Million-Q free space meta-optical resonator at near-visible wavelengths

Hybridization of excitons with photons to form hybrid quasiparticlesexciton-polaritons (EPs)-has been widely investigated in a range of semiconductor material systems coupled to photonic cavities. Self-hybridization occurs when the semiconductor itself can serve as the photonic cavity medium, resulting in strongly coupled EPs with Rabi splitting energies (ħΩ) of >200 meV at room temperature, which were recently observed in layered two-dimensional excitonic materials. Here we report an extreme version of this phenomenon-an ultrastrong EP coupling-in a nascent, two-dimensional excitonic system, namely, the metal-organic chalcogenolate compound called mithrene. The resulting self-hybridized EPs in mithrene crystals placed on Au substrates show Rabi splitting in the ultrastrong-coupling range (ħΩ > 600 meV) due to the strong oscillator strength of the excitons concurrent with the large refractive indices of mithrene. We further show that bright EP emission occurs at room temperature as well as EP dispersions at low temperatures. Importantly, we find lower EP emission linewidth narrowing to ~1 nm when mithrene crystals are placed in closed Fabry-Pérot cavities. Our results suggest that metalorganic chalcogenolate materials are ideal for polaritonics in the deep green-blue part of the spectrum in which strong excitonic materials with large optical constants are particularly scarce.

Exciton-polaritons are part-light, part-matter quasiparticles that are the result of energy being exchanged between a photon trapped in a cavity and an exciton (Coulomb-bound electron-hole pair) state that fundamentally change the optical dispersion of a system. Since exciton-polaritons are the result of strong light-matter interactions, their properties can be leveraged in optoelectronic devices such as lasers 1,2 , light-emitting diodes 3,4 and photovoltaics 5,6 . The rate at which energy is exchanged between the light and matter states is described by the coupling parameter g. When g is smaller than the loss rates of the unperturbed exciton (Γ x ) and cavity (Γ c ), the energy is dissipated faster than it is exchanged between the states, and no exciton-polaritons are formed. In this case, the system is said to be in the weak-coupling regime. However, when the coupling parameter is larger than either state's decay rate (g > |Γ x - Γ c |/4), the system enters the strong-coupling (SC) regime in which the excited light and matter states hybridize to form upper exciton-polaritons (UEPs) and lower exciton-polaritons (LEPs) with properties of both light and matter 7,8 . In the SC regime, only first-order (absorption and emission) and compared with an open-cavity system, as well as multiple states with ~1 nm linewidth emission at low temperatures (80 K). Our findings demonstrate that mithrene is a new material that can be used to probe ultrastrong light-matter interactions. The emissive properties of the exciton-polaritons also demonstrate that mithrene can be used as a monochromatic light source in the blue to green region of the visible spectrum.

Our cavity mode is a lossy Fabry-Pérot cavity that is formed by the highly reflective substrate and the air-mithrene interface that is reflective due to the large refractive index of mithrene 34,35 . Since the Fabry-Pérot cavity is formed by the top and bottom of the mithrene crystal, the cavity energy (E c ) can be tuned by varying its thickness (t = λ c /4n, where t is the thickness of mithrene, λ c is the cavity wavelength and n is the real part of the refractive index of mithrene). The lossy Fabry-Pérot cavity then hybridizes with mithrene's exciton to form a higher-energy UEP and smaller-energy LEP, where the lower polariton state is found to emit blue light (Fig. 1a). Mithrene on the Au sample was prepared by drop casting mithrene in a propylamine-H 2 O solution on the Au substrate 26 . Atomic force microscopy was used to show that this process yielded mithrene flakes of ~30 µm × 30 µm in the lateral area with a thickness of 554 nm (Supplementary Fig. 1). The refractive index of mithrene is measured using spectroscopic ellipsometry (Supplementary Fig. 2). The reflectance of the system is then simulated using the complex refractive index and the transfer matrix method (TMM) 36 . The TMM is found to accurately predict the energies of the UEP and LEP, and simulations clearly show the anticrossing behaviour for mithrene on Au, which is a clear signature of the SC regime (Fig. 1b). The coupling parameter is then calculated to be 347 meV by extracting the UEP and LEP energies for various cavity energies and fitting it to the quantum Rabi model [37][38][39] (Supplementary Section 1). Here g is 13% of the exciton energy, placing the exciton-polaritons in the USC regime, and the Rabi splitting (ℏΩ

2 ) is 678 meV.

