Abstract
Semiconductor microcavity polaritons, formed via strong excitonphoton coupling, provide a quantum manybody system on a chip, featuring rich physics phenomena for better photonic technology. However, conventional polariton cavities are bulky, difficult to integrate, and inflexible for mode control, especially for roomtemperature materials. Here we demonstrate subwavelengththick, onedimensional photonic crystals as a designable, compact, and practical platform for strong coupling with atomically thin van der Waals crystals. Polariton dispersions and mode anticrossings are measured up to room temperature. Nonradiative decay to dark excitons is suppressed due to polariton enhancement of the radiative decay. Unusual features, including highly anisotropic dispersions and adjustable Fano resonances in reflectance, may facilitate high temperature polariton condensation in variable dimensions. Combining slab photonic crystals and van der Waals crystals in the strong coupling regime allows unprecedented engineering flexibility for exploring novel polariton phenomena and device concepts.
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Introduction
Control of lightmatter interactions is elementary to the development of photonic devices. Existing photonic technologies are based on weakly coupled matterlight systems, where the optical structure perturbatively modifies the electronic properties of the active media. As the matterlight interaction becomes stronger and no longer perturbative, light and matter couple to form hybrid quasiparticles—polaritons. In particular, quantumwell (QW) microcavity exciton polaritons feature simultaneously strong excitonic nonlinearity, robust photonlike coherence, and a metastable ground state, providing a fertile ground for quantum manybody physics phenomena^{1,2} that promise new photonic technology^{3}. Numerous novel types of manybody quantum states with polaritons and polariton quantum technologies have been conceived, such as topological polaritons^{4,5,6}, polariton neurons^{7}, nonclassical state generators^{8,9,10}, and quantum simulators^{11,12,13}. Their implementation require confined and coupled polariton systems with engineered properties, which, on one hand, can be created by engineering the optical component of the strongly coupled modes, on the other hand, is difficult experimentally using conventional polariton systems.
Conventional polariton system are based on vertical Fabry Perot (FP) cavities made of thick stacks of planar, distributed Bragg reflectors (DBRs), which have no free design parameter for mode engineering and are relatively rigid and bulky against postprocessing. Different cavity structures have been challenging to implement for polariton systems as conventional materials are sensitive to free surfaces and lattice mismatch with embedding crystals. The recently emerged twodimensional (2D) semiconductor van der Waals crystals (vdWCs)^{14,15} are uniquely compatible with diverse substrate without lattice matching^{16}. However, most studies of vdWC polaritons so far continue to use FP cavities^{17,18,19,20,21,22,23}, which are even more limiting for vdWCs than for conventional materials. This is because monolayerthick vdWCs need to be sandwiched in between separately fabricated DBR stacks and positioned very close to the cavityfield maximum. The process is complex, hard to control, and may change or degrade the optical properties of vdWCs^{22,24}. Alternatively, metal mirrors and plasmonic structures have been implemented^{25,26,27,28}. They are more compact and flexible, but suffer from intrinsically large absorption loss and poor dipoleoverlap between the exciton and field^{25,29}.
Here we demonstrate subwavelengththick, onedimensional dielectric photonic crystals (PCs) as a readily designable platform for strong coupling, which is also ultracompact, practical, and especially well suited to the atomically thin vdWCs. Pristine vdWCs can be directly laid on top of the PC without further processing. Properties of the optical modes, and in turn the polariton modes, can be modified with different designs of the PC. We confirm polariton modes up to room temperature by measuring the polariton dispersions and mode anticrossing in both reflectance and photoluminescence (PL) spectra. Strongly suppressed nonradiative decay to dark excitons due to the polaritonic enhancement is observed. We show that these polaritons have anisotropic polariton dispersions and adjustable reflectance, suggesting greater flexibility in controlling the excitations in the system to reaching vdWCpolariton condensation at lower densities in variable dimensions. Extension to more elaborate PC designs and 2D PCs will facilitate research on polariton physics and devices beyond 2D condensates.
