Abstract
Time crystals spontaneously break the time translation symmetry, as recently has been frequently reported in quantum systems. Here we describe the observation of classical analogs of both 1 + 1-dimensional and 2 + 1-dimensional discrete space-time crystals in a liquid crystal system driven by a Floquet electrical signal. These classical time crystals comprise particle-like structural features and exist over a wide range of temperatures and electrical driving conditions. The phenomenon-enabling period-doubling effect in 1 + 1-dimensional discrete space-time crystals comes from their topological Majorana-like quasiparticle features, where periodic inter-transformations of co-existing topological solitons and disclinations emerge in response to external stimuli and play pivotal roles. Our discrete space-time crystals exhibit robustness against temporal perturbations and spatial defects. Our findings show that the simultaneous symmetry breaking in time and space can be a widespread occurrence in numerous open systems, not only in quantum but also in a classical soft matter context.
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Acknowledgments
We thank T. Lee for technical assistance. This research was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-SC0019293 with the University of Colorado at Boulder. I.I.S. and R.Z. thank the International Institute for Sustainability with Knotted Chiral Meta Matter at Hiroshima University for supporting exchange visits that initiated this collaboration.
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H.Z. performed experiments under the supervision of I.I.S. H.Z. and R.Z. performed the numerical modeling. I.I.S. initiated and directed the research. H.Z. and I.I.S. wrote the manuscript, with feedback and contributions from all authors.
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The authors declare the following competing financial interests: I.I.S. and H.Z. filed patent applications related to discrete space-time crystals submitted by the University of Colorado, and an additional patent was filed concurrently with this paper. The other authors declare no competing interests.
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Zhao, H., Zhang, R. & Smalyukh, I.I. Emergent discrete space-time crystal of Majorana-like quasiparticles in chiral liquid crystals. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70880-8
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DOI: https://doi.org/10.1038/s41467-026-70880-8
