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. 2022 Nov 14;13:6935. doi: 10.1038/s41467-022-34705-8

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Schematics of NLA switching in conventional inorganic semiconductors (top) and the corresponding NLA evolution as a function of pump intensity (bottom), according to standard SA and RSA, where the RSA can stem from two-photon absorption (2PA). CB and VB denote conduction band and valence band respectively. ΔT denotes the NLA induced transmittance difference. b NLA of organic molecules based on excited state absorption (ESA) leading to an inverse transition from RSA to SA. S_0-2 represent the separated energy level. σ is the absorption cross-section. c NLA process of quasi-2D (PEA)₂FAPb₂I₇ perovskite film in our work, where the competition between non-thermalized carrier induced bleaching and many-body effect induced excitonic absorption enhancement results in a conversion from RSA to SA. d Schematic of the initial carrier evolution process in deposited quasi-2D perovskite film under femtosecond laser pulse excitation, where the blue blocks represent the bilayer perovskite grains. The left inserted illustration demonstrates the 2D lattice structure, and the right inset illustrates the initially ultrafast intra-band relaxation of photon generated carriers. Red arrow indicates the transition from VB to CB. E_g is the bandgap. Solid and dash lines represent the non-thermalized carrier and hot-carrier distribution, respectively. N_NTC and N_HC denote the non-thermalized carrier and hot carrier qualities at the resonance with incident photon energy (ħω). T_C is hot carrier temperature reflecting the carrier distribution after thermalization. Compared with the high T_C distribution (green), low T_C distribution (orange) will reduce the value of N_HC and weaken the bleaching induced by band filling.