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Stereochemical expression of ns2 electron pairs in metal halide perovskites

Abstract

Metal halide perovskites (MHPs) are characterized as strongly anharmonic and dynamic lattices. While there is a consensus on the solvation-like polarization effect in these materials, whether static polarization, that is, ferroelectricity, exists or not in 3D MHPs remains controversial. In this Review, we resolve this controversy by analysing the stereochemical expression (SE) of the ns2 electron pair (NSEP) on group IV metal cations. The SE-NSEP is key to lattice instability, which governs the breaking of inversion symmetry and induces ferroelectricity. The SE-NSEP is diminishingly small in commonly studied 3D lead iodide or bromide perovskites, indicating an absence of ferroelectricity. In contrast, 2D MHPs promote the SE-NSEP and produce unambiguous ferroelectricity or antiferroelectricity. Irrespective of ferroelectricity, the dynamic manifestation of the SE-NSEP provides the missing link to understanding polar fluctuations and efficient dielectric screening in MHPs, thus, contributing to the long carrier lifetimes and diffusion lengths.

Key points

  • The stereochemical expression of the ns2 electron pair (SE-NSEP) on group IV metal cations governs the breaking of inversion symmetry and induces ferroelectricity in metal halide perovskites.

  • The tendency of the SE-NSEP increases with lighter group IV cations, more electronegative halides and larger A-site cations.

  • The SE-NSEP is diminishingly small in commonly studied 3D lead halide perovskites, suggesting the absence of ferroelectricity.

  • Dimensionality reduction promotes the SE-NSEP and produces unambiguous ferroelectricity or antiferroelectricity in 2D lead halide perovskites.

  • The inherent driving force for the SE-NSEP in 3D perovskites results in dynamic symmetry breaking, strong phonon anharmonicity and polar fluctuations, giving rise to efficient dielectric screening of charge carriers.

  • Emerging halide perovskites with the SE-NSEP offer exciting systems to understand the origin of the remarkable photophysical properties in metal halide perovskites.

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Fig. 1: Crystal structures of 3D and 2D halide perovskites.
Fig. 2: Lattice distortions in 3D perovskites.
Fig. 3: Lattice distortion and polarization in a ferroelectric 2D perovskite.
Fig. 4: Lattice distortions in 2D Ruddlesden–Popper halide perovskites.
Fig. 5: Dynamic B-cation off-centre displacement and lattice anharmonicity in halide perovskites.
Fig. 6: Dielectric solvation of charge carriers in 3D halide perovskites.

References

  1. Kojima, A., Teshima, K., Shirai, Y. & Miyasaka, T. Organometal halide perovskites as visible-light sensitizers for photovoltaic cells. J. Am. Chem. Soc. 131, 6050–6051 (2009).

    CAS  PubMed  Google Scholar 

  2. Lee, M. M., Teuscher, J., Miyasaka, T., Murakami, T. N. & Snaith, H. J. Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science 338, 643–647 (2012).

    CAS  PubMed  Google Scholar 

  3. Xing, G. et al. Low-temperature solution-processed wavelength-tunable perovskites for lasing. Nat. Mater. 13, 476–480 (2014).

    CAS  PubMed  Google Scholar 

  4. Zhu, H. et al. Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors. Nat. Mater. 14, 636–642 (2015).

    CAS  PubMed  Google Scholar 

  5. Fu, Y. et al. Metal halide perovskite nanostructures for optoelectronic applications and the study of physical properties. Nat. Rev. Mater. 4, 169–188 (2019).

    CAS  Google Scholar 

  6. Yin, W.-J., Shi, T. & Yan, Y. Unusual defect physics in CH3NH3PbI3 perovskite solar cell absorber. Appl. Phys. Lett. 104, 63903 (2014).

    Google Scholar 

  7. Akkerman, Q. A., Rainò, G., Kovalenko, M. V. & Manna, L. Genesis, challenges and opportunities for colloidal lead halide perovskite nanocrystals. Nat. Mater. 17, 394–405 (2018).

    CAS  PubMed  Google Scholar 

  8. Meggiolaro, D. et al. Iodine chemistry determines the defect tolerance of lead-halide perovskites. Energy Environ. Sci. 11, 702–713 (2018).

    CAS  Google Scholar 

  9. Kang, J. & Wang, L.-W. High defect tolerance in lead halide perovskite CsPbBr3. J. Phys. Chem. Lett. 8, 489–493 (2017).

    CAS  PubMed  Google Scholar 

  10. Huang, H., Bodnarchuk, M. I., Kershaw, S. V., Kovalenko, M. V. & Rogach, A. L. Lead halide perovskite nanocrystals in the research spotlight: stability and defect tolerance. ACS Energy Lett. 2, 2071–2083 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. Zhang, X., Turiansky, M. E. & Van de Walle, C. G. Correctly assessing defect tolerance in halide perovskites. J. Phys. Chem. C 124, 6022–6027 (2020).

