Superfluorescence from lead halide perovskite quantum dot superlattices

An ensemble of emitters can behave very differently from its individual constituents when they interact coherently via a common light field. After excitation of such an ensemble, collective coupling can give rise to a many-body quantum phenomenon that results in short, intense bursts of light—so-called superfluorescence1. Because this phenomenon requires a fine balance of interactions between the emitters and their decoupling from the environment, together with close identity of the individual emitters, superfluorescence has thus far been observed only in a limited number of systems, such as certain atomic and molecular gases and a few solid-state systems2–7. The generation of superfluorescent light in colloidal nanocrystals (which are bright photonic sources practically suited for optoelectronics8,9) has been precluded by inhomogeneous emission broadening, low oscillator strength, and fast exciton dephasing. Here we show that caesium lead halide (CsPbX3, X = Cl, Br) perovskite nanocrystals10–13 that are self-organized into highly ordered three-dimensional superlattices exhibit key signatures of superfluorescence. These are dynamically red-shifted emission with more than 20-fold accelerated radiative decay, extension of the first-order coherence time by more than a factor of four, photon bunching, and delayed emission pulses with Burnham–Chiao ringing behaviour14 at high excitation density. These mesoscopically extended coherent states could be used to boost the performance of opto-electronic devices15 and enable entangled multi-photon quantum light sources16,17. Cooperative quantum effects in superlattices of quantum dots made of caesium lead halide perovskite give rise to superfluorescence, with the individual emitters interacting coherently to give intense bursts of light.

photon bunching, and delayed emission pulses with Burnham-Chiao ringing behaviour 15 at high excitation density. These mesoscopically extended coherent states can be employed to boost opto-electronic device performances 16,17 and enable entangled multi-photon quantum light sources [18][19][20] .
Spontaneous emission (SE) of photons, such as fluorescence commonly used in displays or lighting, occurs due to coupling excited two-level systems (TLS) to the vacuum modes of the electromagnetic field, effectively stimulated by its zero-point fluctuations 21  due to the strong light-matter interaction, known as Burnham-Chiao ringing 15,23 .
SF was first observed in a dense gas of hydrogen fluoride 2 , followed by a limited number of solid state systems, such as CuCl nanocrystals (NCs) embedded in a NaCl matrix 4 , KCl crystals doped with peroxide anions ( 2 − ) (ref. 3 ) and some select semiconductor crystals 5,6 . However, the restrictions on the materials imposed by the requirement for high oscillator strength, small inhomogeneous line-broadening, together with little dephasing, make it difficult to exploit SF for solid-state applications, such as ultrafast light-emitting diodes or quantum sources of entangled photons. Colloidal semiconductor NCs or quantum dots (QDs) could fill this gap as they are inexpensive, easily processable, and a versatile material class already employed for advanced photonic applications 8,24 ; however, up to now, they have not been able to match the stringent properties necessary for SF.
Here, we use colloidal NCs of caesium lead halide perovskites (CsPbX3, X = Cl, Br, or I) that can be produced with narrow size dispersion and are known to exhibit moderate quantum confinement effects, resulting in narrow-band emission combined with exceptionally large oscillator strength from a bright triplet state 9,10,25 . In order to foster cooperative behaviour, we employ structurally well-defined, long-range ordered, and densely packed arrays of such NCs, known as superlattices, constructed by means of solvent-drying-induced spontaneous assembly 13,14,26,27 . Similarly, regular arrays of II-VI semiconductor NCs have been used to obtain collective effects in the electronic domain, i.e., band-like transport 17 . Figure   superlattice at 5 K exhibiting two peaks. The high-energy emission peak coincides with the single-peaked spectrum of an ensemble of CsPbBr3 NCs in an amorphous (glassy) film and is therefore assigned to non-coupled QDs. In addition, a narrow, red-shifted emission peak appears in superlattices, which we assign to the cooperative emission of QDs. We can exclude that this feature, which is typically red-shifted by 7090 meV from the uncoupled QD emission, originates from the emission from trions, bi-excitons, or multi-excitons, because their energy shifts are reportedly 1020 meV (refs. 10,11 ). The number and interaction strength of coherently coupled QDs determine the magnitude of the energetic shift. In most superlattices, we observe a sub-structure in this red-shifted emission band, which we attribute to the presence of several, slightly different independent SF domains within the same individual superlattice.
A central feature of the cooperative emission is the modification of the radiative lifetime 22 , as demonstrated experimentally with several quantum emitters 6,16 . In time-resolved PL decay measurements, we observe an accelerated PL decay of the SF emission peak in comparison to the PL decay of uncoupled QDs with 1/ decay times of SF = 148 ps and QD = 400 ps, respectively, for an excitation density of 500 nJ/cm 2 per pulse ( Figure 3b). In contrast to the predominantly mono-exponential decay of the uncoupled QDs, the SF emission decay is approximated well by a stretched exponential 28 , because the number of excited coupled emitters, and therefore the speed-up, varies during the decay. Furthermore, in contrast to the uncoupled QDs, the SF decay time is strongly dependent on excitation power (inset Figure 3b) because it scales with the coupling strength among the QDs, given by the intensity in the common light-field that effectively corresponds to a change in the number of coherently coupled QDs. When the spectrally and temporally integrated emission is fitted with a power law, we obtain an exponent of 1 (Extended Data Figure 1b Yet, it is a robust effect that is observed with pulsed excitation and for mixed-halide (CsPbBr2Cl, emitting at higher energies) QD superlattices too (see Extended Data Figure 3a and 4b, respectively). Remarkably, some superlattices with supposedly well-isolated coherently coupled QDs exhibit (2) ( ) > 2 (inset Figure 4), similar to superthermal emission 31 . The exponential decay time of the second-order correlation is of the order of the radiative decay of the SF emission for low excitation densities ( (2) = 224 ps).
Very distinct characteristics of SF emission concern the time evolution of the emitted light under strong driving conditions. Figure 5a shows a streak camera image acquired at an excitation density of 1600 μJ/cm 2 , where in addition to a drastically shortened radiative decay, As SF crucially depends on low decoherence and low inhomogeneous spread, it should be noted that SF coupling is strongly affected by the environment around the QDs (number of free ligands), the superlattice assembly, and by the quality of the QDs themselves.
Thus, while a large fraction of the superlattices displays a red-shifted peak from the cooperative emission, the amount of photon-bunching and Burnham-Chiao ringing varied from superlattice to superlattice. However, experiments employing different batches of NCs and superlattice assemblies of CsPbBr3 and CsPbBr2Cl NCs were consistently reproducible, but further optimization of the synthesis and assembly is likely to improve the yield of SF domains.
Our measurements reveal that coherent SF coupling can be achieved in long-range  supervised the work.