Results
The system
We use two kinds of transition metal dichalcogenides (TMDs) as the active media: a monolayer of tungsten diselenide (WSe_{2}) or a monolayer of tungsten disulfide (WS_{2}). The monolayers are placed over a PC made of a siliconnitride (SiN) grating, as illustrated in Fig. 1a. The total thickness of the grating t is around 100 nm, much shorter than half a wavelength, making the structure an attractive candidate for compact, integrated polaritonics. In comparison, typical dielectric FP cavity structures are many tens of wavelengths in size. A schematic and scanning electron microscopy images of the TMDPC polariton device are shown in Fig. 1. More details of the structure and its fabrication are described in Methods. Since the grating is anisotropic inplane, its modes are sensitive to both the propagation and polarization directions of the field. As illustrated in Fig. 1a, we define the direction along the grating bars as the xdirection, across the grating bars as the ydirection, and perpendicular to the grating plane as the zdirection. For the polarization, along the grating corresponds to transverseelectric (TE), and across the bar, transversemagnetic (TM). The TMpolarized modes are far off resonance with the exciton. Hence TM excitons remain in the weakcoupling regime, which provides a direct reference for the energies of the uncoupled exciton mode. We focus on the TEpolarized PC modes in the main text and discuss the TM measurements in the Supplementary Figure 1.
WSe_{2}PC polaritons
We first characterize a monolayer WSe_{2}PC device at 10 K. The energymomentum mode structures are measured via angleresolved microreflectance (Fig. 2a, b) and microPL (Fig. 2c) spectroscopy, in both the alongbar (top row) and acrossbar (bottom row) directions. The data (left panels) are compared with numerical simulations (right panels), done with rigorous coupled wave analysis (RCWA).
Without the monolayer, a clear and sharp PC mode is measured with a highly anisotropic dispersion (Fig. 2a, left panels) and is well reproduced by simulation (Fig. 2a, right panels). The broad lowreflectance band in the background is an FP resonance formed by the SiO_{2} capping layer and the substrate. The PC mode half linewidth is γ_{cav} = 6.5 meV. This corresponds to a quality factor Q or finesse of about 270, much higher than most TMD cavities^{17,19,20,25,26,27} and comparable to the best DBRDBR ones^{18,21}.
With a WSe_{2} monolayer laid on top of the PC (Fig. 1c), two modes that anticross are clearly seen in both the reflectance and PL spectra (Fig. 2b, c) and match very well with simulations, suggesting strong coupling between WSe_{2} exciton and PC modes. Strong anisotropy of the dispersion is evident comparing E_{LP,UP}(k_{ x }, k_{ y } = 0) (top row) and E_{LP,UP}(k_{ x } = 0, k_{ y }) (bottom row), resulting from the anisotropic dispersion of the PC modes. Correspondingly, the effective mass and group velocity of the polaritons are also highly anisotropic, which provide new degrees of freedom to verify polariton condensation and to control its dynamics and transport properties^{30}.
To confirm strong coupling, we fit the measured dispersion with that of coupled modes, and we compare the coupling strength and Rabi splitting obtained from the fitting with the exciton and photon linewidth. In the strong coupling regime, the eigenenergies of the polariton modes E_{LP,UP} at given inplane wavenumber \(k_\parallel\) and the corresponding vacuum Rabi splitting 2ħΩ are given by:
Here E_{exc} is the exciton energy, γ_{exc} and γ_{cav} are the halfwidths of the uncoupled exciton and PC resonances, respectively, and g is the excitonphoton coupling strength. A nonvanishing Rabi splitting 2ħΩ requires \(g > \gamma _{{\mathrm{exc}}}  \gamma _{{\mathrm{cav}}}{\mathrm{/}}2\); but this is insufficient for strong coupling. For the two resonances to be spectrally separable, the minimum modesplitting needs to be greater than the sum of the half linewidths of the modes:
In frequency domain, Eq. (3) corresponds to requiring coherent, reversible energy transfer between the exciton and photon mode. We first fit our measured PL spectra to obtain the mode dispersion E_{LP,UP}(k_{x,y}), as shown by the symbols in Fig. 2d. We then fit E_{LP,UP}(k_{x,y}) with (1), with g and E_{cav}(k_{x,y} = 0) as the only fitting parameters. The exciton energy E_{exc} and halfwidth γ_{exc} are measured from the TMpolarized exciton PL from the same device, while the wavenumber dependence of E_{cav} and γ_{cav} are measured from the reflectance spectrum of the bare PC (Supplementary Figure 2b). We obtain g = 8.9 ± 0.23 and 7.5 ± 0.87 meV for dispersions along k_{ x } and k_{ y }, respectively, corresponding to a Rabi splitting of 2ħΩ ~ 17.6 and 14.9 meV. In comparison, γ_{exc} = 5.7 meV and γ_{cav} = 3.25 meV. Therefore g is much greater than not only (γ_{exc} − γ_{cav)}/2 = 1.2 meV but also \(\sqrt {(\gamma _{{\mathrm{exc}}}^2 + \gamma _{{\mathrm{cav}}}^2){\mathrm{/}}2} = 4.6\) meV, which confirms the system is well into the strong coupling regime.
