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Motile dislocations knead odd crystals into whorls


The competition between thermal fluctuations and potential forces governs the stability of matter in equilibrium, in particular the proliferation and annihilation of topological defects. However, driving matter out of equilibrium allows for a new class of forces that are neither attractive nor repulsive, but rather transverse. The possibility of activating transverse forces raises the question of how they affect basic principles of material self-organization and control. Here we show that transverse forces organize colloidal spinners into odd elastic crystals crisscrossed by motile dislocations. These motile topological defects organize into a polycrystal made of grains with tunable length scale and rotation rate. The self-kneading dynamics drive super-diffusive mass transport, which can be controlled over orders of magnitude by varying the spinning rate. Simulations of both a minimal model and fully resolved hydrodynamics establish the generic nature of this crystal whorl state. Using a continuum theory, we show that both odd and Hall stresses can destabilize odd elastic crystals, giving rise to a generic state of crystalline active matter. Adding rotations to a material’s constituents has far-reaching consequences for continuous control of structures and transport at all scales.

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Fig. 1: A crystal whorl state.
Fig. 2: Motile dislocations.
Fig. 3: Transport in the crystalline whorl state.
Fig. 4: Odd response in the steady state.
Fig. 5: Measuring an elasto-hydrodynamic instability.

Data availability

The data contained in the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The minimal model simulations were performed using freely available HOOMD-Blue codes38. Hydrodynamic simulations were carried out using codes based on the publicly available code at Input files are available on request to the authors.


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We acknowledge discussions with P. Wiegmann, A. Abanov, D. Nelson, C. Scheibner, M. Han, M. Fruchart, S. Gokhale, N. Fakhri and J. Dunkel. We thank V. Vitelli for an insightful discussion on the importance of odd stress on defect motility. We thank W. Yan for useful conversations. This work was primarily supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the National Science Foundation (NSF) under award no. DMR-2011854. Additional support was provided by NSF DMR-1905974, NSF EFRI NewLAW 1741685 and the Packard Foundation. M.J.S. acknowledges support from NSF grants DMR-1420073 (NYU-MRSEC) and DMR-2004469. D.B. acknowledges support from ARN grant WTF and IdexLyon Tore. E.S.B. was supported by the National Science Foundation Graduate Research Fellowship under grant no. 1746045. D.B. and W.T.M.I. gratefully acknowledge support from the Chicago-France FACCTS programme. F.B.U. acknowledges support from ‘la Caixa’ Foundation (ID 100010434), fellowship LCF/BQ/PI20/11760014 and from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 847648. The University of Chicago’s Research Computing Center and the University of Chicago’s GPU-based high-performance computing system (NSF DMR-1828629) are acknowledged for access to computational resources and the Chicago MRSEC (US NSF grant no. DMR-2011854) for access to its shared experimental facilities.

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Authors and Affiliations



E.S.B. designed and performed experiments and analysed data. Y.A.G. designed and performed minimal model simulations and elastic theory. F.B.U. designed and performed fully hydrodynamic simulations. V.S. and S.M. contributed to experiments and analytical tools. A.P., D.B., Y.A.G., E.S.B., W.T.M.I. and M.J.S. performed continuum modelling. W.T.M.I., D.B. and M.J.S. designed and supervised research. All authors discussed the results and analysis.

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Correspondence to Michael J. Shelley, Denis Bartolo or William T. M. Irvine.

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Peer review information Nature Physics thanks Juho Lintuvuori and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Bililign, E.S., Balboa Usabiaga, F., Ganan, Y.A. et al. Motile dislocations knead odd crystals into whorls. Nat. Phys. 18, 212–218 (2022).

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