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Abstract
In addition to their attractive technological applications in photovoltaics and light emitters, the perovskite family of semiconductors has recently emerged as an excellent excitonic material for fundamental studies. Specifically, the 2D hybrid organic-inorganic perovskite (HOIP) offers the added advantage of room temperature investigations owing to their large exciton binding energy. In this work, we strongly couple excitons in 2D HOIP crystals to planar microcavity photons sustaining exciton-polaritons under ambient conditions resulting in a Rabi splitting of 290 meV. Dark excitons directly pump the polariton branch along its dispersion in resonance with the Stokes shifted emission state (radiative pumping), creating a high density of polaritons at higher in-plane momentum (k||). We further probe the nonlinear polariton dispersion dynamics at varying input laser fluence, which indicates efficient polariton-polariton scattering and decay to k|| = 0 from higher k||. The observation of Stokes shift-assisted energy exchange of dark states with lower polaritons coupled with evidence of efficient polariton-polariton scattering makes 2D HOIPs an attractive platform to study exciton-polariton many-body physics and Bose-Einstein like condensation (BEC) at room temperature.
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Ruddlesden-Popper 2D HOIPs have emerged as excellent hosts to study the formation of exciton-polaritons at ambient temperatures due to their exceptional oscillator strength and high binding energy of the exciton species [1–4]. Such perovskites offer more attractive avenues for studying exciton physics than III-V semiconductors, which sustain excitons only at cryogenic temperatures beyond which they ionize owing to their small binding energy [5,6]. These perovskites also exhibit natural isolation of the active, exciton-hosting, inorganic layer via surrounding organic layers on either side, imitating a quantum well-like structure [7,8]. Since the organic layers are bound by weak van der Waals forces, they facilitate mechanical exfoliation and are an attractive candidate for thickness-dependent optical microcavity experiments [9]. Owing to their high quantum yield and bandgap tunability by changing the underlying composition, 2D perovskites are promising candidates for exploring functional visible light coupled devices [10]. Room temperature excitons sustained in such perovskites show strong exciton-exciton interaction with a value of g ∼ 3 µeVµm2, which is more than one to two orders greater than that observed in 2D transition metal dichalcogenides and their heterostructures supporting interlayer excitons [3,11,12].
When one tunes the interaction of such excitons to a cavity photon faster than their dissipation rates, it gives rise to new eigenstates having physical properties of both light and matter, called exciton-polaritons. Realizing such particle formation has been of interest in organic and inorganic systems, with applications ranging from polariton spin switches [13,14], optical transistors [15,16], and polariton light emitting diodes [17], amongst others. Exploring nonlinearities in the half-light, half-matter constituent particles which arise from their excitonic component has gained prominence [18–20]. Various groups have studied nonlinear polaritonic properties like optical bistability [21], parametric scattering [22], and lasing [23–24]. The small effective mass of polariton systems (∼10−5 times that of an electron) makes them ideal candidates for studying and realizing condensation at elevated temperatures.
Exciton-polaritons have been extensively studied in inorganic and composite organic-inorganic perovskites, 2D, and 3D systems [25–27]. Su et al. reported a room-temperature polariton condensate lattice in Cs-based perovskites [28], while Zhu et al. were the first to report lasing in nanowire perovskites [29]. Polimeno et al. [30] recently observed polariton condensation at 4 K cryogenic temperature in 2D lead iodide-based perovskites; however, room temperature condensation in such systems is yet to be observed. This paper studies the spectral formation dynamics of exciton-polaritons in a strongly coupled Fabry-Pérot cavity with single-crystal perovskites. We probe the response of the polariton photoluminescence (PL) as a function of non-resonant input pump power. We show evidence of a strong radiative pumping effect in creating these polaritons and their scattering to the ground state at ambient conditions. We then discuss effective polariton pumping and scattering schemes in such systems for studying exciton-polariton dynamics and nonlinearity.
Phenethylammonium lead iodide (PEA)2PbI4 single crystals were synthesized using an anti-solvent vapor-assisted crystallization method reported previously [31]. Briefly, PEAI and PbI2 precursors with a molar ratio of 2:1 were dissolved in a γ-butyrolactone/acetonitrile solvent mixture (60:40 [v/v]) and stored in an atmosphere of chlorobenzene vapor. After several days, PEA2PbI4 2D perovskite single crystals with a size of a few millimeters were obtained.