    CAS  Google Scholar 

  12. Yaffe, O. et al. Local polar fluctuations in lead halide perovskite crystals. Phys. Rev. Lett. 118, 136001 (2017). This original paper provides important insights into the anharmonic, local polar fluctuations in lead halide perovskites.

    PubMed  Google Scholar 

  13. Beecher, A. N. et al. Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide perovskite. ACS Energy Lett. 1, 880–887 (2016).

    CAS  Google Scholar 

  14. Wasylishen, R. E., Knop, O. & Macdonald, J. B. Cation rotation in methylammonium lead halides. Solid State Commun. 56, 581–582 (1985).

    CAS  Google Scholar 

  15. Whalley, L. D., Skelton, J. M., Frost, J. M. & Walsh, A. Phonon anharmonicity, lifetimes, and thermal transport in CH3NH3PbI3 from many-body perturbation theory. Phys. Rev. B 94, 220301 (2016).

    Google Scholar 

  16. Baikie, T. et al. A combined single crystal neutron/X-ray diffraction and solid-state nuclear magnetic resonance study of the hybrid perovskites CH3NH3PbX3 (X = I, Br and Cl). J. Mater. Chem. A 3, 9298–9307 (2015).

    CAS  Google Scholar 

  17. Franssen, W. M. J., van Es, S. G. D., Dervisoglu, R., de Wijs, G. A. & Kentgens, A. P. M. Symmetry, dynamics, and defects in methylammonium lead halide perovskites. J. Phys. Chem. Lett. 8, 61–66 (2017).

    CAS  PubMed  Google Scholar 

  18. Marronnier, A. et al. Structural instabilities related to highly anharmonic phonons in halide perovskites. J. Phys. Chem. Lett. 8, 2659–2665 (2017).

    CAS  PubMed  Google Scholar 

  19. Frost, J. M. et al. Atomistic origins of high-performance in hybrid halide perovskite solar cells. Nano Lett. 14, 2584–2590 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Ma, J. & Wang, L.-W. Nanoscale charge localization induced by random orientations of organic molecules in hybrid perovskite CH3NH3PbI3. Nano Lett. 15, 248–253 (2015).

    CAS  PubMed  Google Scholar 

  21. Liu, S. et al. Ferroelectric domain wall induced band gap reduction and charge separation in organometal halide perovskites. J. Phys. Chem. Lett. 6, 693–699 (2015).

    CAS  PubMed  Google Scholar 

  22. Miyata, K. et al. Large polarons in lead halide perovskites. Sci. Adv. 3, e1701217 (2017).

    PubMed  PubMed Central  Google Scholar 

  23. Zhu, X. Y. & Podzorov, V. Charge carriers in hybrid organic–inorganic lead halide perovskites might be protected as large polarons. J. Phys. Chem. Lett. 6, 4758–4761 (2015).

    CAS  PubMed  Google Scholar 

  24. Anusca, I. et al. Dielectric response: answer to many questions in the methylammonium lead halide solar cell absorbers. Adv. Energy Mater. 7, 1700600 (2017).

    Google Scholar 

  25. Zhu, H. et al. Screening in crystalline liquids protects energetic carriers in hybrid perovskites. Science 353, 1409–1413 (2016).

    CAS  PubMed  Google Scholar 

  26. Etienne, T., Mosconi, E. & De Angelis, F. Dynamical origin of the Rashba effect in organohalide lead perovskites: A key to suppressed carrier recombination in perovskite solar cells? J. Phys. Chem. Lett. 7, 1638–1645 (2016).

    CAS  PubMed  Google Scholar 

  27. Zheng, F., Tan, L. Z., Liu, S. & Rappe, A. M. Rashba spin–orbit coupling enhanced carrier lifetime in CH3NH3PbI3. Nano Lett. 15, 7794–7800 (2015).

    CAS  PubMed  Google Scholar 

  28. Hutter, E. M. et al. Direct–indirect character of the bandgap in methylammonium lead iodide perovskite. Nat. Mater. 16, 115–120 (2017).

    CAS  PubMed  Google Scholar 

  29. Stranks, S. D. & Plochocka, P. The influence of the Rashba effect. Nat. Mater. 17, 381–382 (2018).

    CAS  PubMed  Google Scholar 

  30. Miyata, K. & Zhu, X.-Y. Ferroelectric large polarons. Nat. Mater. 17, 379–381 (2018). This short note was the first to propose the ferroelectric polaron, in which the charge carrier induces local ordering of symmetry-breaking unit cells.

    CAS  PubMed  Google Scholar 

  31. Wang, F. et al. Solvated electrons in solids — ferroelectric large polarons in lead halide perovskites. J. Am. Chem. Soc. 143, 5–16 (2021). This is an up-to-date review dealing with efficient dielectric screening in metal halide perovskites.