The decay rates of the exciton and open cavity are 80 and 228 meV, respectively. Due to the experimental limitations of the detector under normal incidence, the UEP can only be observed in thick mithrene flakes in which the UEP wavelength is >400 nm. To further confirm the dispersion of the UEP at shorter wavelengths, imaging spectroscopy ellipsometry is used to observe the UEP at wavelengths down to 250 nm through the relative phase (ϕ) difference of transverse-electric and transverse-magnetic polarized light (Δ = ϕ TM - ϕ TE ) (Fig. 1c). However, ellipsometry is performed at the angle of incidence of 40°, which is the smallest possible value for the ellipsometer. Still, both UEP and LEP follow the simulated dispersion, and polaritons do not intersect the region with the primary excitons of mithrene 40 , showing the hybridized nature of the system. The experimental spectra used to identify the LEP and UEP (Fig. 1b,c) are shown in Supplementary Fig. 3. Most other low-dimensional semiconductors only host exciton-polaritons in the SC regime (Fig. 1d). The USC regime is typically achieved by either using low-energy transitions in the mid-infrared to microwave ranges, which lowers the required coupling parameter and allows for smaller mode volumes relative to the wavelength of light 41 , by coupling a high-quality (Q)-factor cavity to organic molecules whose Frenkel excitons have extremely large oscillator strengths 16 , or by introducing plasmons into the system to form exciton-plasmon-polaritons and plexcitons 42 . Out of these methods, Frenkel excitons have been shown to exhibit USC in the blue region, but their large binding energies and short diffusion lengths limit the efficiency of optoelectronic devices using them 43,44 . However, mithrene differs from these because its bandgap is in the blue region of light (468 nm), and the estimated value of its exciton binding energy (400 meV) along with the semiconductor layers being inorganic suggests that it hosts Wannier-Mott excitons 27,45 . Despite mithrene not using either of these strategies for USC, it still supports exciton-polaritons in the USC regime due to its excitons having extraordinarily large oscillator strengths and the crystal (exciton medium) concurrently second-order (scattering) effects need to be considered. However, as the coupling parameter increases further, the exciton-polariton enters the ultrastrong-coupling (USC) regime in which higher-order (HO) effects cannot be ignored [9][10][11] . The transition between the SC and USC regimes is continuous, unlike the transition between the weak-coupling and strong-coupling regimes with the sudden hybridization of states, but by convention, the exciton-polariton is said to be in the USC regime when the coupling parameter is more than 10% of the exciton energy (E x ). In the USC regime, a population of virtual photons forms in the ground state of the system, shifting its energy. The USC regime enables exotic quantum mechanical phenomena (such as the dynamical Casimir effect 12,13 and photon pair production 14 ) and practical phenomena (such as switching on the scale of 10 fs) 15 . So far, USC has only been observed in the visible range using closed-cavity geometries [16][17][18] , but it has not been observed in a self-hybridized system due to the lack of large-bandgap semiconductor materials with strong oscillator strengths in the excitonic resonance.

Self-hybridized exciton-polaritons from transition metal dichalcogenides (TMDCs) have been recently explored for both basic 19 and applied research such as light-emitting diodes 20,21 . One of the major limitations in a self-hybridized TMDC is the absence of polariton emission from multilayer TMDCs owing to their indirect-bandgap nature. Alternative strategies such as the preparation of TMDC superlattices that decouple electronic interactions in multilayers are yet to demonstrate polariton emission 22 . The material with the largest bandgap available in the conventional TMDC family (WS 2 ) is around 2 eV, which illustrates the lack of materials with blue emission (~2.5 eV). So far, three-dimensional inorganic materials such as ZnO (ref. 23) and GaN (ref. 24) are the only materials with polariton emission in the blue region. Further, three-dimensional materials are challenging with regard to device integration due to lattice strain and complexity involved in the device fabrication. In this work, we report polariton emission in the blue region from a new two-dimensional materialmithrene-which is part of a class of layered, bulk metal-organic chalcogenolate materials 25 . Mithrene consists of two-dimensional, inorganic AgSe layers separated by organic insulator layers (phenyl groups) to form a multiquantum-well system 26 . Its excitonic properties make it a strong candidate for optoelectronic devices since it is both direct bandgap and supports excitons with binding energies up to 400 meV (ref. 27). High exciton binding energy, along with the advantageous direct bandgap of mithrene in the blue region, can be used in light-emitting devices and photodetectors. In addition, the solution processability of mithrene at low temperatures (<200 °C) and its van der Waals nature enables easier integration on Si-based platforms compared with its counterparts such as III-V and oxide-based semiconductors in which lattice strain is detrimental to device performance. The large exciton binding energy is the result of the quantum confinement effects of multiquantum-well geometry, and it enables the excitons to have large oscillator strengths ( f ) at room temperature. Not only do large oscillator strengths make the excitons highly absorptive, they also increase the coupling parameter of exciton-polaritons as

, where V m is the mode volume of the cavity. Strong excitons in other quantum-confined semiconductors have been shown to be excellent for optoelectronic applications 28,29 . However, mithrene is still a relatively new material; therefore, most research has focused on its growth/characterization 26,[30][31][32] or basic optical properties 27,33 .