Single crystal flakes of (PEA)2PbI4 with n = 1 perovskite were mechanically exfoliated and transferred onto an 8.5 period symmetric distributed Bragg reflector (DBR) with alternating λ/4 thick layers of SiO2 and TiO2. The n denotes the number of inorganic lead halide layers sandwiched between two organic layers. The DBR reflection band is centered at 2.43 eV, and the stop band extends from 2.12 eV to 2.74 eV. The thickness of the exfoliated flake was measured to be 115 nm. A dielectric polymethyl methacrylate (PMMA) spacer of thickness 70 nm was spun on the top, which not only acts as a cavity spacer but is also observed to protect the perovskite flake from laser-induced damage. The cavity structure was completed by depositing a 50 nm Ag top mirror using E-beam evaporation, and the whole cavity is illustrated in Fig. 1(a). All experiments were performed at ambient conditions. The absorption of the bare crystal peaks at 2.389 eV, and the emission maxima are spectrally located at 2.332 eV, resulting in a Stokes shift of ∼ 57 meV, as shown in Fig. 1(b). The exciton absorption of the perovskite crystal is coupled to a 20 meV positively detuned cavity mode. We performed angle-resolved white light reflection measurements to show strong coupling and characteristic anti-crossing behavior, as shown in Fig. 1(c). A two-coupled oscillator model with the solution to the Hamiltonian given in Eq. (1) was fit to the white light reflectivity data.
Fig. 1. Exciton-photon strong coupling. (a) Schematic showing the cavity structure with bottom DBR and top Ag mirror with the exfoliated perovskite crystal. (b) Absorption and PL spectra of the bare perovskite. (c) Angle-resolved white light reflection of the cavity sample showing anti-crossing behavior. The dashed lines are the fitting results of a coupled oscillator model (d) Line-cut spectra of the reflection plot at zero degrees (k|| = 0). The energy difference is attributed to a rabi splitting (ħΩR) of 290 meV.
Note that since the cavity mode is positively detuned compared to the exciton absorption, the lower polariton has a higher excitonic fraction at all k's, as seen in Fig. 2(b).
Fig. 2. Polariton emission characteristics. (a) Angle-resolved PL emission from the lower polariton branch. (b) Calculated Hopfield coefficients of the lower polariton branch showing majority contribution from the excitonic component at all angles. (c) Surface plot of the PL from the lower branch as a function of emission angle and pump power. A bottleneck region is visible wherein the PL intensity maximum occurs at ∼ 28°.
The cavity mode was designed to be blue-detuned compared to the exciton resonance so that the lower branch acquires a greater excitonic fraction. Previous studies have demonstrated in detail the contribution of an increasing excitonic component in the polariton branch to achieve pump-dependent optical non-linearities for both organic and inorganic materials [32,33]. Based on this, we believe that an increased excitonic component with the polariton branch would lead to efficient scattering of polaritons along its dispersion curve once populated. Based on this, we believe that an increased excitonic component with the polariton branch would lead to efficient scattering of polaritons along its dispersion curve once populated. As such, we explored varying pump power-induced behavior in the emission of the lower polariton branch. A non-resonant 2.988 eV (415 nm), 100 fs pulsed laser with an 80 MHz repetition rate was used to pump the exciton reservoir. The emission intensity, blueshift, and linewidth of the lower polariton dispersion were studied as a function of this input pump beam. Figure 2(a) shows the polariton emission dispersion collected by a 50×, 0.8 NA objective for a single power. A 500 nm long pass filter was used to cut off the pump laser for PL measurements. The steady-state angle resolved PL is plotted as a function of input pump power density in Fig. 2(c). Evidently, from the surface plot, the PL is highly concentrated at finite k, at approximately 28° in the dispersion graph, rather than emitting homogeneously throughout its dispersion at all k’s. This concentration of PL emission at k ∼ 28° provoked further probing into polariton emission and the role of dark states, as explained below. We found higher power densities to be detrimental to the perovskite sample, thus we restricted our study to densities below 16 µW/µm2.
Pumping non-resonantly (2.988 eV) leads to the excitation of the upper polariton branch (energetically higher than bare absorption of the crystal) followed by a fast relaxation to the exciton reservoir (as shown in Fig. 3, blue curve). The emission spectrum of these excitons (as shown in Fig. 3, pink curve) overlaps with the lower polariton branch and the emission maximum is resonant at k ∼ 28°. Owing to the high binding energy in 2D HOIPs, photo-excited charge carriers hybridize with the cavity mode to form polariton states, resulting in the appearance of two new energy eigenstates at the expense of excitonic states (from the ‘bright’ or cavity coupled excitons) and the domination of radiative recombination in 2D perovskites by free exciton emission [34]. This favorable spectral overlap facilitates efficient energy transfer from the exciton reservoir and results in the exciton emission state efficiently populating the polariton branch, as seen from the above schematic in Fig. 3, and bright emission spots in PL dispersion in Fig. 2(a). Due to the Stokes shift, such a mechanism of direct population transfer to the polariton state has been observed in fluorescent dyes like BODIPY-Br [35,36] and Rhodamine 6 G [37], among other molecular systems. Radiative pumping-assisted thermalization of exciton-polaritons at room temperature was recently achieved in a red fluorescent protein [32]. A BEC phase transition was also reported using the same technique in an organic microcavity at very low condensation threshold densities [38].