    CAS  PubMed  Google Scholar 

  32. Grinberg, I. et al. Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials. Nature 503, 509–512 (2013).

    CAS  PubMed  Google Scholar 

  33. Rappe, A. M., Grinberg, I. & Spanier, J. E. Getting a charge out of hybrid perovskites. Proc. Natl Acad. Sci. USA 114, 7191–7193 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  34. Liu, Y. et al. Chemical nature of ferroelastic twin domains in CH3NH3PbI3 perovskite. Nat. Mater. 17, 1013–1019 (2018).

    CAS  PubMed  Google Scholar 

  35. Gómez, A., Wang, Q., Goñi, A. R., Campoy-Quiles, M. & Abate, A. Ferroelectricity-free lead halide perovskites. Energy Environ. Sci. 12, 2537–2547 (2019).

    PubMed  PubMed Central  Google Scholar 

  36. Röhm, H., Leonhard, T., Hoffmann, M. J. & Colsmann, A. Ferroelectric domains in methylammonium lead iodide perovskite thin-films. Energy Environ. Sci. 10, 950–955 (2017).

    Google Scholar 

  37. Rakita, Y. et al. Tetragonal CH3NH3PbI3 is ferroelectric. Proc. Natl Acad. Sci. USA 114, 5504–5512 (2017).

    Google Scholar 

  38. Garten, L. M. et al. The existence and impact of persistent ferroelectric domains in MAPbI3. Sci. Adv. 5, eaas9311 (2019).

    PubMed  PubMed Central  Google Scholar 

  39. Gao, Z.-R. et al. Ferroelectricity of the orthorhombic and tetragonal MAPbBr3 single crystal. J. Phys. Chem. Lett. 10, 2522–2527 (2019).

    CAS  PubMed  Google Scholar 

  40. G, S. et al. Is CH3NH3PbI3 polar? J. Phys. Chem. Lett. 7, 2412–2419 (2016).

    CAS  PubMed  Google Scholar 

  41. Beilsten-Edmands, J., Eperon, G. E., Johnson, R. D., Snaith, H. J. & Radaelli, P. G. Non-ferroelectric nature of the conductance hysteresis in CH3NH3PbI3 perovskite-based photovoltaic devices. Appl. Phys. Lett. 106, 173502 (2015).

    Google Scholar 

  42. Benedek, N. A. & Fennie, C. J. Why are there so few perovskite ferroelectrics? J. Phys. Chem. C 117, 13339–13349 (2013).

    CAS  Google Scholar 

  43. Zhong, W. & Vanderbilt, D. Competing structural instabilities in cubic perovskites. Phys. Rev. Lett. 74, 2587–2590 (1995).

    CAS  PubMed  Google Scholar 

  44. Woodward, P. Octahedral tilting in perovskites. I. Geometrical considerations. Acta Crystallogr. Sect. B 53, 32–43 (1997). This seminal paper provides a comprehensive understanding on the structural distortion in perovskite lattices.

    Google Scholar 

  45. Woodward, P. Octahedral tilting in perovskites. II. Structure stabilizing forces. Acta Crystallogr. Sect. B 53, 44–66 (1997).

    Google Scholar 

  46. Cohen, R. E. Origin of ferroelectricity in perovskite oxides. Nature 358, 136–138 (1992).

    CAS  Google Scholar 

  47. Angel, R. J., Zhao, J. & Ross, N. L. General rules for predicting phase transitions in perovskites due to octahedral tilting. Phys. Rev. Lett. 95, 25503 (2005).

    CAS  Google Scholar 

  48. Liao, W.-Q. et al. A lead-halide perovskite molecular ferroelectric semiconductor. Nat. Commun. 6, 7338 (2015). This original paper reports unambiguous ferroelectricity in a 2D lead halide perovskite.

    PubMed  Google Scholar 

  49. Wang, S. et al. An unprecedented biaxial trilayered hybrid perovskite ferroelectric with directionally tunable photovoltaic effects. J. Am. Chem. Soc. 141, 7693–7697 (2019).

    CAS  PubMed  Google Scholar 

  50. Li, L. et al. Bilayered hybrid perovskite ferroelectric with giant two-photon absorption. J. Am. Chem. Soc. 140, 6806–6809 (2018).

    CAS  PubMed  Google Scholar 

  51. Wu, Z. et al. Discovery of an above-room-temperature antiferroelectric in two-dimensional hybrid perovskite. J. Am. Chem. Soc. 141, 3812–3816 (2019).

    CAS  PubMed  Google Scholar 

  52. Li, L. et al. Two-dimensional hybrid perovskite-type ferroelectric for highly polarization-sensitive shortwave photodetection. J. Am. Chem. Soc. 141, 2623–2629 (2019).

