Room temperature continuous-wave excited biexciton emission in perovskite nanoplatelets via plasmonic nonlinear fano resonance

Biexcitons are a manifestation of many-body excitonic interactions, which are crucial for quantum information and computation in the construction of coherent combinations of quantum states. However, due to their small binding energy and low transition efficiency, most biexcitons in conventional semiconductors exist either at cryogenic temperatures or under femto-second pulse laser excitation. Herein, we demonstrated strong biexciton emissions from CsPbBr3 nanoplatelets with continuous-wave excitation at room temperature by coupling them with a plasmonic nanogap. The exciton occupancy required to generate biexciton was reduced ~106 times in the Ag nanowire–Ag film nanogaps. The extremely large enhancement of biexciton emissions was driven by nonlinear Fano resonance between biexcitons and surface plasmon cavity modes. These results provide new pathways to develop high efficiency non-blinking single photon sources of biexciton (with spectral filter for biexciton), entangled light sources, and lasers based on biexciton states. The quasiparticle the biexciton is expected to be an important component in the construction and application of quantum states in quantum information computing but is typically not stable under ambient conditions. Here, the authors use nanoplasmonics to achieve the generation of biexcitons at room temperature in perovskite nanoplatelets.

L ead halide perovskites, with their outstanding carrier transport characteristics, high emission quantum yields, tunable bandgaps, and large absorption coefficients [1][2][3][4] , have attracted considerable interest for applications across a range of technologies from solar energy conversion 1,2,5 to light-emitting diodes (LEDs) 6 . Recently the energy conversion and LED efficiencies of lead halid perovsktes reached 23.2% and 20.7%, respectively 7,8 . In perovskites, electrons and holes are confined to inorganic [PbX 6 ] 4− (X = Cl, Br, I) octahedral networks, which leads to enormous Coulomb interactions between electrons and holes and thereby, strong excitonic effects 9,10 . In low-dimensional perovskite structures, i.e., nanocrystals (NCs) or nanoplatelets (NPLs), the electron-hole interactions are further enlarged as a result of the increased spatial overlap between electrons and holes. For instance, the exciton-binding energy of CsPbBr 3 bulk crystals is 40 meV 11 , while the value increases to 120 meV in NCs 12 . Furthermore, CsPbBr 3 perovskite NCs exhibit high photoluminescence (PL) quantum yield of~90% 13 . The large excitonbinding energy and high-quantum efficiencies of CsPbBr 3 perovskite NCs hold the key to the development of excitonic and quantum devices due to their stable excitons at room temperature. Furthermore, excitons in perovskite NCs may be coupled with free carriers, forming trions 14 . A trion can decay to a single electron (hole) by the emission of circularly polarized light, and it can achieve population inversion and laser action. The trion state shows a lower threshold compared with the neutral state, which requires a higher excited state to achieve optical gain. This is advantageous to realize low-threshold lasers 15 .
A biexciton is formed by two free excitons in condensed exciton systems 16 , two photon absorption 17 , or excitation from the single exciton state to the biexciton state. Biexcitons are of fundamental interest and practical importance for quantum information and computation due to their overwhelming advantage for constructing of coherent combinations of quantum states. The coherent control of biexcitons via their four physically distinguishable quantum states can be applied to basic quantum operations, i.e. two-bit physical quantum and conditional quantum logic gates [18][19][20] . If fine structure splitting of the exciton state is smaller than the natural linewidth, the two indistinguishable radiative decay pathways of a biexciton can render a source of polarization entangled photon pairs. Furthermore, the nonlinear optical nature of the biexciton process can generate probabilistic number of entangled-photon pairs per excitation cycle 21 , which is similar to the standard entangled source parametric down conversion 22 and four-wave mixing sources 23 . Moreover, light sources based on biexciton may achieve no blinking and high saturation intensity 24,25 . These intrinsic outstanding physical properties make biexciton interesting for inherent and coherent light sources including lasers, light emitting diodes, etc. 26,27 . Till now, biexcitons have been realized in semiconductor heterostructures 28 , NCs 26 , and two-dimensional semiconductors 16,29 , etc. Due to the small biexciton-binding energy and large Auger effect, biexcitonic effects have only been realized either under intense pumping by short pulsed lasers (~MW/cm 2 ) or in cryogenic conditions, which severely limits their practical applications. Resonant excitations can increase the probability of biexciton transition. For example, in quantum wells, biexciton emission was observed under a continuous wave (CW) excitation beam with a power of~70 mW/cm 2 , but only below liquid helium temperature due to the small biexciton-binding energy 30,31 . So far, CW excitation of biexciton at room temperature, which has fundamental practical significance is extremely challenging.
