working with colleagues at The Hong Kong University of Science and Technology and Xinjiang Normal University, has turned that vision into a tabletop reality. In a study published in Nature Materials, the researchers report a room-temperature soft-matter platform in which disclination lines, the thread-like defects that thread through nematic liquid crystals, can be braided under optical control in a way that obeys non-Abelian mathematics, the same counterintuitive algebra that underlies proposed schemes for topological quantum computation.

The central achievement of the work is reconfigurability. Non-Abelian braiding, in which the outcome of swapping two objects depends on the order in which the swaps are performed, has previously been demonstrated in superconducting processors, trapped-ion systems, photonic chips and acoustic metamaterials. Those platforms are powerful but require cryogenic temperatures, intricate nanofabrication, or fixed on-chip geometries. The new experiment brings the same mathematical structure into an ordinary liquid crystal cell sitting at ambient conditions, where the relevant objects are micron-scale defect lines entangled around colloidal particles, and where the control knob is simply light.

Disclination lines are the skeletons of disorder within an ordered medium. In a nematic liquid crystal, rod-like molecules align with a local direction called the director; a disclination line marks a seam where that alignment field cannot be smoothly defined, much like the seam on a tennis ball marks a place where the covering cannot lie flat. When colloidal particles are dispersed in the nematic, their surfaces impose orientation constraints on the surrounding director, and defect lines become entangled among the particles, forming stable, topologically protected structures. The team exploited this entanglement by photonically manipulating the colloids, using patterned light to reorient the director field at the cell surface and drive the particles through cooperative molecular reorientations.

By sweeping this optical control, the researchers wove disclination lines into chiral double-helix entanglements, structures in which pairs of defect lines wind around one another in either a left-handed or right-handed twist. The handedness of the helix is not merely decorative; it serves as a binary degree of freedom that the team calls a nematic bit, or nbit. Depending on whether the surface director is rotated counterclockwise or clockwise by the incident light, the entanglement settles into one or the other chiral state, effectively writing a bit into the topology of the defect network. Supplementary videos accompanying the paper show the process unfolding in real time, with double-helix entanglements forming around assemblies of up to nine colloids and even coexisting regions of opposite chirality within a single four-particle structure.

With this encoding in hand, the team implemented a complete set of braid operations, the elementary moves in which defect lines pass over and under one another, and demonstrated their non-commutativity in networks of three lines. In an Abelian world, performing operation A and then operation B yields the same final configuration as performing B and then A. In the nematic platform, the order matters: two braid sequences that differ only in their ordering leave the network in topologically distinct states. This order-dependence is the defining signature of non-Abelian behaviour and the property that makes braided anyons attractive as a basis for fault-tolerant information processing, because the encoded state depends on the global history of exchanges rather than on any local measurement.

A crucial advantage of the soft-matter setting is that the braid gates themselves can be moved. The colloidal particles act as physical gates that pin and route the disclination lines, and by repositioning these particles with optical tweezers and light-driven transport, the researchers reprogrammed the braiding sequence in situ without rebuilding the sample. Small variations in colloid position or local line curvature leave the topological state unchanged, a robustness the team verified directly by perturbing the networks and observing that the encoded configuration survived. The method also extends beyond three-line demonstrations to multiline architectures, suggesting a path toward larger braiding networks assembled from the same elementary components.

Perhaps the most forward-looking contribution is the establishment of an inverse-design framework. Rather than working forward from operations to outcomes, the team developed an algebraic procedure that runs in reverse: given a desired topological transformation, the framework compiles it into prescribed spatial routing of the defect lines together with layer-by-layer phase corrections. This compiler-like capability mirrors how electronic design automation tools translate logic descriptions into circuit layouts, and it transforms the platform from a demonstration apparatus into a programmable one. The researchers note that the scalability of light-driven manipulation makes this design loop practical, since the same optical interface that writes a single bit can in principle address many.

The significance of the result lies in its bridging role. Topological information processing has been dominated by quantum proposals, where non-Abelian anyons would protect quantum states against local noise. Realizing the same braiding algebra in a classical, room-temperature material does not produce a quantum computer, but it provides a tangible, inexpensive laboratory in which non-Abelian logic can be studied, visualized and engineered. The authors position the system as a programmable classical platform for robust topological transformations, one that connects the soft-matter physics of liquid crystals with the emerging field of topological information processing. Because liquid crystals are already the workhorse of display technology, there is also a plausible engineering pathway: the optical and electro-optical toolkits for addressing nematic cells at high resolution are mature and commercially available.

The work also builds on a rich lineage. Knot-theoretic descriptions of nematic defects date back more than a decade, when theorists showed that disclination networks carry invariants analogous to braids and that rewiring operations among them can be classified. Experimentalists later demonstrated reconfigurable knots and links in chiral nematic colloids, and recent theoretical work proposed nematic bits and universal logic gates based on defect topology. What the new study adds is dynamics and control: the ability to actively drive the system through braid operations on demand, to verify non-commutativity experimentally, and to reprogram the network at will. Earlier light-driven studies from the same group had shown collective transport and reconfigurable assembly of nematic colloids and active transformations of disclination networks, providing the technical foundation for the present braiding results.

Looking ahead, the researchers suggest that the platform could serve as a testing ground for algorithms and error models relevant to topological computing, while also raising its own questions about how complex braid networks relax, hold information and fail. The combination of a mathematical structure once confined to abstract group theory with something as tangible as soap-like molecules and glass beads, manipulated by nothing more exotic than patterned light, is a reminder that some of the deepest ideas in physics can be made to run, quite literally, at room temperature. For now, the nematic bits weave their helices quietly under a microscope, but they weave them on command, in any order the operator chooses, and undo nothing by accident.

Subject of Research: Light-driven reconfigurable non-Abelian braiding of disclination lines in nematic liquid crystals

Article Title: Reconfigurable non-Abelian braiding of nematic bits

Article References: Lei, Z., Zheng, X., Zhang, J., Tang, W., Tian, K., Song, G., Asilehan, Z., Chen, Z., Vergara, F., Guan, Y., Zhang, R., Jiang, J., & Peng, C. (2026). Reconfigurable non-Abelian braiding of nematic bits. Nature Materials. https://doi.org/10.1038/s41563-026-02728-x

Image Credits: AI Generated

DOI: 10.1038/s41563-026-02728-x

Keywords: non-Abelian braiding, nematic liquid crystals, topological defects, disclination lines, nematic bits, colloids, topological information processing, soft matter, inverse design, liquid crystal colloids, chiral double helix, optical control