    CAS  PubMed  Google Scholar 

  53. Shi, P.-P. et al. Two-dimensional organic–inorganic perovskite ferroelectric semiconductors with fluorinated aromatic spacers. J. Am. Chem. Soc. 141, 18334–18340 (2019).

    CAS  PubMed  Google Scholar 

  54. Han, S. et al. High-temperature antiferroelectric of lead iodide hybrid perovskites. J. Am. Chem. Soc. 141, 12470–12474 (2019).

    CAS  PubMed  Google Scholar 

  55. Fabini, D. H. et al. Dynamic stereochemical activity of the Sn2+ lone pair in perovskite CsSnBr3. J. Am. Chem. Soc. 138, 11820–11832 (2016). This original paper reports dynamic B-cation off-centre displacement in CsSnBr3 upon heating.

    CAS  PubMed  Google Scholar 

  56. Fabini, D. H., Seshadri, R. & Kanatzidis, M. G. The underappreciated lone pair in halide perovskites underpins their unusual properties. MRS Bull. 45, 467–477 (2020).

    Google Scholar 

  57. McCall, K. M., Morad, V., Benin, B. M. & Kovalenko, M. V. Efficient lone-pair-driven luminescence: structure–property relationships in emissive 5s2 metal halides. ACS Mater. Lett. 2, 1218–1232 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  58. Stern, E. A. Character of order-disorder and displacive components in barium titanate. Phys. Rev. Lett. 93, 37601 (2004).

    Google Scholar 

  59. Sicron, N. et al. Nature of the ferroelectric phase transition in PbTiO3. Phys. Rev. B 50, 13168–13180 (1994).

    CAS  Google Scholar 

  60. Seshadri, R. & Hill, N. A. Visualizing the role of Bi 6s “lone pairs” in the off-center distortion in ferromagnetic BiMnO3. Chem. Mater. 13, 2892–2899 (2001).

    CAS  Google Scholar 

  61. Kuroiwa, Y. et al. Evidence for Pb-O covalency in tetragonal PbTiO3. Phys. Rev. Lett. 87, 217601 (2001).

    CAS  PubMed  Google Scholar 

  62. Steigmeier, E. F. & Harbeke, G. Soft phonon mode and ferroelectricity in GeTe. Solid State Commun. 8, 1275–1279 (1970).

    CAS  Google Scholar 

  63. Waghmare, U. V., Spaldin, N. A., Kandpal, H. C. & Seshadri, R. First-principles indicators of metallicity and cation off-centricity in the IV-VI rocksalt chalcogenides of divalent Ge, Sn, and Pb. Phys. Rev. B 67, 125111 (2003).

    Google Scholar 

  64. Zhang, Y. et al. The first organic–inorganic hybrid luminescent multiferroic: (pyrrolidinium)MnBr3. Adv. Mater. 27, 3942–3946 (2015).

    CAS  PubMed  Google Scholar 

  65. Zalar, B., Laguta, V. V. & Blinc, R. NMR evidence for the coexistence of order-disorder and displacive components in barium titanate. Phys. Rev. Lett. 90, 37601 (2003).

    Google Scholar 

  66. Fons, P. et al. Phase transition in crystalline GeTe: pitfalls of averaging effects. Phys. Rev. B 82, 155209 (2010).

    Google Scholar 

  67. Mao, L., Stoumpos, C. C. & Kanatzidis, M. G. Two-dimensional hybrid halide perovskites: principles and promises. J. Am. Chem. Soc. 141, 1171–1190 (2019).

    CAS  PubMed  Google Scholar 

  68. Saparov, B. & Mitzi, D. B. Organic–inorganic perovskites: structural versatility for functional materials design. Chem. Rev. 116, 4558–4596 (2016).

    CAS  PubMed  Google Scholar 

  69. Zhang, Y., Ke, X., Kent, P. R. C., Yang, J. & Chen, C. Anomalous lattice dynamics near the ferroelectric instability in PbTe. Phys. Rev. Lett. 107, 175503 (2011).

    PubMed  Google Scholar 

  70. Liao, W.-Q., Tang, Y.-Y., Li, P.-F., You, Y.-M. & Xiong, R.-G. Competitive halogen bond in the molecular ferroelectric with large piezoelectric response. J. Am. Chem. Soc. 140, 3975–3980 (2018).

    CAS  PubMed  Google Scholar 

  71. Ye, H.-Y. et al. High-temperature ferroelectricity and photoluminescence in a hybrid organic–inorganic compound: (3-pyrrolinium)MnCl3. J. Am. Chem. Soc. 137, 13148–13154 (2015).