Plasmonic nanogap structures have been extensively explored in quantum electromagnetic dynamics due to their extraordinary capabilities for tailoring strong and weak light-matter interactions in the deep-subwavelength regime [32][33][34] . In the last decade, plasmonic nanogap have been widely used to enhance a variety of linear and nonlinear optical processes including emissions, hot carrier generation, Raman, high harmonic generation, etc. [35][36][37][38] . Near a metal structure, the increasing local density of states in a plasmonic nanostructure can shorten the fluorescence lifetime and greatly suppress Auger recombination, even to the point where Auger recombination is negligible 39 . When coupled to a metal structure, quantum dots (QDs) show super-Poissonian statistics of photon emissions, which is different from the behavior of QDs on quartz substrates that exhibit photon antibunching as single quantum emitters 40 . In this case, QDs exhibit strong photon bunching which leads to multiexciton emissions 41 . This provides a way to achieve biexciton emissions with a significantly lower pump energy, which consequently highly suppresses the biexciton Auger recombination with decreasing pump density [42][43][44] . The interactions between plasmons and QDs have been widely discussed 41,45,46 . Surface plasmons are regarded as continuous energy states while quantum dot excitations are discrete energy levels. The coupling between continuous and discrete energy states leads to Fano effect 47,48 . With increasing incident light intensity and enhanced coupling strength, the two-photon process will take the place of a single photon process which leads to nonlinear Fano effect 45,49 .
In this work, we demonstrate strong biexciton emissions from CsPbBr 3 NPLs with continuous-wave excitation at room temperature, and the biexcitonic behavior is validated through experiments and simulations. By utilizing a Ag nanowire-Ag film nanogap structure, the exciton occupancy for biexciton emissions of CsPbBr 3 NPLs is reduced~10 6 times. The extremely large enhancement of biexciton emissions is attributed to the nonlinear Fano resonance between the biexciton and surface plasmon cavity modes. Our experimental results provide new pathways to develop high efficiency non-blinking single photon sources with spectral filtering of biexciton emission, entangled light sources, lasers, and high-efficiency LED based on biexciton states.

Results
Schematic of biexciton and plasmonic structure. Figure 1a shows the energy level diagrams for the excitation and decay of a single exciton. The single exciton bright state can decay to the ground state by emitting one photon, while the dark state decays to the ground state mainly by nonradiative processes. Two states are coupled by a spin-flip process. For perovskite NCs, the dark state exhibit microsecond-order decay times with a lower energy 50 . The dark state energy may be higher than that of the exciton due to the large Rashba spin-orbital effect 51 . Figure 1b shows the energy level diagrams of a biexciton. Biexciton is composed of two bright excitons and can decay to either of two single exciton states (bright state) accompanied by the emission of one photon 32 . The biexciton emission energy ħω xx is determined by the energy gap between the biexciton energy, E xx and single exciton emission E x via ħω xx = E xx -E x . Therefore, when two excitons bind together to form one biexciton, the energy of the whole system decreases by Δ xx = ħω x -ħω xx , which is the so-called biexciton-binding energy. Figure 1c shows the two processes for the plasmon-enhanced biexciton state: NPLs absorb one electron-hole excitation to the exciton state (I) and then reach the biexciton state (II) by absorbing another one, while the electron-hole excitations in metal relax to the ground state. The plasmon excited by optical pumping decay by two following channels: (1) via transformation into photons and (2) via nonradiative decay into electron-hole excitations. The latter fall into two categories: intraband excitations and interband excitations 52 . As the dephasing time of perovskite is much longer than silver nanowire 53 , electron-hole excitations in plasmonic cavity decay and perovskite NPLs obtain the energy. The resonant effect between the plasmonic cavity and the perovskite biexciton energy extensively promote excitation cross-section of biexciton, which leads to an increased biexciton transition. The electron-hole excitations in metallic material loses energy via electron-phonon coupling on a picosecond time scale 54 . The Fano resonance can be set up within 10 fs which is much faster than electron-hole excitations decay time in plasmon 55 . Our designed structure is shown in Fig. 1d, which is a sandwiched structure of silver (Ag) nanowire/NPLs/Ag film. A thin layer of SiO 2 and perovskite NPLs were coated onto Ag film step by step. SiO 2 was used to control the gap width d G between the Ag nanowire and film and also prevent the perovskite NPLs from PL quenching nearby metal surface. To reduce the scattering and radiation losses in the plasmonic nanogap due to surface discontinuity, the growth condition of the SiO 2 /Ag film was optimized with a