Temperature dependence of WSe_{2}PC polaritons
At elevated temperatures, increased phonon scattering leads to faster exciton dephasing, which drives the system into the weakcoupling regime. We characterize this transition by the temperature dependence of the WSe_{2}PC system; we also show the effect of strong coupling on exciton quantum yield.
We measure independently the temperature dependence of the uncoupled excitons via TM exciton PL, the uncoupled PC modes via reflectance from the bare PC, and the coupled modes via PL from the WSe2PC device. We show in Fig. 3a the results obtained for k_{ x } = 3.1 μm^{−1}, k_{ y } = 0 μm^{−1} as an example. For the uncoupled excitons, with increasing T, the resonance energy E_{exc}(T) decreases due to bandgap reduction^{31}, as shown in Fig. 3a, while the linewidth 2γ_{exc} broadens due to phonon dephasing^{32}, as shown in Fig. 3b. Both results are very well fitted by models for conventional semiconductors (see more details in Methods). For the uncoupled PC modes, the energy E_{cav} = 1.74 eV and half linewidth γ_{cav} = 6.5 meV change negligibly (Supplementary Figure 2c). The exciton and PCphoton resonances cross, as shown in Fig. 3a, at around 50 K. In contrast, the modes from the WSe_{2}PC device anticross between 10 and 100 K and clearly split from the uncoupled modes, suggesting strong coupling up to 100 K. Above 130 K, it becomes difficult to distinguish the modes from WSe_{2}PC device and the uncoupled exciton and photon modes, suggesting the transition to the weakcoupling regime.
We compare quantitatively in Fig. 3b the coupling strength g with \(\sqrt {(\gamma _{{\mathrm{exc}}}^2 + \gamma _{{\mathrm{cav}}}^2){\mathrm{/}}2}\) and (γ_{exc} − γ_{cav})/2 to check the criterion given in Eq. (3). The strong coupling regime persists up to about 110 K, above which, due to the increase of the exciton linewidth, g(T) drops to below \(\sqrt {(\gamma _{{\mathrm{exc}}}^2 + \gamma _{{\mathrm{cav}}}^2){\mathrm{/}}2}\) and the system transitions to the weakcoupling regime, which corresponds well to the existence/disappearance of modesplitting in Fig. 3 below/above 110 K. On the other hand, \(g > (\gamma _{{\mathrm{exc}}}  \gamma _{{\mathrm{cav}}}){\mathrm{/}}2\) is maintained up to about 185 K. Between 110 and 185 K, coherent polariton modes are no longer supported in the structure but modesplitting remains in the reflectance spectrum (Supplementary Figure 3).
Importantly, the temperature dependence of the polariton PL intensity reveals that strong coupling enables significant enhancement of the quantum yield of WSe_{2} at low temperatures. It has been shown that the quantum yield of the bright excitonic states is strongly suppressed by 10 to 100fold in bare WSe_{2} monolayers due to relaxation to dark excitons lying at lower energies than the bright excitons^{33,34}. In contrast, the WSe_{2}PC polariton intensity decreases by less than 2fold from 200 to 10 K. This is because coupling with the PC greatly enhances the radiative decay of the WSe_{2} excitonpolariton states in comparison with scattering to the dark exciton states, effectively improving the quantum yield of the bright excitons.
