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Visualization of dynamic polaronic strain fields in hybrid lead halide perovskites


Excitation localization involving dynamic nanoscale distortions is a central aspect of photocatalysis1, quantum materials2 and molecular optoelectronics3. Experimental characterization of such distortions requires techniques sensitive to the formation of point-defect-like local structural rearrangements in real time. Here, we visualize excitation-induced strain fields in a prototypical member of the lead halide perovskites4 via femtosecond resolution diffuse X-ray scattering measurements. This enables momentum-resolved phonon spectroscopy of the locally distorted structure and reveals radially expanding nanometre-scale strain fields associated with the formation and relaxation of polarons in photoexcited perovskites. Quantitative estimates of the magnitude and shape of this polaronic distortion are obtained, providing direct insights into the dynamic structural distortions that occur in these materials5,6,7,8,9. Optical pump–probe reflection spectroscopy corroborates these results and shows how these large polaronic distortions transiently modify the carrier effective mass, providing a unified picture of the coupled structural and electronic dynamics that underlie the optoelectronic functionality of the hybrid perovskites.

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Fig. 1: Experimental setup and observation of temporally delayed transient structural responses.
Fig. 2: Phonon-momentum-resolved time scans for selected Bragg peaks.
Fig. 3: Analytical model for diffuse scattering from expanding polaronic strains.
Fig. 4: Ultrafast transient reflectivity studies and effects of polaron formation on optoelectronic properties.

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Data availability

The data represented in Figs. 1, 2, 3 and 4 are provided with the paper as source data. Other datasets generated and/or analysed during the current study are available from A.M.L. upon reasonable request. Source data are provided with this paper.


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This work is supported by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract no. DE-AC02-76SF00515 (B.G., M.T., S.T., G.A.D.L.P., H.I.K. and A.M.L.). Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515. M.D.S. is supported by a graduate fellowship from the Center for Molecular Analysis and Design (CMAD) at Stanford University. T.W. and F.D. acknowledge funding from an EPSRC NI grant (EP/R044481/1). S.F. acknowledges funding from the EPSRC and the Studienstiftung des deutschen Volkes. T.J.W.V.D.G. acknowledges support from the EPSRC Cambridge NanoDTC, EP/L015978/1 and the Schiff Foundation. S.A.B. acknowledges support from the EPSRC Centre for Doctoral Training in Graphene Technology (EP/L016087/1). F.D. acknowledges support from the DFG Emmy Noether Programme (project no. 387651688) and the Winton Programme for the Physics of Sustainability. T.W. received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 838772. M.F.T. and H.-G.S. acknowledge support from the Center for Hybrid Organic Inorganic Semiconductors for Energy (CHOISE), an Energy Frontier Research Center funded by the Office of Basic Energy Sciences, Office of Science within the US Department of Energy through contract no. DE-AC36-08G028308 for assistance with the LCLS experiments and interpretation. We thank Y. Rakita for support with single crystal growth.

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Authors and Affiliations



A.M.L., B.G. and M.D.S. conceived the experiment; B.G. led the LCLS experimental team consisting of B.G., T.J.W.V.D.G., M.D.S., M.T., S.T., H.-G.S., G.A.D.L.P., R.A.-M., T.S. and A.M.L. Data analysis of the time-resolved X-ray scattering measurements was performed by B.G. with contributions from T.J.W.V.D.G., M.T. and S.T. The data were interpreted by B.G. and A.M.L. with contributions from T.J.W.V.D.G., H.-G.S., M.T., S.T., M.F.T. and F.D. Perovskite single crystal samples were synthesized by M.D.S. who also performed their static characterizations. A.M.L. performed the polaron model calculations. T.W., S.A.B., S.F. and F.D. performed the transient reflectivity measurements. S.F. performed the transient grating photoluminescence measurements and static optical characterization. T.W. and F.D. analysed and interpreted the transient reflectivity data. A.M.L., F.D., M.F.T., H.I.K. and D.Z. supervised the research. B.G., A.M.L., T.W. and F.D. wrote the paper with contributions from all authors.

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Correspondence to Aaron M. Lindenberg.

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Peer review information Nature Materials thanks Paul Beaud, Elbert Chia and Sergei Tretiak for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–17, Sections 1–11 and refs. 1–29.

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Source Data Fig. 1

Source data for Fig. 1 with each panel given as different tab.

Source Data Fig. 2

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Source Data Fig. 3

Source data for Figure 3 with each panel given as different tab.

Source Data Fig. 4

Source data for Figure 4 with each panel given as different tab.

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Guzelturk, B., Winkler, T., Van de Goor, T.W.J. et al. Visualization of dynamic polaronic strain fields in hybrid lead halide perovskites. Nat. Mater. 20, 618–623 (2021).

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