Supplementary Information for Room Temperature Polariton Lasing in All-Inorganic Perovskite Nanoplatelets Rui Su, Carole Diederichs,, Jun Wang, ǁ Timothy C.H. Liew, Jiaxin Zhao, Sheng Liu, Weigao Xu, Zhanghai Chen, ǁ Qihua Xiong,,,* Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore. MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore Laboratoire Pierre Aigrain, Département de physique de l ENS, Ecole normale supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC Univ. Paris 6, CNRS, 755 Paris, France ǁ State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 2433, People s Republic of China NOVITAS, Nanoelectronics Center of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore. *To whom correspondence should be addressed. E-mail address: Qihua@ntu.edu.sg 1
1. CsPbCl3 perovskite silicon and mica substrates. In addition to transferring CsPbCl 3 perovskite to a bottom DBR, we could also directly grow CsPbCl 3 nanoplatelets on a bottom DBR or directly on silicon substrate for investigation of polariton behaviors. The square crystals exhibit high crystalline quality. 1μm 5 μm Figure S1. Top panel, microscope image of directly synthesized CsPCl 3 nanoplatelets on top of Silicon substrate with silicon dioxide layer and the corresponding fluorescence image. Bottom panel, microscope image of CsPCl 3 nanoplatelets on mica substrate and the corresponding fluorescence image. As shown in Figure S2, the emission of a ~ 2 μm thick CsPbCl 3 platelet on silicon substrate exhibits multiple peaks with unequal energy spacing. Similar results can be observed in CsPbCl 3 platelets on DBR substrate. The CsPbCl 3 platelet is thick enough to serve as a cavity. 2
a b 1. 1. Emission Intensity (a.u).8.6.4.2 Emission Intensity (a.u).8.6.4.2.. 2.7 2.8 2.9 3. 3.1 3.2 2.7 2.8 2.9 3. 3.1 3.2 Figure S2. Room temperature photoluminescence spectra. a, Room temperature photoluminescence spectrum of a ~ 2 μm thick CsPbCl 3 platelet on Si substrate, showing polariton emission with unequal spacing. The perovskite crystal is thick enough to serve as a cavity. b, Room temperature photoluminescence spectrum of a ~ 2 μm thick CsPbCl 3 platelet on DBR substrate, showing polariton emission with unequal spacing. The perovskite crystal is thick enough to serve as a cavity. 2. Reflectivity of bottom and top DBRs Figure S3a shows the reflectivity of a 7 pairs bottom DBR. The stop band ranges from 2.7 ev to 3.2 ev nm with maximum reflectivity of 97%. As shown in Figure S3b, the stop band of a 13 pairs bottom DBR before perovskite synthesis process is designed to range from 2.5 ev to 2.95 ev with maximum reflectivity of 99.7%. After the perovskite synthesis procedure, the stop band of the bottom DBR blueshifts by.25 ev, ranging from 2.75 ev to 3.15 ev with maximum reflectivity of 99.3%. 3
a b 1 Top DBR 1 Before CVD After CVD Reflectivity (%) 8 6 4 2 2. 2.5 3. 3.5 4. Reflectivity (%) 8 6 4 2 2. 2.5 3. 3.5 4. Figure S3. Reflectivity of top and bottom DBRs. a, Reflectivity measurement of a 7 pairs top DBR, centered at 2.92 ev with maximum reflectivity of 97%. b, Reflectivity measurement of a 13 pairs bottom DBR before and after CVD growth procedure. The center wavelength changes from around 2.65 ev to 2.92 ev after CVD growth procedure, with a slight decrease of the maximum reflectivity from 99.7% to 99.3%. 3. Angle-resolved reflectivity dispersion of the bare microcavity. The bare microcavity without any perovskite inside shows a parabolic dispersion in Figure S4, which is consistent with the parabolic dispersion in Figure 2a. 4