surface roughness~1.1 nm (Supplementary Note 1). Figure 1e shows the schematic of the biexcitons of CsPbBr 3 PLNs in the plasmonic nanogap. Perovskite NPLs (Supplementary Note 2) were deposited onto the SiO 2 layer by solution-processed spin-coating methods. To isolate the perovskite NPLs with Ag nanowire, the 4-Methyl-1-acetoxycalix [6]arene (4M1AC6, 0.5% in chlorobenzene) polymer film was spin-coated onto the CsPbBr 3 NPLs. The thickness of the perovskite NPL layer and polymer film was 13 nm, as measured by ellipsometry (Supplementary Note 3). A cross-section SEM image (Fig. 1f) shows that the perovskite NPL layer was uniform in scale of millimeters. Cavity-coupled perovskite NPLs fluorescence. To probe the biexciton effect in perovskite NPLs, PL of the perovskite NPLs on and off the plasmonic nanogaps was performed with a CW laser (Fig. 3, wavelength: 405 nm; spot diameter: 2 μm). The PL spectrum far from the plasmonic nanogap (P1, blue line) was assigned to single exciton recombination of CsPbBr 3 56 . It shows a single symmetric peak located at 500 nm, which corresponds to a free exciton when the excitation power P is 1.6 μW. In contrast, on the nanogap (P2, red line), a new peak arouse at 520 nm with an intensity much higher than that of single exciton emission. Although the nanowire is much smaller than the excitation spot diameter. Two obvious phenomena can be seen: (1) the strong biexciton emission is observed, which comes from the perovskite NPLs in the plasmonic cavity due to nonlinear Fano effect; (2) the a d e

Si
Ag film NPLs exciton emission signal on silver nanowire is about three times (Fig. 3) than that off nanowire, which is attributed to the perovskite NPLs in the plasmonic cavity area due to strong field enhancement. These results suggest that the plasmonic nanocavities yield a strong effect in the biexciton emission process (the corresponding linear coordinate PL spectrum is shown in Supplementary Note 6). The energy difference between the single exciton (500 nm, 2.480 eV) and new emission peak (520 nm, 2.385 eV) was~95 meV, which is almost the same as the biexciton-binding energy of CsPbBr 3 quantum dot reported previously (~100 meV) 27 .
Power law of perovskite NPLs PL integral intensities. Under full thermal equilibrium conditions of the biexciton recombination process, the emission intensity of biexciton I bx is proportional to the square of the single exciton emission intensity I ex 57,58 . And biexciton lifetime is about half of single exciton lifetime. Excitation power-dependent PL and time-resolved PL (TRPL) spectroscopy were conducted to confirm the occurrence of biexciton. Figure 4a, b shows the power-dependent PL spectra on and off the Ag nanowire on the Ag film, respectively. Figure 4c shows the integrated emission intensity of exciton (I ex ) and biexciton (I bx ) as a function of the fluence intensity P. As the pumping power increased from 20 to 130 μW, the PL spectrum away from the plasmonic nanogap (Fig. 4a) showed one emission peak at 500 nm with the intensity I exhibiting a linear dependence on the pumping power P (Fig. 4c, purple), which is ascribed to single exciton recombination. However, on the plasmonic nanogap, a 520 nm peak due to biexciton emissions emerged, with the intensity I bx growing more rapidly than that of the single exciton (Fig. 4b). Although the biexciton emission peak onset emerged when P > 100 mW/cm 2 (0.5 μW,~20 μm) (Supplementary Note 7), we performed emission spectroscopy with P > 500 W/ cm 2 (20 μW,~2 μm) to lower the fitting error, when separating the power dependence of the biexciton emission from that of the single exciton emission. Figure  Lifetimes of excited states. Further, TRPL spectroscopy was conducted to probe the exciton and biexciton dynamics. Quantitatively under the condition of thermal equilibrium, the time evolution of the exciton and biexciton can be modeled with the transition function 59 n bx $ n 0 bx e À2t=τ ex , where exchange interactions between excitons with different spin are ignored. In other words, the biexciton decay rate is indeed about twice that of single exciton, as suggested in bulk semiconductor 60 , QDs 59 , quantum wells 61 , and 2D semiconductors 62 . Figure 5a, b show the TRPL spectra of the CsPbBr 3 NPLs on (a) and off (b) the plasmonic nanogap. To avoid any biexciton effects away from plasmonic nanogap under high pumping conditions, the excitation fluence of the femto-second pulsed laser was~0.1 nJ/cm 2 , and thereby, the PL spectra showed only single exciton emission. The single exciton recombination curve could be well fit by a single exponential decay function with a time constant of τ ex = 1170 ± 10 ps. The TRPL spectroscopy of the biexciton emission was pumped with a power~70 nJ/cm 2 and could be well-fit by a single exponential decay curve, suggesting the emissions on the plasmonic nanogap were dominated by biexciton recombination. The lifetime of the biexciton τ bx = 510 ± 5 ps, was half of single the exciton lifetime (1170 ± 10 ps), which is consistent with the transition properties of the biexciton states as discussed above. Therefore, we can conclude that the 520 nm peak arising on plasmonic nanogap was due to biexciton recombination.
