Disoriented order

Disoriented order

Mon, 26/06/2023


Publication of the Physics Laboratory in the journal Nature on June 14, 2023. Communication of the CNRS-INP on June 14, 2023.

A research team involving members of the Physics Laboratory of ENS de Lyon has demonstrated the existence of a new form of order never before identified in nature: 'non-orientable' order, which can endow simple structures with properties that enable them to store information. This work is published in the journal Nature.


From atomic crystals to animal flocks, the emergence of order in nature is captured by the concept of spontaneous symmetry breaking. However, this cornerstone of physics is challenged when broken symmetry phases are frustrated by geometrical constraints. Such frustration dictates the behaviour of systems as diverse as spin ices, confined colloidal suspensions and crumpled paper sheets. These systems typically exhibit strongly degenerated and heterogeneous ground states and hence escape the Ginzburg–Landau paradigm of phase ordering. Here, combining experiments, simulations and theory we uncover an unanticipated form of topological order in globally frustrated matter: non-orientable order. We demonstrate this concept by designing globally frustrated metamaterials that spontaneously break a discrete Z2 symmetry. We observe that their equilibria are necessarily heteregeneous and extensively degenerated. We explain our observations by generalizing the theory of elasticity to non-orientable order-parameter bundles. We show that non-orientable equilibria are extensively degenerated due to the arbitrary location of topologically protected nodes and lines where the order parameter must vanish. We further show that non-orientable order applies more broadly to objects that are non-orientable themselves, such as buckled Möbius strips and Klein bottles. Finally, by applying time-dependent local perturbations to metamaterials with non-orientable order, we engineer topologically protected mechanical memories, achieve non-commutative responses and show that they carry an imprint of the braiding of the loads’ trajectories. Beyond mechanics, we envision non-orientability as a robust design principle for metamaterials that can effectively store information across scales, in fields as diverse as colloidal science, photonics, magnetism and atomic physics.

Figure _c_Xiaofei Guo et al
A- Example of an artificial material whose elementary bricks, diamonds, rotate in alternating directions. When pressure is applied to the ring, an order develops along the ring, corresponding to an alternating rotation whose amplitude is represented by the intensity of the pink colour. In the presence of an odd number of diamonds, the order of this ring is frustrated: a white zone appears, indicating an absence of rotation whatever the stress applied (bottom figure, in white). B- A Möbius strip is a non-orientable surface made by twisting a strip and gluing the two ends together. Bottom figure: experimental measurement of the deformation of the ribbon under compression, shown with the same colour code as in A. C- When the artificial material forms a torus, the deformations under global compression cannot be homogeneous and mimic those of a non-orientable surface that cannot be represented in our three-dimensional space.
Credits - Xiaofei Guo, Marcelo Guzman, David Carpentier, Denis Bartolo, Corentin Coulais

Reference: Non-orientable order and non-commutative response in frustrated metamaterials. Xiaofei Guo, Marcelo Guzman, David Carpentier, Denis Bartolo, Corentin Coulais. Nature, June 14, 2023.
DOI: 10.1038/s41586-023-06022-7
arXiv: 10.48550/arXiv.2111.13933

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