3.2 Max 3.15 3.1 3.5 3. 2.95 2.9 Min -6-3 3 Angle ( ) 6 Figure S4. Angle-resolved reflectivity dispersion of the bare microcavity without any perovskite inside. 4. Polariton dispersion based on a thinner (36 nm) perovskite microcavity. We also provide in Figure S5 reflectivity and Photoluminescence measurements performed on a slightly thinner (~ 36 nm) and wider perovskite microcavity, associated to a positive detuning (Δ= + 7 mev). The flatter dispersion of the lower polariton branch is resolved on both sets of data; along with the bare cavity mode in the PL (the laser spot was moved closer to the platelet s edge for the PL measurements as a result of sample degradation after pulse laser measurements). A small fraction of the dispersion of a Bragg mode (BM) is also visible at large angles (+/- 6 ). We conclude that the strong coupling regime and polariton emission are reached for different detunings in inorganic perovskites. 5
Figure S5. Angle-resolved dispersion on 36 nm thick perovskite microcavity. Angleresolved reflectivity (a) and photoluminescence (b) measured below the polariton lasing threshold, at positive detuning (Δ= + 7 mev). The dispersions of the lower polariton (LP) and the Bragg mode (BM) are observed in reflectivity and PL, and the additional bare cavity mode (when no perovskite is embedded in the microcavity) is only observed in PL. Coupled oscillator fits of the lower polariton (LP) and upper polariton (UP) dispersions are displayed along with the dispersions of the uncoupled exciton (X) and cavity (C) modes. The extracted Rabi splitting is 273 mev. Finally, coupled oscillator fits applied to both reflectivity and PL results at positive detuning of Δ= + 7 mev allow us to unambiguously extract the Rabi splitting of around 273 mev. The transition from strong coupling region to weak coupling region was demonstrated on the sample showing a positive detuning Δ= + 7 mev (i.e. sample used for the reflectivity and PL measurements in Figure S5). Due to the decreasing optical trap formed by the lower polariton branch at the chosen positive detuning, it is in fact more likely to reach a sufficiently high carrier density in the reservoir for the formation of an electron-hole plasma (EHP) and for the appearance of an eventual photon lasing process in the weak coupling regime. 6
We present in Figure S6 the angular resolved emission (a-c) along with the real space image of the sample emission (d-f) as a function of pump fluence. By comparison with the reflectivity and PL measurements presented in Figure S5, a much stronger emission is observed at the lower polariton ground state, E LP (k =)=2.94 ev, from P th = 55 µj/cm². In real space, whereas the emission spot reflects the laser spot intensity distribution just below P th (at P =.9 P th for example), the strong emission above P th is localized on a 4 µm diameter spot within the laser spot diameter of about 25 µm. When further increasing the pump fluence (at P = 5. P th for example), an emission at a lower energy than the polariton one (i.e. at ~2.9 ev) characterized by a flat dispersion is observed, while the emission of the lower polariton branch is still visible with much lower intensity. We attribute this additional contribution to the EHP emission in the weak coupling regime which is accompanied by a band-gap renormalization at high pump fluence as previously observed in ZnO microcavities for example (H. Franke et al., New J. Phys. 14, 1337 (212)). Apart from the flat dispersion of the EHP emission, we also observe a very different emission diagram in the real space since the emission from the edge of the belt-type perovskite platelet dominates at high pump fluence (at P = 5. P th for example). With these results, the polariton emission in the strong coupling regime can be clearly distinguished from the EHP emission in the weak coupling regime. 7