In this paper, we present the first study of light-matter interactions in mithrene and observe the formation of self-hybridized, USC exciton-polaritons in mithrene with the largest observed normalized coupling parameter (g/E x = 0.13) in the visible range. We also find that the light-matter states are emissive, allowing for geometrically tunable emission from the exciton wavelength to the lower exciton-polariton wavelength (468 nm to 515 nm). When encapsulated by Ag to form a closed-cavity system, we observed a longer exciton-polariton lifetime Article https://doi.org/10.1038/s41566-024-01590-0 possessing a large refractive index (due to its part-inorganic nature) that enables small mode volumes.

To confirm the hybrid nature of our observed absorption modes, thin films of mithrene on an Au substrate are studied since excitonpolaritons cannot form in films much thinner than the wavelength of light (t < λ/4n). Therefore, the uncoupled exciton states can be seen in a thin film of mithrene (t = 50 nm) using its reflectance and photoluminescence (PL) spectra (Fig. 2). In the thin film of mithrene, both simulated and experimental reflectance spectra show an absorption peak at the exciton wavelength, confirming the unhybridized nature of the system. Furthermore, PL is observed at the same wavelength, demonstrating the direct-bandgap nature of mithrene. However, when the mithrene thickness is increased to 486 nm, new absorptive modes are observed both above and below the exciton, which are the UEP and LEP, respectively. Sub-bandgap emission was also observed in the thicker flakes in the PL because the LEP can emit due to its part-exciton characteristics. In addition to the UEP and LEP, the thicker mithrene flakes also hosted an HO mode similar to what we previously observed in perovskites of comparable thicknesses 46 . The HO mode emerges from the next HO mode of the Fabry-Pérot cavity coupling to the exciton. However, since the detuning between the HO cavity mode and exciton is highly negative, the HO is predominately excitonic in nature, and it is only slightly redshifted from the exciton resonance. The detuning between the HO mode and the exciton can be decreased by increasing the mithrene thickness (increasing the cavity wavelength), which increases the fraction of the cavity state in the HO mode. Eventually, the state would be approximately half-exciton, half-cavity, making it an LEP. This continuous transition between the HO mode can be clearly seen in simulations in which the HO continuously redshifts with an increased mithrene thickness until it is called an LEP (Supplementary Fig. 4). The emissive properties of the sub-bandgap modes further confirm that they are exciton-polaritons with an electronic nature since unperturbed cavity modes cannot emit sub-bandgap photons.

The emissive properties of exciton-polaritons in mithrene are further investigated by comparing mithrene in open-and closed-cavity systems. From top to bottom, the open-cavity system is mithrene (943 nm)/Al 2 O 3 (10 nm)/Ag (100 nm) (Fig. 3a), and the closed-cavity system is poly(methyl methacrylate) (PMMA) (~250 nm)/Ag (15 nm)/ Al 2 O 3 (10 nm)/mithrene (943 nm)/Al 2 O 3 (10 nm)/Ag (100 nm) (Fig. 3b). Ag is used as the metal in both systems since it is less absorptive than Au in the visible range (Supplementary Fig. 5), and the Ag substrate has 10 nm of Al 2 O 3 on top, which is deposited using atomic layer 46 , CsPbCl 3 , WS 2 superlattice 22 , organic 53 , J-aggregate 54,55 and carbon nanotube 56 ).

