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Two-dimensional overdamped fluctuations of the soft perovskite lattice in CsPbBr3


Lead halide perovskites exhibit structural instabilities and large atomic fluctuations thought to impact their optical and thermal properties, yet detailed structural and temporal correlations of their atomic motions remain poorly understood. Here, these correlations are resolved in CsPbBr3 crystals using momentum-resolved neutron and X-ray scattering measurements as a function of temperature, complemented with first-principles simulations. We uncover a striking network of diffuse scattering rods, arising from the liquid-like damping of low-energy Br-dominated phonons, reproduced in our simulations of the anharmonic phonon self-energy. These overdamped modes cover a continuum of wave vectors along the edges of the cubic Brillouin zone, corresponding to two-dimensional sheets of correlated rotations in real space, and could represent precursors to proposed two-dimensional polarons. Further, these motions directly impact the electronic gap edge states, linking soft anharmonic lattice dynamics and optoelectronic properties. These results provide insights into the highly unusual atomic dynamics of halide perovskites, relevant to further optimization of their optical and thermal properties.

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Fig. 1: Structural distortions and cubic phonon dispersions.
Fig. 2: Diffuse scattering revealing network of rods from overdamped phonons.
Fig. 3: Overdamping of phonon modes along M–R in the cubic and tetragonal phases.
Fig. 4: Damping of anharmonic phonons and their effect on the electronic structure.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.


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We thank D. Mitzi and V. Blum for discussions. We thank O. Hellman for providing access to the TDEP software package. T.L.-A. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0019299. X.H. and O.D. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0019978. Initial support of T.L.-A. by Duke Energy Initiative seed funds is acknowledged. Work at Argonne (synthesis, characterization and X-ray and neutron scattering measurements) is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The use of Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. We acknowledge the support of the National Institute of Standards and Technology, US Department of Commerce, in providing the neutron research facilities used in this work. Theoretical calculations were performed using resources of the National Energy Research Scientific Computing Center, a US Department of Energy Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231.

Author information




Neutron scattering measurements and analysis were performed by T.L.-A., R.O., M.J.K., X.H., S.R. and O.D., with support from D.M.P., D.L.A., G.N.M.N.X. and Z.X. X-ray scattering measurements were performed by M.J.K., S.R. and R.O. and were analysed by M.J.K. Sample synthesis was performed by D.-Y.C. X.H. performed the first-principles simulations. T.L.-A., X.H. and O.D. wrote the manuscript and all authors commented on it.

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Correspondence to R. Osborn or O. Delaire.

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Peer review information Nature Materials thanks Felix Fernandez-Alonso, Antonietta Guagliardi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–34, Discussion and Tables 1–4.

Supplementary Video 1

Animation for M-mode soft phonon.

Supplementary Video 2

Animation for R-mode soft phonon.

Source data

Source Data Fig. 1

Source data for graphs in Fig. 1.

Source Data Fig. 2

Source data for graphs in Fig. 2.

Source Data Fig. 3

Source data for graphs in Fig. 3.

Source Data Fig. 4

Source data for graphs in Fig. 4.

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Lanigan-Atkins, T., He, X., Krogstad, M.J. et al. Two-dimensional overdamped fluctuations of the soft perovskite lattice in CsPbBr3. Nat. Mater. 20, 977–983 (2021).

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