Fig. 3. Radiative pumping and the role of dark states. A schematic view of resonant excitation of polaritons around k ∼ 28° by uncoupled or weakly coupled excitons which do not participate in energy exchange with cavity photons responsible for strong coupling. The absorption and emission maxima have a spectral difference of ∼ 57 meV resulting in a considerable Stokes shift, unlike inorganic excitonic materials.
Recently, Fujiware et al. observed intersystem crossing to a long-lived triplet state at high pump powers using time-resolved PL measurements in 2D HOIPs [38]. Such a mechanism is detrimental to the accumulation of polariton population in a planar Fabry-Pérot cavity. It can hinder a BEC-like phase transition that relies on a polariton occupation number greater than a critical density. Our observation of Stokes shift-assisted radiative pumping in such 2D HOIPs will significantly enhance the polariton population by depleting the exciton reservoir since the relaxation of polaritons to this resonance state is energetically favorable. This will also have the favorable consequence of lowering the critical polariton density as reported in similar organic microcavities, also avoiding the difficulties in fabricating a high Q cavity [39]. In addition to dark excitons playing a role in polariton relaxation dynamics, vibrationally assisted scattering (VAS) of polaritons has been reported in TDBC and ladder-type polymer MeLPPP organic microcavities [40,16]. Such a relaxation mechanism could also be dominant in 2D HOIPs characterized by a strong vibrational mode at 1477 cm-1 (see Supplement 1). Although these vibrational modes originate in the organic ligands, they are seen to have an influence on the optical properties of excitons residing in the inorganic octahedra [41]. Tuning the polariton branch to be energetically one vibronic energy away from the exciton reservoir (∼183 meV) could result in significant polariton occupation at this resonance, analogous to the radiative pumping effect in 2D HOIPs. The comparison between threshold densities at the onset of nonlinear polariton interactions formed by radiatively pumping and VAS remains an interesting question and is the scope of future studies.
Next, we probed the behavior of polaritons along the dispersion under the influence of increasing pump density. In order to understand the scattering of polaritons after most of them are initially populated by radiative pumping, we plot the integrated polariton emission from the spot of resonant radiative pumping (red) and the ground state of the polariton dispersion, k ∼ 0° (blue) as shown in Fig. 4(a). Emission from polaritons at k ∼ 28° saturates with increasing power. On the other hand, emission from the k ∼ 0° state increases with a faster rate as compared to k ∼ 28° on the integrated area plot, with a hint of saturation at the highest power. This indicates that not only do we have the highest polariton occupation at k ∼ 28° initially, but they also effectively undergo polariton-polariton scattering and relax to the ground state within their lifetime, limited by the Q factor of the cavity. We also note that the shape of the dispersion remains the same with increasing pump power, as seen from the similar blueshifts of polaritons at both these momenta-separated spots, plotted in Fig. 4(b).
Fig. 4. Polariton nonlinearity at different k as a function of pump density. (a) Comparison between integrated PL area at the radiatively pumped region (k ∼ 28°) and the polariton ground state (k ∼ 0°) on a log-log scale. (b) The respective blue shift of the polariton branch along the exact locations in the dispersion.
In summary, we strongly couple the excitonic transition of a 2D hybrid perovskite single crystal to a positively detuned cavity resulting in a Rabi splitting of 290 meV at room temperature. Our observations prove that the exciton reservoir directly pumps the polariton branch along the emission maximum in these 2D HOIPs and plays a significant role in populating the polaritonic states. Furthermore, we also present evidence of polariton-polariton scattering resulting in a significant population at k = 0° away from the radiatively pumped momentum spot. The demonstration of efficient radiative pumping mainly observed in organic systems, and the occurrence of polariton scattering, seen majorly in inorganic systems, make 2D hybrid perovskites an attractive platform to study room temperature polaritonic devices.
Funding
Office of Science (DE-SC0012458); Directorate for Mathematical and Physical Sciences (DMR-2019444).
Acknowledgments
V.M and P.D were supported through the NSF Center Integration of Modern Optoelectronic Materials on Demand (IMOD), an NSF Science and Technology Center (STC) supported by NSF grant DMR-2019444. B.P.R. and L.Z. acknowledge funding from the U.S. Department of Energy, Office of Basic Energy Sciences under award no. DE-SC0012458.
Disclosures
The authors declare no conflicts of interest.
Data Availability
The data supporting the claims in this paper is available from the corresponding author upon request.
Supplemental document
See Supplement 1 for supporting content.
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