Article

https://doi.org/10.1038/s41566-024-01590-0 deposition to prevent oxidation. For the closed-cavity system, 10 nm of atomic-layer-deposited Al 2 O 3 is placed on top of mithrene to protect it during the Ag sputtering process, and PMMA is spin coated on top of the second Ag layer to prevent oxidation. By depositing Ag on top to make the closed-cavity system, the Q-factor of the largest PL peak is increased by a factor of 2.26 compared with the open-cavity system since the top interface of the lossy Fabry-Pérot cavity is more reflective than the open-cavity system (Supplementary Fig. 6). The increased Q-factor is seen as a narrowing of the peaks in both reflectance (Fig. 3c) and room-temperature (Fig. 3d) PL. Additionally, the coupling parameter increases to 359 meV in the closed-cavity system due to the decrease in cavity-mode volume and cavity loss (Supplementary Fig. matches closely with the simulation data. The shift in the polariton branches between the experiment and simulation is attributed to the thickness estimation error in the atomic force microscopy measurement. c, PL spectroscopy showing exciton emission at 468 nm, whereas exciton-polariton shows emission at 468 nm (UEP), 474 nm (HO mode) and 527 nm (LEP). A g su bs tr at e Open cavity Closed cavity a b 10 nm A l 2 O3 Mithrene A g su bs tr at e PMMA 15 nm Ag Mithrene c d e 10 nm A l 2 O3 10 nm Al 2 O 3 Wavelength (nm) Reflectance Wavelength (nm) Normalized PL Wavelength (nm) Normalized PL T = 80 K 5.87 nm 1.0 nm 1.0 0.5 0 1.0 400 600 800 450 500 550 425 450 475 500 0.5 0 1.0 Open cavity Closed cavity Open cavity Exciton PL Closed cavity Excitonpolariton PL (closed cavity) 0.5 0 Fig. 3 | Exciton-polaritons in open-and closed-cavity mithrene. a,b, Open cavity refers to mithrene/10 nm Al 2 O 3 /100 nm Ag (a) and closed cavity refers to PMMA/15 nm Ag/10 nm Al 2 O 3 /PMMA/ mithrene/10 nm Al 2 O 3 /100 nm Ag (b). c,d, Reflectance (c) and PL (d) from open and closed cavities. e, PL recorded at 80 K shows a linewidth narrowing of the exciton-polariton emission from the closed cavity compared with the exciton emission. The exciton emission is measured by exfoliating 50 nm of mithrene on a quartz substrate. The transparent substrate inhibits a cavity mode from forming to couple to the bare exciton.

Article https://doi.org/10.1038/s41566-024-01590-0 blueshift, along with the exciton, due to its large exciton fraction. The closed-cavity system was also cooled down to 80 K, and its linewidths further decrease to sub-nanometre values due to decreased photon scattering (Fig. 3e). The linewidth of an LEP is inversely related to its lifetime, and the lifetime of the LEP is a weighted average of the cavity and exciton lifetimes 47 . At room temperature, we hypothesize that the non-radiative lifetime of the exciton plays a crucial role in the LEP lifetime. Therefore, as the temperature is reduced, the non-radiative lifetime of the exciton is prolonged, and the radiative lifetime of the cavity dominates the lifetime of the LEP. This is further confirmed by the PL at 80 K of mithrene on a quartz substrate. The transmissive property of the substrate prevents cavity modes from forming; therefore, its emission is purely excitonic. The exciton emission shows a larger linewidth than the LEP emission, indicating that the HO Fabry-Pérot cavity modes reduce the linewidth of the LEP.

On further cooling of the closed-cavity system to <100 K, the anticrossing of exciton-polaritons is observed in the angle-dependent PL (Fig. 4a,b) 48 . The emission is measured for temperatures ranging from 5 K to 150 K at which the PL can no longer be observed by the angle-dependent PL system (Supplementary Fig. 8). Since the pump wavelength is above the bandgap of mithrene, it creates a population of excitons that are then hybridized into exciton-polaritons. The excitons then relax into the LEP branches, and subsequently emit a photon on relaxation to the ground state. The observed PL of the sub-bandgap states validates that the states are exciton-polaritons, which are part matter and part light. Additionally, the flattening of the polariton bands is not observed as the numerical aperture (0.75) does not allow large-enough incident angles, but flattening is observed in the experimental spectra measured using imaging spectroscopic ellipsometry and in the simulated dispersion (Supplementary Fig. 9). The flattening at large angles is due to the anticrossing behaviour of exciton-polaritons. As the LEP wavelength approaches the exciton wavelength with increasing angles, the LEP cannot continue its parabolic dispersion without crossing the exciton wavelength. As a result, the LEP dispersion flattens out at high angles. The HO LEP (closer to the exciton wavelength) also shows more horizontal dispersion due to its increased exciton fraction, which has also been observed in similar multipolariton systems 49 .

The lifetimes of multiple LEP branches are also studied in both open-and closed-cavity systems using time-resolved PL (TRPL) (Fig. 4c,d). The lifetimes in both systems are found to increase as the LEP redshifts. The lifetime increases the LEP wavelength since the LEP cavity fraction also increases 50 . In this case, the energy will spend more time in the cavity than the exciton state, which decreases the probability of emission occurring over a fixed period of time. The system also does not show a large-enough fast component due to Purcell enhancement to be measurable, as observed in similar systems with perovskites 51 . Therefore, the emission properties are dominated by the USC exciton-polariton instead of the local field enhancement. This is because in both open-and closed-cavity systems, the cavity mode has a longer lifetime than the exciton lifetime (0.27 ns). The closed-cavity system shows an enhancement in lifetime over the open cavity by a factor of 1.86. The biggest enhancement is observed at 454 nm compared with other emission wavelengths of the exciton-polaritons.