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A) NANOCRYSTAL SYNTHESIS AND SUPERLATTICE FORMATION
Synthesis of CsPbBr3 nanocrystals. In a 25 ml three-necked flask, PbBr2 (69 mg, 0.188 mmol, Aldrich, 99%) was suspended in octadecene (5 ml), dried at 100°C for 30 min, and mixed with oleic acid (0.5 ml, vacuum-dried at 100°C) and oleylamine (0.5 ml vacuum-dried at 100°C). When PbBr2 was dissolved, the reaction mixture was heated up to 180°C and preheated caesium oleate in octadecene (0.4 ml, 0.125 M) was injected. The reaction mixture was cooled immediately with an ice bath to room temperature.
Purification and size-selection of CsPbBr3 nanocrystals. A critical factor for self-assembly of cubic-shaped CsPbX3 NCs is to start with an initially high level of monodispersity. The crude solution was centrifuged at 12100 rpm for 5 min, following which the supernatant was discarded, and the precipitate was dissolved in 300 μl hexane. The hexane solution was centrifuged again and the precipitate was discarded. The supernatant was diluted two times and used for further purification. Subsequently, two methods of purification of the NCs were applied: (a) 50 μl hexane, 0.6 μl oleic acid, and 0.6 μl oleylamine were added to 50 μl NCs in hexane. The colloid was destabilized by adding 50 μl acetone, followed by centrifuging and dispersing the NCs in 300 μl toluene. This solution was used further for the preparation of the 3D-superlattices. (b) 50 μl hexane and 100 μl toluene were added to 50 μl NCs in hexane.
The colloid was destabilized by adding 50 μl acetonitrile, followed by centrifuging and dispersing the NCs in 300 μl toluene. This solution was used further for the preparation of the 3D-superlattices.