Fano effect of silver nanowire and perovskite NPLs. In the plasmonic nanogap, biexciton emission was observed when the pumping fluence exceeded 100 mW/cm 2 (Supplementary Note 7). The estimated exciton occupancy 〈N〉~10 −5 was much lower than 1, which indicates that the biexciton emission were not produced by exciton-exciton bounding in this nanogap region. However, the enhancement factor should be much larger than the local field enhancement factor (<100, Supplementary Note 8) in the plasmonic nanogap. This indicates that the enhanced biexciton emission was not mainly due to local field enhancement. Moreover, the Purcell effect of the NPLs was observed in the plasmon nanocavity and the factor is~2.5 (Supplementary Note 9). However, it did not play an important role in biexciton formation process and can be negligible.
Biexciton forms mainly through the following three methods: (1) two photon absorption, (2) exciton-exciton bounding in condensed exciton environment, and (3) resonant excitation from a single exciton. The first two pathways required intense pumping, which is not feasible under CW excitation conditions. To confirm that the plasmon mode affected the biexciton between the Ag nanowire and Ag film, the emission polarization behavior was measured. As shown in Fig. 6a, the biexciton emission was strongest when the excitation polarization direction was parallel to the long axis of the nanowires (0°, 180°) and weakest when the excitation polarization direction was perpendicular to the long axis (90°, 270°). However, the emission intensity of the perovskite NPLs away from the Ag nanowire was almost the same (Supplementary Note 10). The polarization resolved emission properties of the 520 nm peak suggests the modulation of the Ag nanowire's plasmonic mode which is transverse magnetic mode. Moreover, an asymmetric peak appeared with a zero detuning position around the perovskite biexciton resonant energy, resulting from Fano interference between biexciton resonance excitation and background continuum states excitation of surface plasmon modes as shown in Fig. 6b. The scattering spectra were fitted with Fano-line profiles, ð Þ=Γ, Γ is the resonant width and E 0 is the resonant energy, which is centered at the biexciton emission position 63 . The fitted Fano factors were −0.25 and −0.2, when the polarization was parallel and vertical to long axis of nanowire, respectively. The scattering lineshape was simulated by the finite-difference time-domain (FDTD) method, as shown in Fig. 6c. It is noticed that the nonlinear Fano resonance lineshape was only observed in the scattering spectra of the Ag nanowire-NPLs-Ag film system with strong biexciton emissions, which suggests that the exciton-plasmon energy transfer plays a vital role in the formation of biexciton. Plasmon resonant energy transfer can only occur when the plasmon peak overlaps with the biexciton states (Supplementary Note 11). Without energy transfer, the NPLs in the gap only show exciton emission (Supplementary Note 12). The nonlinear interaction witnessed as the Fano resonance contributed to the biexciton emission.
The nonlinear Fano resonance suffers from the distance of metal structure with NPLs and external field. With a gap of 13 nm and external field of 0.1 W/cm 2 , the interaction can be viewed as linear interaction dominant, which can be seen as the threshold of biexcion emissions 45,49 . Due to the large binding energy of the CsPbBr 3 NPLs, room temperature biexciton emissions off the The biexciton emission peak of 520 nm at high excitation fluence. With increasing pumping power, the biexciton, however, grows much faster than that of single exciton. The same color map is used to make a clear comparison. c A log-log scale was adopted to plot the integrated emission intensity strength, I p , as a function of the exciton emission strength P. The purple line is a power-law fit I p = P k , with a power-law constant k 1 = 0.96, while the red line k 2 = 1.83. The ratio l = k 2 /k 1 , has a value of 1.91. This provides strong evidence that a shows exciton luminescence while b shows biexciton fluorescence. The error bar corresponds to the standard deviation of the measurements nanogap could be excited only by fs laser pulse of amplifier (1 kHz, 80 fs) and the pumping fluence was on the magnitude of 10 11 W/cm 2 with an estimated average NPL exciton occupancy 〈N〉~30 (Supplementary Note 13). The threshold in our system was much higher than 〈N〉~1, since a larger pump intensity leads to ionization 64 and a faster Auger recombination rate with a very rapid growth of the carrier density 65 . To make sure the NPLs is not damaged, the increasing and decreasing power-dependent PL is measured (Supplementary Note 14). Moreover, the powerdependent PL is also pumped with fs laser pulses of oscillator (80 MHz, 100 fs), however, biexciton is not emerged until NPLs is damaged (Supplementary Note 15). Therefore, the exciton occupancy to generate biexciton in the plasmonic nanogap was reduced by~10 6 times when comparing with fs laser pulse of amplifier.