    CAS  PubMed  Google Scholar 

  72. Rakita, Y. et al. CH3NH3PbBr3 is not pyroelectric, excluding ferroelectric-enhanced photovoltaic performance. APL Mater. 4, 51101 (2016).

    Google Scholar 

  73. Sun, Z. et al. A photoferroelectric perovskite-type organometallic halide with exceptional anisotropy of bulk photovoltaic effects. Angew. Chem. Int. Ed. 55, 6545–6550 (2016).

    CAS  Google Scholar 

  74. Li, L. et al. A potential Sn-based hybrid perovskite ferroelectric semiconductor. J. Am. Chem. Soc. 142, 1159–1163 (2020).

    CAS  PubMed  Google Scholar 

  75. Borriello, I., Cantele, G. & Ninno, D. Ab initio investigation of hybrid organic-inorganic perovskites based on tin halides. Phys. Rev. B 77, 235214 (2008).

    Google Scholar 

  76. Radha, S. K., Bhandari, C. & Lambrecht, W. R. L. Distortion modes in halide perovskites: to twist or to stretch, a matter of tolerance and lone pairs. Phys. Rev. Mater. 2, 63605 (2018).

    CAS  Google Scholar 

  77. Bechtel, J. S. & Van der Ven, A. Octahedral tilting instabilities in inorganic halide perovskites. Phys. Rev. Mater. 2, 25401 (2018).

    CAS  Google Scholar 

  78. Yang, R. X., Skelton, J. M., da Silva, E. L., Frost, J. M. & Walsh, A. Assessment of dynamic structural instabilities across 24 cubic inorganic halide perovskites. J. Chem. Phys. 152, 24703 (2020).

    CAS  Google Scholar 

  79. Boschker, J. E., Wang, R. & Calarco, R. GeTe: a simple compound blessed with a plethora of properties. CrystEngComm 19, 5324–5335 (2017).

    CAS  Google Scholar 

  80. Marronnier, A. et al. Anharmonicity and disorder in the black phases of cesium lead iodide used for stable inorganic perovskite solar cells. ACS Nano 12, 3477–3486 (2018).

    CAS  PubMed  Google Scholar 

  81. Whitfield, P. S. et al. Structures, phase transitions and tricritical behavior of the hybrid perovskite methyl ammonium lead iodide. Sci. Rep. 6, 35685 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. Poglitsch, A. & Weber, D. Dynamic disorder in methylammoniumtrihalogenoplumbates (II) observed by millimeter-wave spectroscopy. J. Chem. Phys. 87, 6373–6378 (1987).

    CAS  Google Scholar 

  83. Stoumpos, C. C., Malliakas, C. D. & Kanatzidis, M. G. Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties. Inorg. Chem. 52, 9019–9038 (2013).

    CAS  PubMed  Google Scholar 

  84. Frohna, K. et al. Inversion symmetry and bulk Rashba effect in methylammonium lead iodide perovskite single crystals. Nat. Commun. 9, 1829 (2018).

    PubMed  PubMed Central  Google Scholar 

  85. Morrow, D. J. et al. Disentangling second harmonic generation from multiphoton photoluminescence in halide perovskites using multidimensional harmonic generation. J. Phys. Chem. Lett. 11, 6551–6559 (2020).

    CAS  PubMed  Google Scholar 

  86. Breternitz, J., Lehmann, F., Barnett, S. A., Nowell, H. & Schorr, S. Role of the iodide–methylammonium interaction in the ferroelectricity of CH3NH3PbI3. Angew. Chem. Int. Ed. 59, 424–428 (2020).

    CAS  Google Scholar 

  87. Dang, Y. et al. Bulk crystal growth of hybrid perovskite material CH3NH3PbI3. CrystEngComm 17, 665–670 (2015).

    CAS  Google Scholar 

  88. Leguy, A. M. A. et al. The dynamics of methylammonium ions in hybrid organic–inorganic perovskite solar cells. Nat. Commun. 6, 7124 (2015).

    PubMed  Google Scholar 

  89. Bakulin, A. A. et al. Real-time observation of organic cation reorientation in methylammonium lead iodide perovskites. J. Phys. Chem. Lett. 6, 3663–3669 (2015).

    CAS  PubMed  Google Scholar 

  90. Selig, O. et al. Organic cation rotation and immobilization in pure and mixed methylammonium lead-halide perovskites. J. Am. Chem. Soc. 139, 4068–4074 (2017).

    CAS  PubMed  Google Scholar 

  91. Chi, L. et al. The ordered phase of methylammonium lead chloride CH3ND3PbCl3. J. Solid State Chem. 178, 1376–1385 (2005).

    CAS  Google Scholar 

  92. Swainson, I. P., Hammond, R. P., Soullière, C., Knop, O. & Massa, W. Phase transitions in the perovskite methylammonium lead bromide, CH3ND3PbBr3. J. Solid State Chem. 176, 97–104 (2003).