Preparation of 3D-superlattices.
CsPbBr3 NC superlattices were prepared on glass or on 5  7 mm silicon substrates. Shortly before the self-assembly process, the silicon substrate was dipped into 4% solution of HF in water for 1 min, followed by washing with water. In a typical assembly process, the substrate was placed in a 10  10 mm Teflon well and 10 μl of purified NCs in toluene were spread onto the substrate. The well was covered with a glass slide and the toluene was then allowed to evaporate slowly. 3D-superlattices of CsPbBr3 NCs were formed upon complete evaporation of the toluene. Typical lateral dimensions of individual superlattices ranged from 1 to 10 μm wherein some of them arrange into clusters of several superlattices and others remain spatially well-isolated so that PL measurements can be performed on an individual superlattice.
More intense purification or greater polydispersity of NCs led to disordered or 2D assemblies (glassy films). Furthermore, the formation of NC superlattices can serve to further narrow the size distribution and shape uniformity within the ensemble (with smaller or larger NCs being repelled from the NC domain), especially in the case of simple cubic packing of cubes, which is particularly intolerant to size and shape variations.

A) SUPERRADIANCE, SUPERFLUORESCENCE, AND SUBRADIANCE
As shown in Figure 3b, we observed that the PL decay of the SF state is initially very fast and cannot be described with a single exponential because the decay rate is dependent on the number of excited TLS, Γ( ) ∼ , and therefore decreases during the decay. Consequently, the SF decay rate should converge towards the decay rate of the uncoupled nanocrystals.
However, we observe that the SF decay trace crosses the bi-exponential PL decay of the uncoupled QDs after 97% of the photons are emitted due to long decay components. These long decay components might originate from coupled QDs where the individual dipoles are out of phase and interfere destructively, known as subradiance (SBR) 28,34 . In ensembles with inhomogeneously broadened PL, SF and subradiant states can coexist, and we find a good agreement of the predicted excited state population with the measured PL decay 35 .
An out-of-phase coupling amongst the QDs is expected to result in a higher photon energy of the subradiant state compared to the SF state. In Extended Data Figure  In the lower panel of Figure 5c, we plot the delay time as a function of the excitation power. In our analysis, the delay time is composed of the actual delay time due to the SF build-up and a systematic, constant time-offset because the absolute arrival time of the excitation pulse (which has a different wavelength than the emission) at the sample cannot be measured reliably at the required precision from the streak camera data. We observe a decrease in D of ~4 ps when increasing the excitation density by almost 2 orders of magnitude. We have fitted this behaviour with D = offset + ⋅ ln ( Exc + 1)/( Exc + 1) because we assume that D ∼ ln ( )/ and that the number of excited coupled emitters ∼ Exc + 1 is proportional to the excitation power. Herein, we use a fixed value = 0.148 ± 0.004 2 , which we obtained from the fit of the effective decay in the upper panel of Figure   5c. The resulting fit agrees very well with the data. To obtain the absolute time delay, we subtracted the constant offset of the time-delay fit from the time-delay data points. SF occurs when √ SF D < 2 * , where 2 * is the exciton pure dephasing time. Considering that the coherence time 2 < 2 * extracted from the full-width at half-maximum of single QDs 10 is of the order of 2 = 6.6 ps, our measurements reveal a fast decay of ~8 ps and a delay time of < 1 ps which satisfies the criterion for the appearance of SF.
Extended Data Figure 1 | Power dependent PL properties. a, Colour-coded PL emission of a single superlattice in the low-power excitation regime, shown for increasing excitation fluence of 10 nJ/cm 2 (light green), 60 nJ/cm 2 (light blue), 150 nJ/cm 2 (yellow), 310 nJ/cm 2 (dark green) and 600 nJ/cm 2 (dark blue). b, PL intensity integrated over the spectral emission range of the uncoupled QDs (blue circles) and coupled QDs (red circles) in a log-log plot and the total emitted intensity (yellow circles). Fits to the data reveal a perfectly linear behaviour, as represented by a fitted power-law exponent of 1. c, Colour-coded PL emission of a single superlattice in the high-power excitation regime, shown for increasing excitation fluence of 330 μJ/cm 2 (light green), 1270 μJ/cm 2 (light blue), 2130 μJ/cm 2 (yellow), 3470 μJ/cm 2 (dark green) and 6330 μJ/cm 2 (dark blue). d, PL intensity integrated over the spectral emission range of the uncoupled QDs (blue) and coupled QDs (red) in a log-log plot and the total emitted intensity (yellow). Fits to the data reveal a power-law behaviour with a linear increase for the SF emission, a slightly sublinear increase for the uncoupled QDs and a less sublinear increase for the total emitted intensity.