Discussion
A resonant excitation process is proposed to explain the huge biexciton effect driven by surface plasmon cavity. As shown in Fig. 1b, since the single exciton-biexciton transition energy was nearly the surface plasmon energy, a nonlinear process with energies ω and ωʹ can be absorbed though resonant energy transfer from surface plasmons to NPLs, leading to the excitation of biexciton and annihilation of surface plasmons. The interference of the two excitation processes results in the nonlinear Fano resonance lineshape in the scattering spectra, where an asymmetric peak confirmed the process occurred. The surface plasmon-driven mechanism is similar to the biexciton generation by a resonant pump-probe in single carbon nanotube 66 . The highly populated energy of plasmon was confirmed by zero detuning position of scattering spectra, which is almost overlapped with the biexciton transition energy. The resonance effect extensively promoted the excitation cross-section of biexciton from exciton states.
In conclusion, we found clear evidence for the presence of high-efficiency biexciton generation in perovskite NPLs in a metallic nanostructure under CW pumping at room temperature. The observation of the biexciton was a consequence of the clear emission spectra besides exciton with a binding energy~95 meV, which was verified by the activation energy. The fluorescence power law and lifetime provided further evidence of the biexciton emission. Moreover, the nonlinear Fano effects were confirmed by measuring the scattering spectrum. By fitting the spectrum with Fano parameters and FDTD simulations, we are sure that this demonstration of the four-particle complex in plasmonic nanostructure will give rise to new interesting effects, such like quantum logic gates, Bose-Einstein condensation of exciton, source of polarization-entangled photons, single-photon source and high-efficiency LEDs.

Methods
Sample preparation. The SiO 2 /silver substrate was made though magnetron sputtering with silver thickness of 50 nm and SiO 2 thickness of 5 nm on a SiO 2 /Si substrate. CsPbBr 3 NPLs were spin-coated on the SiO 2 /silver substrate at a speed of 3000 r/min. The 4-Methyl-1-acetoxycalix [6]arene (4M1AC6, 0.5% in chlorobenzene) was spin-coated on the CsPbBr 3 NPLs at a speed of 5000 r/min. After waiting for about 30 min to allow the 4M1AC6 to dry, silver nanowires were spincoated in isopropyl alcohol at a speed 2000 r/min. SEM and TEM measurements. The samples were forced apart after liquid nitrogen treatment. The SEM equipment was a Merlin-61-53 with a working distance of 4.3 mm and a voltage of 5 kV. The perovskite NPLs for the TEM measurement were dropped onto TEM grids. High-resolution transmission electron microscopy (HRTEM) was performed with an FEI Tecnai F20 operated with an acceleration voltage of 200 kV.
Time-resolved PL spectroscopy. For time-resolved PL measurements, the excitation pulses (wavelength 400 nm) were doubled frequencies of a Coherent Mira 900 (120 fs, 800 nm, 76 MHz) and filtered by a 655 short-pass filter to generate 400 nm light. The backscattered signal was collected using a time correlated single photon counting (TCSPC, SPC-150) which has an ultimate temporal resolution of ∼40 ps. A 442 nm long-pass filter was placed before the optical fiber to filter out the residual 400 nm light.
PL measurements. The output from a 405 nm CW laser was circularly polarized by a quarter-wave plate, and focused on a sample by a microscope objective lens (×100, NA = 0.95, with spot size~2 μm). The PL signal was then back collected by the same lens, and filtered by a long-pass filter before entering a spectrometer (PI Acton 2500i with a liquid nitrogen-cooled charge coupled device-CCD camera). The low-temperature PL was measured when the sample was in the liquid nitrogen refrigeration cryogenic instrument.
FDTD simulation. The FDTD simulations of the silver nanowire and QDs were simulated using the Lorentz model 67 . We modeled the CsPbBr 3 nanoplatelet layer using a dielectric function as a single Lorentzian function. The dielectric constant for bulk CsPbBr 3 is 3.8 68 . The biexciton energy and plasmon resonant energy transfer were considered, while other high-order transitions were ignored. The biexciton linewidth was used as the transition linewidth. The metal dielectric function was treated as a Lorentz-Drude model.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.