Figure S6. Transition from strong coupling to weak coupling regime. a-c, Angle resolved photoluminescence spectrum obtained at 1. P th, 1.6 P th and 5. P th, showing a transition from polariton condensate regime to weak coupling regime with a sharp decrease of emission intensity. d-f, Real space images obtained at.9 P th, 1.6 P th and 5. P th, showing a broad emission distribution below threshold, while above threshold, a localized polariton condensate shows up in the body of the platelet. Further increasing the pump fluence to 5. P th, the polariton condensate vanishes while an extremely stronger emission appears at the edges of the platelet. In order to better understand the emission properties observed in the strong and weak coupling regimes, we present in Figure S7 as an analysis of the measurements shown in Figure S6, in particular the power dependence of the emission intensities (Fig. S7, a), linewidths (Fig. S7, a) and peak energy positions (Fig. S7 b). We first observe, in the strong coupling regime at P th = 55 µj/cm², a transition associated with a sharp increase of the polariton emission intensity, a narrowing of the emission linewidth (FWHM) and a continuous blueshift in emission energy due to polariton-polariton interactions. This transition defines the pump threshold of the polariton laser induced by the spatially localized polariton condensate observed in the real space image in 8
Figure S6 at P = 1.6 P th. Then, the increase of the pump fluence well above the polariton lasing threshold, i.e., above 1 µj/cm², leads to the polariton condensate vanishing and the related decrease of the emission intensity at the lower polariton ground state energy and increase of the emission linewidth. This decrease of emission intensity could be explained by the change of cavity direction from vertical to horizontal. Meanwhile, the EHP emission appears and dominates the signal above P th2 = 18 µj/cm², mainly at the belt edges. The latter pump fluence defines a second threshold for the transition to the weak coupling regime in the sample. This statement is further confirmed by the continuous redshift of the EHP emission and the superlinear behavior of the EHP emission intensity above P th2 (Fig. S7, b and c, respectively). Additional precise studies of the EHP emission still need to be done to determine whether the second threshold corresponds to a photon lasing threshold where the photon laser cavity would be defined by the lateral belt facets, or only to the weak coupling threshold where the EHP emission is preferentially detected through the leaky modes of the structure. Figure S7 Characterizations of polariton lasing in 36 nm thick perovskite microcavity. a, Ground state emission intensity and FWHM at k = as a function of pump fluence. A typical S shape power dependent emission relationship suggests the occurrence of polariton lasing with a first threshold P th of 55 μj/cm 2, while the emission intensity decreases sharply crossing a pump fluence P th2 of 18 μj/cm 2. The FWHM first slightly increases (from 1.1 mev to 11.4 mev) below threshold Pth and narrows from 11 mev to 3.5 mev when crossing the threshold P th, and then increases until 19 mev with the further increase of pump fluence. b, Ground state emission peak position at k = as a function of pump fluence. The emission peak position in the strong 9
