Abstract
Crystals spontaneously break the continuous translation symmetry of free space. Analogously, time crystals lift translational invariance in time. Here we demonstrate a robust continuous time crystal in an electron–nuclear spin system of a semiconductor tailored by tuning the material composition. Continuous, time-independent external driving of the sample produces periodic auto-oscillations with a coherence time exceeding hours. Varying the experimental parameters reveals wide ranges in which the time crystal remains stable. At the edges of these ranges, we find chaotic behaviour with a lifted periodicity corresponding to the melting of the crystal. The time crystal state enables fundamental studies of nonlinear interactions and has potential applications as a precise on-chip frequency standard.
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The data are publicly available in a repository: https://doi.org/10.6084/m9.figshare.22731122.
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Acknowledgements
We thank D. R. Yakovlev for fruitful discussions. We acknowledge financial support from the German Research Foundation through the International Collaborative Research Centre (grant no. TRR160, Project A1). A.G. and M.B. acknowledge support from the Federal Ministry of Education and Research, Germany (Project QR.X, contract no. 16KISQ011). M.B. acknowledges support from the Research Alliance Ruhr. The Resource Center Nanophotonics of Saint-Petersburg State University provided the epilayer sample.
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V.L.K. and A.G. conceived the experiment. A.N.K., P.S.S. and A.G. built the experimental apparatus and performed the measurements. A.N.K., N.E.K., P.S.S., V.L.K. and A.G. analysed the data. N.E.K. and V.L.K. provided the theoretical description. All authors contributed to the interpretation of the data. N.E.K., V.L.K. and A.G. wrote the manuscript in close consultation with M.B., who supervised the project.
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Greilich, A., Kopteva, N.E., Kamenskii, A.N. et al. Robust continuous time crystal in an electron–nuclear spin system. Nat. Phys. 20, 631–636 (2024). https://doi.org/10.1038/s41567-023-02351-6
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DOI: https://doi.org/10.1038/s41567-023-02351-6