Roomtemperature WS_{2}PC polaritons
To form excitonpolaritons at room temperature, we use WS_{2} because of the large oscillator strength to linewidth ratio at 300 K compared to WSe_{2} (Supplementary Figure 4). We use a onedimensional (1D) PC that matches the resonance of the WS_{2} exciton at 300 K. The angleresolved reflectance spectrum from the bare PC again shows a clear, sharp dispersion (Fig. 4a). The broadband background pattern is due to the FP resonance of the substrate. With a monolayer of WS_{2} placed on top, anticrossing LP and UP branches form, as clearly seen in both the reflectance and PL spectra (Fig. 4b, c). The data (left panels) are in excellent agreement with the simulated results (right panels). The dispersions measured from PL fit very well with the coupled oscillator model in Eq. (1), from which we obtain an excitonphoton interaction strength of g = 12.4 ± 0.36 meV, above γ_{exc} = 11 meV, γ_{cav} = 4.5 meV, and \(\sqrt {(\gamma _{{\mathrm{exc}}}^2 + \gamma _{{\mathrm{cav}}}^2){\mathrm{/}}2} = 8.4 \;{\mathrm{meV}}\). The Rabi splitting is 2ħΩ = 22.2 meV.
Adjustable reflectance spectra with Fano resonances
Lastly, we look into two unconventional properties of the reflectance of the TMDPC polariton systems: adjustable background; and Fano resonances.
As shown in Figs. 2 and 4, the reflectance around the PC polariton resonances can vary from nearly zero to close to unity. The background reflectance is determined by the FP resonances of the substrate. It features broad FP bands, with location, height, and width of the band readily adjusted by the thickness of the SiO_{2} spacer layer, uncorrelated with the quality factor of the PC modes or the lifetime of the polaritons. For example, the WSe_{2}PC polaritons are in the lowreflectance region of the FP bands (Fig. 5a), while the WS_{2}PC polaritons are in the highreflectance region (Fig. 5b). In contrast, in conventional FP cavities, high cavity quality factor dictates that the polariton modes are inside a broad highreflectance stopband, making it difficult to excite or probe the polariton systems at wavelengths within the stopband. The adjustability of the reflectance in PC polariton systems will allow much more flexible access to the polariton modes and therefore may facilitate realization of polariton lasers, switches, and other polariton nonlinear devices.
Interestingly, the reflectance line shape of the PC polariton resonances are also distinctly different between the two devices (Fig. 5). A characteristic asymmetric Fano line shape is measured and varies with both the background FP band and the photonexciton detuning. The Fano resonance arises from coupling between the sharp, discrete PC or PC polariton modes and the continuum of freespace radiation modes intrinsic to the 2Dslab structure^{35}. It can be described by:
The first term describes the Fano resonance, where R_{F} is the amplitude coefficient, q is the asymmetry factor, \(\varepsilon = \frac{{\hbar (\omega  \omega _0)}}{{\gamma _0}}\) is the reduced energy, and ħω_{0} and γ_{0} are the resonant energy and half linewidth of the discrete mode, respectively. R_{FP}(ω) and I_{b} are the FP background reflectance and a constant ambient background, respectively. We use the transfer matrix method to calculate R_{FP}, then fit our data to Eq. (4) to determine the Fano parameters.
We first compare the very different Fano line shapes of the WSe_{2}PC and the WS_{2}PC (Fig. 5a, b). For WSe_{2}PC, we obtain q_{cav} = 5.0, q_{LP} = 3.5, and q_{UP} = 4.1, for the PC, LP, and UP modes, respectively. The large values of q suggest small degrees of asymmetry and line shapes close to Lorentzian, as seen in Fig. 5a. For the WS_{2} device, we obtain q_{cav} = 0.93, q_{LP} = 0.83, and q_{UP} = 0.18, which strongly deviates from a Lorentzian line, corresponding to a more asymmetric line shape with a sharp Fanofeature, as seen in Fig. 5b. The two devices are made with gratings and substrates of different thicknesses to move the polariton resonances from the valley to the peak of the FP bands, with correspondingly a phase change of π of the FP modes, leading to the sharp contrast between the Fano line shapes of the polaritons.