coupling regime shows continuous blueshift with two different slopes below P th2. When crossing the second threshold P th2 of 18 μj/cm 2 to weak coupling regime, the energy position of another arisen peak corresponding to the EHP emission shows redshift with the increase of pump fluence. c, Edge emission intensity as a function of pump fluence, extracted from the real space images of the perovskite microcavity. A clear threshold P th2 of 18 μj/cm 2 was observed for the emission in the lateral modes. With these additional results, we believe that we have brought a clear proof that the lasing behavior observed in our perovskite samples corresponds to a polariton lasing effect induced by the formation of a polariton condensate, and not to the more classical photonic lasing effect observed in the weak exciton-photon coupling regime. This conclusion is supported by the dispersion, threshold and the spatial coherence measurements. 5. Polariton photoluminescence dispersion with disorder effects. Polariton dispersion above the threshold is obtained from a typical sample on the same chip, showing obvious signatures of disorder effects near the ground state. 3.1 3.5 3. 2.95 2.9-4 -2 2 4 Emission angle ( ) 1
Figure S8. Lower polariton photoluminescence dispersion above the threshold, showing obvious disorder effects. 6. Theoretical calculation of polariton condensate localization in real space. The theoretical calculation is an extent of the previous Gross-Pitaevskii theory (which was used to fit the blueshift dependence) which accounts for spatial dynamics. Using the dispersion obtained from coupled oscillator fits and including some disorder in the exciton energy, the localization effect can be successfully reproduced. The disorder was generated from a white noise convoluted with a Gaussian, giving a disorder profile characterized by a spatial correlation length (taken to be 1μm) and a root mean squared amplitude (taken to be 1 mev). a c 1 1. 9.95 9.9 9.85 9.8 9.75 9.7 9.65 9.6 9.55 9.5 9.45 9.4 9.35 9.3 9.25 9.2 9.15 9.1 9.5 9. 8.95 8.9 8.85 8.8 8.75 8.7 8.65 8.6 8.55 8.5 8.45 8.4 8.35 8.3 8.25 8.2 8.15 8.1 8.5 8. 7.95 7.9 7.85 7.8 7.75 7.7 7.65 7.6 7.55 7.5 7.45 7.4 7.35 7.3 7.25 7.2 7.15 7.1 7.5 7. 6.95 6.9 6.85 6.8 6.75 6.7 6.65 6.6 6.55 6.5 6.45 6.4 6.35 6.3 6.25 6.2 6.15 6.1 6.5 6. 5.95 5.9 5.85 5.8 5.75 5.7 5.65 5.6 5.55 5.5 5.45 5.4 5.35 5.3 5.25 5.2 5.15 5.1 5.5 5. 4.95 4.9 4.85 4.8 4.75 4.7 4.65 4.6 4.55 4.5 4.45 4.4 4.35 4.3 4.25 4.2 4.15 4.1 4.5 4. 3.95 3.9 3.85 3.8 3.75 3.7 3.65 3.6 3.55 3.5 3.45 3.4 3.35 3.3 3.25 3.2 3.15 3.1 3.5 3. 2.95 2.9 2.85 2.8 2.75 2.7 2.65 2.6 2.55 2.5 2.45 2.4 2.35 2.3 2.25 2.2 2.15 2.1 2.5 2. 