    CAS  Google Scholar 

  93. Schueller, E. C. et al. Crystal structure evolution and notable thermal expansion in hybrid perovskites formamidinium tin iodide and formamidinium lead bromide. Inorg. Chem. 57, 695–701 (2018).

    CAS  PubMed  Google Scholar 

  94. Keshavarz, M. et al. Tracking structural phase transitions in lead-halide perovskites by means of thermal expansion. Adv. Mater. 31, 1900521 (2019).

    Google Scholar 

  95. Müller, K. A. & Burkard, H. SrTiO3: an intrinsic quantum paraelectric below 4 K. Phys. Rev. B 19, 3593–3602 (1979).

    Google Scholar 

  96. Travis, W., Glover, E. N. K., Bronstein, H., Scanlon, D. O. & Palgrave, R. G. On the application of the tolerance factor to inorganic and hybrid halide perovskites: a revised system. Chem. Sci. 7, 4548–4556 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  97. Kieslich, G., Sun, S. & Cheetham, A. K. Solid-state principles applied to organic–inorganic perovskites: new tricks for an old dog. Chem. Sci. 5, 4712–4715 (2014).

    CAS  Google Scholar 

  98. Ma̧czka, M. et al. Methylhydrazinium lead bromide: noncentrosymmetric three-dimensional perovskite with exceptionally large framework distortion and green photoluminescence. Chem. Mater. 32, 1667–1673 (2020).

    Google Scholar 

  99. Ma̧czka, M. et al. Three-dimensional perovskite methylhydrazinium lead chloride with two polar phases and unusual second-harmonic generation bistability above room temperature. Chem. Mater. 32, 4072–4082 (2020).

    Google Scholar 

  100. Fu, Y. et al. Incorporating large A cations into lead iodide perovskite cages: relaxed Goldschmidt tolerance factor and impact on exciton–phonon interaction. ACS Cent. Sci. 5, 1377–1386 (2019). This original paper reports the incorporation of various oversized A-cations into the perovskite cages, which induces unusually large octahedra distortions.

    CAS  PubMed  PubMed Central  Google Scholar 

  101. Fu, Y. et al. Cation engineering in two-dimensional Ruddlesden–Popper lead iodide perovskites with mixed large A-site cations in the cages. J. Am. Chem. Soc. 142, 4008–4021 (2020).

    CAS  PubMed  Google Scholar 

  102. Li, X. et al. Negative pressure engineering with large cage cations in 2D halide perovskites causes lattice softening. J. Am. Chem. Soc. 142, 11486–11496 (2020).

    CAS  PubMed  Google Scholar 

  103. Hautzinger, M. P. et al. Band edge tuning of two-dimensional Ruddlesden–Popper perovskites by A cation size revealed through nanoplates. ACS Energy Lett. 5, 1430–1437 (2020).

    CAS  Google Scholar 

  104. Ye, H.-Y. et al. Bandgap engineering of lead-halide perovskite-type ferroelectrics. Adv. Mater. 28, 2579–2586 (2016).

    CAS  PubMed  Google Scholar 

  105. Lemmerer, A. & Billing, D. G. Synthesis, characterization and phase transitions of the inorganic–organic layered perovskite-type hybrids [(CnH2n+1NH3)2PbI4], n = 7, 8, 9 and 10. Dalton Trans. 41, 1146–1157 (2012).

    CAS  PubMed  Google Scholar 

  106. Li, L. et al. Tailored engineering of an unusual (C4H9NH3)2(CH3NH3)2Pb3Br10 two-dimensional multilayered perovskite ferroelectric for a high-performance photodetector. Angew. Chem. Int. Ed. 56, 12150–12154 (2017).

    CAS  Google Scholar 

  107. Sha, T.-T. et al. Fluorinated 2D lead iodide perovskite ferroelectrics. Adv. Mater. 31, 1901843 (2019).

    Google Scholar 

  108. Park, I.-H. et al. Ferroelectricity and Rashba effect in a two-dimensional Dion-Jacobson hybrid organic–inorganic perovskite. J. Am. Chem. Soc. 141, 15972–15976 (2019).

    CAS  PubMed  Google Scholar 

  109. Kamminga, M. E. et al. Confinement effects in low-dimensional lead iodide perovskite hybrids. Chem. Mater. 28, 4554–4562 (2016).

    CAS  Google Scholar 

  110. Yang, Y., Lou, F. & Xiang, H. Cooperative nature of ferroelectricity in two-dimensional hybrid organic–inorganic perovskites. Nano Lett. 21, 3170–3176 (2021).

    CAS  PubMed  Google Scholar 

  111. Wu, Z. et al. Alloying n-butylamine into CsPbBr3 to give a two-dimensional bilayered perovskite ferroelectric material. Angew. Chem. Int. Ed. 57, 8140–8143 (2018).

