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Ultrafast formation of topological defects in a two-dimensional charge density wave


Topological defects play a central role in dynamical systems undergoing a non-adiabatic transition. In solids, topological defects as a result of femtosecond laser excitation have attracted increasing interest not only because they are key to understanding phase transitions but also because they can generate a variety of hidden orders that are not accessible in thermal equilibrium. Despite the common occurrence of these defects in a non-equilibrium system, the fundamental limit on how fast they can emerge in solids and the generic pathway for defect creation at such fast timescales have remained open questions. Here we apply ultrafast electron diffraction to study the reciprocal-space signatures of transient defects in a two-dimensional charge density wave, where simultaneous measurements of both defect and phonon dynamics yield a microscopic view of defect formation in the femtosecond regime. We find that one-dimensional domain walls are generated well within 1 ps following photoexcitation, during which the defect growth is not dictated by the amplitude of the order parameter, but is mediated by a non-thermal population of longitudinal optical phonons. Our work provides a framework for the ultrafast engineering of topological defects that are coupled to specific collective modes, which will prove useful for the dynamical control of non-equilibrium phases in correlated materials.

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Fig. 1: 2 × 2 CDW in 1T-TiSe2 and possible types of topological defect in the CDW.
Fig. 2: Photoinduced 1D domain walls in the CDW.
Fig. 3: Photoinduced phonon dynamics in different branches.
Fig. 4: Ultrafast domain wall creation mediated by LO phonons.

Data availability

All data supporting the conclusions are available within the article and its Supplementary Information. Additional data are available from the corresponding authors upon reasonable request.


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We thank Y. He and D. Limmer for helpful discussions. We thank J.-H. Pöhls for providing the calculated phonon dispersions26 and L. P. René de Cotret for providing the Python codes for computing the one-phonon structure factor22. D.X. and J.Z. acknowledge support from the National Key R&D Program of China (no. 2021YFA1400202); the National Natural Science Foundation of China (grant nos. 11925505, 11504232 and 11721091); and the Office of Science and Technology, Shanghai Municipal Government (no. 16DZ2260200). A.Z. acknowledges support from the Miller Institute for Basic Research in Science. L.W., Q.M. and Y.Z. acknowledge support from the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-SC0012704. Y.G. acknowledges support from the National Natural Science Foundation of China (grant no. 11874264). A.K. acknowledges support from the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0023017. M.W.Z. acknowledges funding by the W. M. Keck Foundation, funding from the UC Office of the President within the Multicampus Research Programs and Initiatives (M21PL3263), the Hellman Fellows Fund and the National Science Foundation (NSF-DMR 2247363).

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Authors and Affiliations



A.Z., D.X. and Y.C. conceived the project. Y.C., A.Z., L.W. and Y.Z. analysed the data with important theoretical insights from J.v.W. and A.K. W.X. and Y.G. grew the single crystals. Y.C. collected the ultrafast electron diffraction data, where the MeV ultrafast electron diffraction beamline was constructed and maintained by F.Q., P.Z., X.Z. and T.J. L.W., Q.M. and Y.C. performed the diffraction simulations. A.Z. and Y.C. wrote the paper with critical input from A.K., M.W.Z., Y.Z., D.X. and all other authors. The project was supervised by M.W.Z., J.Z., Y.Z. and D.X.

Corresponding authors

Correspondence to Alfred Zong, Michael W. Zuerch, Jie Zhang, Yimei Zhu or Dao Xiang.

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Nature Physics thanks Isabella Gierz, Dragan Mihailović and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Notes 1–10, Figs. 1–16, Equations 1–7, Table 1, caption of Supplementary Video 1 and References.

Supplementary Video 1

Photoinduced change in the diffraction pattern of 1T-TiSe2 following the incidence of a 3 mJ cm–2, 800 nm pulse, taken at 210 K. To prevent colour saturation at later times, the colour scale also varies with the pump–probe delay. The hexagons mark the Brillouin zones and images in each frame are symmetrized to enhance the statistics.

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Cheng, Y., Zong, A., Wu, L. et al. Ultrafast formation of topological defects in a two-dimensional charge density wave. Nat. Phys. 20, 54–60 (2024).

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