1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.6 1.55 1.5 1.45 1.4 1.35 1.3 1.25 1.2 1.15 1.1 1.5 1..95.9.85.8.75.7.65.6.55.5.45.4.35.3.25.2.15.1.5. E 2 5 b E 1-1 -5 Kx( m-1) 5 Y ( m) 1 1 4.5E+6 4.49E+6 4.48E+6 4.47E+6 4.46E+6 4.45E+6 4.44E+6 4.43E+6 4.42E+6 4.41E+6 4.4E+6 4.39E+6 4.38E+6 4.37E+6 4.36E+6 4.35E+6 4.34E+6 4.33E+6 4.32E+6 4.31E+6 4.3E+6 4.29E+6 4.28E+6 4.27E+6 4.26E+6 4.25E+6 4.24E+6 4.23E+6 4.22E+6 4.21E+6 4.2E+6 4.19E+6 4.18E+6 4.17E+6 4.16E+6 4.15E+6 4.14E+6 4.13E+6 4.12E+6 4.11E+6 4.1E+6 4.9E+6 4.8E+6 4.7E+6 4.6E+6 4.5E+6 4.4E+6 4.3E+6 4.2E+6 4.1E+6 4.E+6 3.99E+6 3.98E+6 3.97E+6 3.96E+6 3.95E+6 3.94E+6 3.93E+6 3.92E+6 3.91E+6 3.9E+6 3.89E+6 3.88E+6 3.87E+6 3.86E+6 3.85E+6 3.84E+6 3.83E+6 3.82E+6 3.81E+6 3.8E+6 3.79E+6 3.78E+6 3.77E+6 3.76E+6 3.75E+6 3.74E+6 3.73E+6 3.72E+6 3.71E+6 3.7E+6 3.69E+6 3.68E+6 3.67E+6 3.66E+6 3.65E+6 3.64E+6 3.63E+6 3.62E+6 3.61E+6 3.6E+6 3.59E+6 3.58E+6 3.57E+6 3.56E+6 3.55E+6 3.54E+6 3.53E+6 3.52E+6 3.51E+6 3.5E+6 3.49E+6 3.48E+6 3.47E+6 3.46E+6 3.45E+6 3.44E+6 3.43E+6 3.42E+6 3.41E+6 3.4E+6 3.39E+6 3.38E+6 3.37E+6 3.36E+6 3.35E+6 3.34E+6 3.33E+6 3.32E+6 3.31E+6 3.3E+6 3.29E+6 3.28E+6 3.27E+6 3.26E+6 3.25E+6 3.24E+6 3.23E+6 3.22E+6 3.21E+6 3.2E+6 3.19E+6 3.18E+6 3.17E+6 3.16E+6 3.15E+6 3.14E+6 3.13E+6 3.12E+6 3.11E+6 3.1E+6 3.9E+6 3.8E+6 3.7E+6 3.6E+6 3.5E+6 3.4E+6 3.3E+6 3.2E+6 3.1E+6 3.E+6 2.99E+6 2.98E+6 2.97E+6 2.96E+6 2.95E+6 2.94E+6 2.93E+6 2.92E+6 2.91E+6 2.9E+6 2.89E+6 2.88E+6 2.87E+6 2.86E+6 2.85E+6 2.84E+6 2.83E+6 2.82E+6 2.81E+6 2.8E+6 2.79E+6 2.78E+6 2.77E+6 2.76E+6 2.75E+6 2.74E+6 2.73E+6 2.72E+6 2.71E+6 2.7E+6 2.69E+6 2.68E+6 2.67E+6 2.66E+6 2.65E+6 2.64E+6 2.63E+6 2.62E+6 2.61E+6 2.6E+6 2.59E+6 2.58E+6 2.57E+6 2.56E+6 2.55E+6 2.54E+6 2.53E+6 2.52E+6 2.51E+6 2.5E+6 2.49E+6 2.48E+6 2.47E+6 2.46E+6 2.45E+6 2.44E+6 2.43E+6 2.42E+6 2.41E+6 2.4E+6 2.39E+6 2.38E+6 2.37E+6 2.36E+6 2.35E+6 2.34E+6 2.33E+6 2.32E+6 2.31E+6 2.3E+6 2.29E+6 2.28E+6 2.27E+6 2.26E+6 2.25E+6 2.24E+6 2.23E+6 2.22E+6 2.21E+6 2.2E+6 2.19E+6 2.18E+6 2.17E+6 2.16E+6 2.15E+6 2.14E+6 2.13E+6 2.12E+6 2.11E+6 2.1E+6 2.9E+6 2.8E+6 2.7E+6 2.6E+6 2.5E+6 2.4E+6 2.3E+6 2.2E+6 2.1E+6 2.E+6 1.99E+6 1.98E+6 1.97E+6 1.96E+6 1.95E+6 1.94E+6 1.93E+6 1.92E+6 1.91E+6 1.9E+6 1.89E+6 1.88E+6 1.87E+6 1.86E+6 1.85E+6 1.84E+6 1.83E+6 1.82E+6 1.81E+6 1.8E+6 1.79E+6 1.78E+6 1.77E+6 1.76E+6 1.75E+6 1.74E+6 1.73E+6 1.72E+6 1.71E+6 1.7E+6 1.69E+6 1.68E+6 1.67E+6 1.66E+6 1.65E+6 1.64E+6 1.63E+6 1.62E+6 1.61E+6 1.6E+6 1.59E+6 1.58E+6 1.57E+6 1.56E+6 1.55E+6 1.54E+6 1.53E+6 1.52E+6 1.51E+6 1.5E+6 1.49E+6 1.48E+6 1.47E+6 1.46E+6 1.45E+6 1.44E+6 1.43E+6 1.42E+6 1.41E+6 1.4E+6 1.39E+6 1.38E+6 1.37E+6 1.36E+6 1.35E+6 1.34E+6 1.33E+6 1.32E+6 1.31E+6 1.3E+6 1.29E+6 1.28E+6 1.27E+6 1.26E+6 1.25E+6 1.24E+6 1.23E+6 1.22E+6 1.21E+6 1.2E+6 1.19E+6 1.18E+6 1.17E+6 1.16E+6 1.15E+6 1.14E+6 1.13E+6 1.12E+6 1.11E+6 1.1E+6 1.9E+6 1.8E+6 1.7E+6 1.6E+6 1.5E+6 1.4E+6 1.3E+6 1.2E+6 1.1E+6 1.E+6 9.9E+5 9.8E+5 9.7E+5 9.6E+5 9.5E+5 9.4E+5 9.3E+5 9.2E+5 9.1E+5 9.E+5 8.9E+5 8.8E+5 8.7E+5 8.6E+5 8.5E+5 8.4E+5 8.3E+5 8.2E+5 8.1E+5 8.E+5 7.9E+5 7.8E+5 7.7E+5 7.6E+5 7.5E+5 7.4E+5 7.3E+5 7.2E+5 7.1E+5 7.E+5 6.9E+5 6.8E+5 6.7E+5 6.6E+5 6.5E+5 6.4E+5 6.3E+5 6.2E+5 6.1E+5 6.E+5 5.9E+5 5.8E+5 5.7E+5 5.6E+5 5.5E+5 5.4E+5 5.3E+5 5.2E+5 5.1E+5 5.E+5 4.9E+5 4.8E+5 4.7E+5 4.6E+5 4.5E+5 4.4E+5 4.3E+5 4.2E+5 4.1E+5 4.E+5 3.9E+5 3.8E+5 3.7E+5 3.6E+5 3.5E+5 3.4E+5 3.3E+5 3.2E+5 3.1E+5 3.E+5 2.9E+5 2.8E+5 2.7E+5 2.6E+5 2.5E+5 2.4E+5 2.3E+5 2.2E+5 2.1E+5 2.E+5 1.9E+5 1.8E+5 1.7E+5 1.6E+5 1.5E+5 1.4E+5 1.3E+5 1.2E+5 1.1E+5 1.E+5 9.E+4 8.E+4 7.E+4 6.E+4 5.E+4 4.E+4 3.E+4 2.E+4 1. -1 5-2 -1-5 Kx( m-1) 5-2 1-1 X ( m) 1 Max Min 2 Figure S9. a, Theoretically simulated photoluminescence dispersion below threshold and, b, above threshold. Note that there is a slight blueshift of the emission with respect to the energy minimum in (a). c, Simulated real-space distribution of polaritons in a disordered environment, showing condensation at localized points. 11