    CAS  Google Scholar 

  112. Hautzinger, M. P. et al. Two-dimensional lead halide perovskites templated by a conjugated asymmetric diammonium. Inorg. Chem. 56, 14991–14998 (2017).

    CAS  PubMed  Google Scholar 

  113. Swainson, I. et al. Orientational ordering, tilting and lone-pair activity in the perovskite methylammonium tin bromide, CH3NH3SnBr3. Acta Crystallogr. Sect. B 66, 422–429 (2010).

    CAS  Google Scholar 

  114. Laurita, G., Fabini, D. H., Stoumpos, C. C., Kanatzidis, M. G. & Seshadri, R. Chemical tuning of dynamic cation off-centering in the cubic phases of hybrid tin and lead halide perovskites. Chem. Sci. 8, 5628–5635 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  115. Božin, E. S. et al. Entropically stabilized local dipole formation in lead chalcogenides. Science 330, 1660–1663 (2010).

    PubMed  Google Scholar 

  116. Xie, H. et al. All-inorganic halide perovskites as potential thermoelectric materials: dynamic cation off-centering induces ultralow thermal conductivity. J. Am. Chem. Soc. 142, 9553–9563 (2020).

    CAS  PubMed  Google Scholar 

  117. Lee, W. et al. Ultralow thermal conductivity in all-inorganic halide perovskites. Proc. Natl Acad. Sci. USA 114, 8693–8697 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  118. Zeier, W. G. et al. Thinking like a chemist: intuition in thermoelectric materials. Angew. Chem. Int. Ed. 55, 6826–6841 (2016).

    CAS  Google Scholar 

  119. Delaire, O. et al. Giant anharmonic phonon scattering in PbTe. Nat. Mater. 10, 614–619 (2011).

    CAS  PubMed  Google Scholar 

  120. Sharma, R. et al. Elucidating the atomistic origin of anharmonicity in tetragonal CH3NH3PbI3 with Raman scattering. Phys. Rev. Mater. 4, 92401 (2020).

    CAS  Google Scholar 

  121. Wilson, J. N., Frost, J. M., Wallace, S. K. & Walsh, A. Dielectric and ferroic properties of metal halide perovskites. APL Mater. 7, 10901 (2019).

    Google Scholar 

  122. Herz, L. M. How lattice dynamics moderate the electronic properties of metal-halide perovskites. J. Phys. Chem. Lett. 9, 6853–6863 (2018).

    CAS  PubMed  Google Scholar 

  123. Burkhard, H., Geick, R., Kästner, P. & Unkelbach, K.-H. Lattice vibrations and free carrier dispersion in PbSe. Phys. Status Solidi 63, 89–96 (1974).

    CAS  Google Scholar 

  124. Huang, L. & Lambrecht, W. R. L. Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3, and CsSnI3. Phys. Rev. B 88, 165203 (2013).

    Google Scholar 

  125. Faizan, M., Bhamu, K.C., Murtaza, G. et al. Electronic and optical properties of vacancy ordered double perovskites A2BX6 (A = Rb, Cs; B = Sn, Pd, Pt; and X = Cl, Br, I): a first principles study. Sci. Rep. 11, 6965 (2021).

    PubMed  PubMed Central  Google Scholar 

  126. Young, K. F. & Frederikse, H. P. R. Compilation of the static dielectric constant of inorganic solids. J. Phys. Chem. Ref. Data 2, 313–410 (1973).

    Google Scholar 

  127. Guo, Y. et al. Dynamic emission Stokes shift and liquid-like dielectric solvation of band edge carriers in lead-halide perovskites. Nat. Commun. 10, 1175 (2019).

    PubMed  PubMed Central  Google Scholar 

  128. Kepenekian, M. et al. Rashba and Dresselhaus effects in hybrid organic–inorganic perovskites: from basics to devices. ACS Nano 9, 11557–11567 (2015).

    CAS  PubMed  Google Scholar 

  129. Kepenekian, M. & Even, J. Rashba and Dresselhaus couplings in halide perovskites: accomplishments and opportunities for spintronics and spin–orbitronics. J. Phys. Chem. Lett. 8, 3362–3370 (2017).

    CAS  PubMed  Google Scholar 

  130. Becker, M. A. et al. Bright triplet excitons in caesium lead halide perovskites. Nature 553, 189–193 (2018).

    CAS  PubMed  Google Scholar 

  131. Wang, F. et al. Switchable Rashba anisotropy in layered hybrid organic–inorganic perovskite by hybrid improper ferroelectricity. NPJ Comput. Mater. 6, 183 (2020).