Next we focus on the WS_{2}PC device to examine the angledependence of the fitted asymmetry parameter q (Fig. 5c) and compare it with the polariton mode anticrossing (Fig. 5d). As shown in Fig. 5c, the Fano asymmetry parameter q for the lower and upper polaritons tunes sensitively with angle near where the polaritons anticross (Fig. 5d), or where the polaritons are nearly halfphoton and halfexciton. In contrast, for large detunings where the modes are mostly photonlike or excitonlike, as well as for the bare PC modes (yellow circles), q is nearly constant over a wide range of angles. This is because, in the absence of strong exciton and photon mixing, the reflection phase of the fardetuned polaritons or the bare PC mode changes only very slowly with angle, which is also reflected in the nearly quadratic dispersion of the excitons or bare PC mode. When the PC mode strongly couples with the TMD exciton mode, the reflection phase becomes strongly dependent on the detuning and thus the angle, leading to the strong angledependence of the Fano line shape.
The Fano line shape sensitively depends on the phase difference between the interfering modes and therefore may enable phasesensitive sensing applications^{35,36}. In polariton systems, Fano resonances have only been reported in a ZnO microwire cavity recently^{37}, driven by secondharmonic generation and tunable due to phase variations of the cavity mode. Polaritons assisted in secondharmonic generation but was otherwise not necessary for forming the Fano resonance. They have not been reported in passive or linear polariton systems nor in FP cavity polaritons. Our results demonstrate Fano resonances in the polariton reflectance spectra and furthermore polaritonenabled tuning of the Fano resonances both over a wide range via the adjusting the FP resonances and finely by angle or excitonphoton detuning.
Discussion
In short, we demonstrate integration of two of the most compact and versatile systems—atomically thin vdWCs as the active media and PCs of deep subwavelength thicknesses as the optical structure—to form an ultracompact and designable polariton system. TMDPC polaritons were observed in monolayer WS_{2} at room temperature and in WSe_{2} up to 110 K, which are the highest temperatures reported for strong coupling for each type of the TMDs in dielectric cavities, respectively. The TMDPC polaritons feature highly anisotropic energymomentum dispersions, adjustable reflectance with sharp Fano resonances, and strong suppression of nonradiative loss to dark excitons. These features will facilitate control and optimization of polariton dynamics for nonlinear polariton phenomena and applications, such as polariton amplifiers^{38}, lasers^{39}, switches^{40}, and sensors^{35,36}.
The demonstrated quasi2D TMDPC polariton system is readily extended to zerodimensional, 1D, and coupled arrays of polaritons^{41,42}. The 1D PC already has many design parameter for mode engineering; it can be extended to 2D PCs for even greater flexibility. For example, 2D PCs can be designed to have chiral modeselectivity^{43,44} or to support modes of both polarizations, for controlling the spinvalley degree of freedom^{45}. The TMDs can be substituted by and integrated with other types of atomically thin crystals, including black phosphorous for wide bandgap tunability^{46}, graphene for electrical control^{47}, and hexagonal boronnitride for field enhancement.
PCs feature unmatched flexibility in opticalmode engineering, while vdWCs allow unprecedented flexibility in integration with other materials, structures, and electrical controls^{48,49}. Combining the two in the strong coupling regime opens a door to novel polariton quantum manybody phenomenon and device applications^{4,5,6,7,8,9,10,11,12,13}.
Methods
Sample fabrication
The devices shown in Fig. 1 were made from a SiN layer grown by lowpressure chemical vapor deposition on a SiO_{2}capped Si substrate. The SiN layer was partially etched to form a 1D grating, which together with the remaining SiN slab support the desired PC modes. The grating was created via electron beam lithography followed by plasma dry etching. Monolayer TMDs are prepared by mechanical exfoliation from bulk crystals from 2D semiconductors and transferred to the grating using polydimethylsiloxane. For the WSe_{2} device, the grating parameters are as follows: Λ = 468 nm; η = 0.88; t = 113 nm; h = 60 nm; and d = 1475 nm. For the WS_{2} device, the grating parameters are as follows: Λ = 413 nm; η = 0.83; t = 78 nm; h = 40 nm; and d = 2000 nm.
Optical measurements
Reflection and PL measurements were carried out by realspace and Fourierspace imaging of the device. An objective lens with numerical aperture (NA) of 0.55 was used for both focusing and collection. For reflection, white light from a tungsten halogen lamp was focused on the sample to a beam size of 15 μm in diameter. For PL, a HeNe laser (633 nm) and a continuouswave solidstate laser (532 nm) were used to excite the monolayer WSe_{2} and WS_{2}, respectively, both with 1.5 mW and a 2 μm focused beam size. The collected signals were polarizationresolved by a linear polarizer then detected by a Princeton Instruments spectrometer with a cooled chargecoupled camera.
