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Optical creation of a supercrystal with three-dimensional nanoscale periodicity


Stimulation with ultrafast light pulses can realize and manipulate states of matter with emergent structural, electronic and magnetic phenomena. However, these non-equilibrium phases are often transient and the challenge is to stabilize them as persistent states. Here, we show that atomic-scale PbTiO3/SrTiO3 superlattices, counterpoising strain and polarization states in alternate layers, are converted by sub-picosecond optical pulses to a supercrystal phase. This phase persists indefinitely under ambient conditions, has not been created via equilibrium routes, and can be erased by heating. X-ray scattering and microscopy show this unusual phase consists of a coherent three-dimensional structure with polar, strain and charge-ordering periodicities of up to 30 nm. By adjusting only dielectric properties, the phase-field model describes this emergent phase as a photo-induced charge-stabilized supercrystal formed from a two-phase equilibrium state. Our results demonstrate opportunities for light-activated pathways to thermally inaccessible and emergent metastable states.

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Data availability

Raw data from the Advanced Photon Source and phase field results are available upon reasonable request. The X-ray diffraction reciprocal space volumes generated with rsMap3D for figures both in the main text and supplementary information are available at together with Python notebooks for interacting with the datasets. For non-Python users, the data can be viewed with the ParaView application available at

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V.A.S., Y.Y., L.W.M., C.D., L.-Q.C., H.W., V.G. and J.W.F. acknowledge support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC-0012375 for the development of the materials and ultrafast experiments. Z.H., S.L. and G.A.S acknowledge support from the National Science Foundation (DMR-1210588) and National Science Foundation Center for Nanoscale Science grant number DMR-1420620. L.-Q. C. also acknowledges support from NSF DMR-1744213. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, under contract no. DE-AC02–06CH11357. PFM data were collected at PSU, University of California, Berkeley, and at the Center for Nanophase Materials Sciences, a DOE Office of Science User Facility at ORNL. N.L. acknowledges support from the Eugene P. Wigner Fellowship at Oak Ridge National Laboratory (ORNL), a US Department of Energy (DOE) facility managed by UT-Battelle, LLC for US DOE Office of Science under contract no. DE-AC05–00OR22725. R.R. and L.W.M. acknowledge funding from the Gordon and Betty Moore Foundation’s EPiQS Initiative, under grant GBMF5307. NL acknowledges use of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory. V.A.S. would like to thank C.M. Schlepütz and J. Hammonds for their development of rsMap3D, valuable discussions with H. Zhou, S Kalinin, Q. Li, Y. Ren, J. Tischler and D.D. Fong, and C.A. Kurtz for technical support.

Author information

V.A.S. conceived of the central concepts and designed the experiments. V.A.S., together with H.W., J.W.F., N.L., Y.Y., Z.Z., M.R.M, D.A.W., A.R.D., J.K. and X.Z., conducted the synchrotron-based X-ray diffraction studies. M.R.M., A.Y., S.D., R.R. and L.W.M. synthesized the materials. C.D., Z.H. and L.-Q.C. conducted the phase-field modelling and analysis in collaboration with V.A.S. N.L., S.L., A.R.D. and V.A.S. conducted the scanning probe-based PFM measurements. Y.Y. and V.A.S. conducted the SHG measurements. G.A.S. measured TEM to confirm sample quality. V.A.S., V.G. and J.W.F. wrote the manuscript with contributions from all authors. All authors discussed the results and implications of the work, and read, edited and commented on the manuscript at all stages.

Competing interests

The authors declare no competing interests.

Correspondence to V. Gopalan or J. W. Freeland.

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    Supplementary Figures 1–12

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Fig. 1: Summary of supercrystal formation.
Fig. 2: Supercrystal observation by X-ray diffraction and microscopy.
Fig. 3: Reversible control of supercrystal phase formation.
Fig. 4: Phase-field model prediction of the supercrystal phase.
Fig. 5: Interplay between order parameters within the supercrystal phase captured by the phase-field model.