    CAS  Google Scholar 

  132. Jenkins, H. D. B. & Waddington, T. C. Lone electron pairs and stereochemistry. Nature 255, 623–625 (1975).

    CAS  Google Scholar 

  133. Pearson, R. G. The second-order Jahn-Teller effect. J. Mol. Struct.: THEOCHEM 103, 25–34 (1983).

    Google Scholar 

  134. Trinquier, G. Double bonds and bridged structures in the heavier analogs of ethylene. J. Am. Chem. Soc. 112, 2130–2137 (1990).

    CAS  Google Scholar 

  135. Orgel, L. E. 769. The stereochemistry of B subgroup metals. Part II. The inert pair. J. Chem. Soc. 3815–3819 (1959).

  136. Wheeler, R. A. & Kumar, P. N. V. P. Stereochemically active or inactive lone pair electrons in some six-coordinate, group 15 halides. J. Am. Chem. Soc. 114, 4776–4784 (1992).

    CAS  Google Scholar 

  137. Walsh, A., Payne, D. J., Egdell, R. G. & Watson, G. W. Stereochemistry of post-transition metal oxides: revision of the classical lone pair model. Chem. Soc. Rev. 40, 4455–4463 (2011). This is an excellent review detailing the stereochemistry of ns2-lone-pair-bearing solids.

    CAS  PubMed  Google Scholar 

  138. Stoltzfus, M. W., Woodward, P. M., Seshadri, R., Klepeis, J.-H. & Bursten, B. Structure and bonding in SnWO4, PbWO4, and BiVO4: lone pairs vs inert pairs. Inorg. Chem. 46, 3839–3850 (2007).

    CAS  PubMed  Google Scholar 

  139. Payne, D. J. et al. Electronic origins of structural distortions in post-transition metal oxides: experimental and theoretical evidence for a revision of the lone pair model. Phys. Rev. Lett. 96, 157403 (2006).

    CAS  PubMed  Google Scholar 

  140. Walsh, A. & Watson, G. W. The origin of the stereochemically active Pb(II) lone pair: DFT calculations on PbO and PbS. J. Solid State Chem. 178, 1422–1428 (2005).

    CAS  Google Scholar 

  141. Ganose, A. M., Butler, K. T., Walsh, A. & Scanlon, D. O. Relativistic electronic structure and band alignment of BiSI and BiSeI: candidate photovoltaic materials. J. Mater. Chem. A 4, 2060–2068 (2016).

    CAS  Google Scholar 

  142. Wang, X. & Liebau, F. Studies on bond and atomic valences. I. correlation between bond valence and bond angles in SbIII chalcogen compounds: the influence of lone-electron pairs. Acta Crystallogr. Sect. B 52, 7–15 (1996).

    Google Scholar 

  143. Skoug, E. J. & Morelli, D. T. Role of lone-pair electrons in producing minimum thermal conductivity in nitrogen-group chalcogenide compounds. Phys. Rev. Lett. 107, 235901 (2011).

    PubMed  Google Scholar 

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Acknowledgements

X.-Y.Z. acknowledges the Vannevar Bush Faculty Fellowship through Office of Naval Research grant no. N00014-18-1-2080 and the US Department of Energy, Office of Energy Sciences, grant DE-SC0010692 for support at various stages of writing of this account. S.J. acknowledges support through the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under award DE-FG02-09ER46664.

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Y.F., S.J. and X.-Y.Z. discussed the content of the article and Y.F. wrote the first version of the manuscript. All authors edited the manuscript prior to submission.

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Glossary

Polaron

A quasiparticle consisting of an electron or a hole dressed by a cloud of local distortion of the lattice. When the distortion is mostly confined within the unit cell, it is a small polaron. If the distortion extends well beyond the unit cell, the result is a large polaron.

Rashba effect

Momentum-dependent splitting of spin bands due to a combined effect of spin–orbit coupling and asymmetry of the crystal potential. In a non-centrosymmetric solid, the static electric field Lorentz transforms into a magnetic field in the reference frame of a moving electron, which then interacts with the electron spin and breaks the spin degeneracy.

Displacive ferroelectrics

Refers to the scenario where ions are displaced from the equilibrium positions to create the spontaneous polarization at temperatures below the Curie temperature.

Second-harmonic generation

A nonlinear optical process in which two photons with the same energy interacting with a nonlinear material are effectively ‘combined’ to form a new photon with twice the energy.

Curie temperatures

The critical temperatures above which a ferroelectric material loses spontaneous polarization. The same concept applies to ferromagnetic materials.

Orthorhombic phase

When the lattice parameters a ≠ b ≠ c and all the angles are 90°.

Stokes shift

Describes the energy difference between the emission peak and the absorption peak.

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Fu, Y., Jin, S. & Zhu, XY. Stereochemical expression of ns2 electron pairs in metal halide perovskites. Nat Rev Chem 5, 838–852 (2021). https://doi.org/10.1038/s41570-021-00335-9

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