RCWA simulation
Simulations are carried out using an opensource implementation of RCWA developed by Pavel Kwiecien to calculate the electricfield distribution of PC modes, as well as the reflection and absorption spectra of the device as a function of momentum and energy. The indices of refraction of the SiO_{2} and SiN are obtained from ellipsometry measurements to be \(n_{{\mathrm{SiO2}}} = 1.45 + \frac{{0.0053}}{{\lambda ^2}}\) and \(n_{{\mathrm{SiN}}} = 2.0 + \frac{{0.013}}{{\lambda ^2}}\), where λ is the wavelength in the unit of μm. The WSe_{2} and WS_{2} monolayers were modeled with a thickness of 0.7 nm, and the inplane permittivities were given by a Lorentz oscillator model:
For WSe_{2}, we used oscillator strength \(f_{{\mathrm{WS}}_2}=0.7 \;{\mathrm{eV}}^2\) to reproduce the Rabi splitting observed in experiments, exciton resonance \(E_{{\mathrm{WSe}}_2} = 1.742 \;{\mathrm{eV}}\) and full linewidth \({\it{\Gamma }}_{{\mathrm{WSe}}_2} = 11.4 \;{\mathrm{meV}}\) based on TM exciton PL, and background permittivity \(\varepsilon _{{\mathrm{B}},{\mathrm{WSe}}_2} = 25\)^{50}. Likewise, for WS_{2}, we used \(f_{{\mathrm{WS}}_2}=1.85 \;{\mathrm{eV}}^2\), \(E_{{\mathrm{WS}}_2} = 2.013 \;{\mathrm{eV}}\), and \({\it{\Gamma }}_{{\mathrm{WS}}_2} = 22 \;{\mathrm{meV}}\) measured from a bare monolayer, and \(\varepsilon _{{\mathrm{B}},{\mathrm{WS}}_2} = 16\)^{51}.
Modeling the temperature dependence of the WSe_{2} exciton energy and linewidth
The exciton resonance energies redshift with increasing temperature as shown in Fig. 3a. It is described by the standard temperature dependence of semiconductor bandgaps^{31} as follows:
Here E_{ g }(0) is the exciton resonance energy at T = 0 K, S is a dimensionless coupling constant, and ħω is the average phonon energy, which is about 15 meV in monolayer TMDs^{52,53}. The fitted parameters are E_{ g }(0) = 1.741 and S = 2.2, which agree with reported results^{52,53}.
The exciton linewidth γ_{exc} as a function of temperature can be described by the following model^{53,54}:
Here γ_{0} is the linewidth at 0 K, the term linear in T depicts the intravalley scattering by acoustic phonons, and the third term describes the intervalley scattering and relaxation to the dark state through optical and acoustic phonons^{54}. The average phonon energy is ħω = 15 meV. The fitted parameters are γ_{0} = 11.6 meV and c_{2} = 25.52 meV, and c_{1} is negligibly small in our case^{53}.
Data availability
The data that support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
All authors acknowledge the support by the Army Research Office under Awards W911NF1710312. L.Z., R.G., and H.D. acknowledge the support by the Air Force Office of Scientific Research under Awards FA95501510240. W.B. and E.T. acknowledge the support by National Science Foundation Grant EECS1610008. The fabrication of the PC was performed in the Lurie Nanofabrication Facility (LNF) at Michigan, which is part of the NSF NNIN network.
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L.Z. fabricated the device and performed the measurements and data analysis. R.G. designed the device. W.B. and E.T. assisted in fabrication. H.D. conceived the experiment. L.Z., R.G., and H.D. wrote the paper. All authors discussed the results, data analysis, and the paper.
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Zhang, L., Gogna, R., Burg, W. et al. Photoniccrystal excitonpolaritons in monolayer semiconductors. Nat Commun 9, 713 (2018). https://doi.org/10.1038/s4146701803188x
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DOI: https://doi.org/10.1038/s4146701803188x
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