Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides

Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides Shao-Yu Chen, Yi-Hsun Chen, Ping-Yuan Lo, Kyle Boschen, Guan-Hao Peng, and 13 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4643091/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Materials capable of light upconversion—transforming low-energy photons into higher-energy ones—are pivotal in advancing optoelectronics, energy solutions, and photocatalysis. However, the discovery in various materials pays little attention on few-layer transition metal dichalcogenides, primarily due to their indirect bandgaps and weaker light-mater interactions. Here, we report a pronounced light upconversion in few-layer transition metal dichalcogenides through upconversion photoluminescence spectroscopy. Our joint theory-experiment study attributes the upconversion photoluminescence to a resonant exciton-exciton annihilation involving a pair of dark excitons with opposite momenta, followed by the spontaneous emission of upconverted bright excitons, which can have a high upconversion efficiency. Additionally, the upconversion photoluminescence is generic in MoS 2 , MoSe 2 , WS 2 , and WSe 2 , showing a high tuneability from green to ultraviolet light (2.34–3.1 eV). The findings pave the way for further exploration of light upconversion regarding fundamental properties and device applications in two-dimensional semiconductors. Physical sciences/Physics/Optical physics/Nonlinear optics Physical sciences/Materials science/Nanoscale materials/Graphene/Optical properties and devices Physical sciences/Nanoscience and technology/Nanoscale materials/Graphene/Optical properties and devices light upconversion exciton-exciton annihilation dark excitons transition metal dichalcogenides 2D materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 INTRODUCTION Upconversion photoluminescence (UPL) is an anti-Stokes phenomenon of light-matter interactions in which a material radiatively emits photons at an energy higher than the excitation energy. Since the process is able to generate high-energy photons, UPL is of interest in a wide range of applications across various fields such as biology 1–3 , medicine 4,5 , and energy 6–8 . Starting from the very first rare-earth doped nanomaterials 9 , the demonstration of UPL has been reported in inorganic 10,11 , organic 12,13 , and organic-inorganic hybrid 14,15 semiconductors. Recent advancements, particularly in molecular systems employing triplet − triplet annihilation, have achieved high-quantum efficiency and/or low excitation density in the upconversion process. 16,17 However, there is still a growing demand for solid-state alternatives due to their enhanced durability and compatibility with existing semiconductor manufacturing technologies, which could open doors for broader applications. Exciton-exciton annihilation (EEA) has a fundamental advantage over other upconversion mechanisms for spontaneous light upconversion in solid-state materials. EEA is a two-body process in which one exciton transfers its energy and momentum to another, effectively doubling the energy of the resulting exciton. 18 The rate of EEA exhibits a quadratic dependence on exciton density 19 , which is more efficient than the cubic dependence in three-body processes, such as Auger recombination 20 , especially in the low-density regime. Despite its potential, EEA phenomena require a dominance of excitonic effects in materials, a condition challenging to achieve in bulk semiconductors due to their small exciton binding energies. Atomically thin 2D semiconducting materials, on the other hand, possess excitons with binding energies reaching several hundreds of meV because of the reduced dielectric screening. 21 Moreover, they host a rich exciton landscape from the intriguing electronic band structures within the Brillouin zone, making them ideal candidates for exploring EEA-driven light upconversion. Indeed, EEA has been demonstrated in low-dimensional materials such as carbon nanotubes 19,22 , graphene nanoribbons 23 , quantum wells 24 , quantum dots 25 , and even 2D semiconductors 26–28 . However, the UPL under the EEA principle has rarely been reported. In this work, we report light upconversion in few-layer transition metal dichalcogenides (TMDs) via a resonant EEA of dark excitons. The resonant EEA involves two momentum-indirect dark excitons with opposite momenta upconverting to higher-energy zero-momentum excitons at Γ valley, supported by layer-dependent dark/bright exciton energies observed in both experiments and theoretical calculations. The quadratic power dependence is characterised in WSe 2 atomic layers by using power dependent measurements, indicating EEA as the mechanism for the upconversion process. We also show that the UPL, initiated by using the continuous-wave laser with a fairly low-power density, is fundamentally different from second harmonic generation (SHG), which often necessitates high-power density through a pulsed laser. Lastly, our study showcases that UPL is remarkably tuneable through material choice (WSe 2 , WS 2 , MoS 2 , and MoSe 2 ) and layer number, with upconversion photon energy ranging from 2.34 to 3.1 eV. Such tunability underscores the strong layer-dependent energy of dark excitons, originating from significant interlayer Coulomb interactions and quantum confinement effects inherent in atomically thin TMDs. RESULTS AND DISCUSSION The initial investigation focuses on identifying excitonic species and UPL in few-layer WSe 2 . The fabrication of WSe 2 samples is described in Methods. The thickness of the samples is identified using optical contrast and low-wavenumber Raman spectroscopy (see Extended Data Fig. 1 ). Figures 1 a,b compare the absorbance and UPL spectra, respectively, of a 5L WSe 2 sample at 80 K. The absorbance spectrum (Fig. 1 a) reveals four pronounced peaks attributed to bright excitons, which are labelled according to their electron/hole configurations, denoted as MN i , where M and N represent the momentum of the electron and hole in the hexagonal Brillouin zone, respectively, and i indicates the index in ascending energy order for identical configurations. The corresponding electron/hole configurations are schematically illustrated in Fig. 1 c. From low to high energy, the first and second peaks, labelled KK A and KK B , correspond to the traditionally known A and B excitons respectively. At higher energy, we assigned the peaks to QQ and ΓΓ excitons based on our theoretical analysis of excitonic band structures (further details in Supplementary note 1 ) and the prior experiments 29 . Notably, ΓΓ excitons are composed of electrons with negative effective mass and holes with positive effective mass. Such atypical conduction and valence bands may result in a nesting of excitonic bands with a high joint density of states. 30–32 In the UPL spectroscopy, we collect luminescence signals spanning energies both below and above the excitation energy (2.33 eV), yielding a typical PL (upconversion PL) spectrum represented by the blue (ruby) curves in Fig. 1 b. Sharp features adjacent to 2.33 eV are attributed to Raman scattering by WSe 2 . The PL emission from KK A and KK B excitons becomes exceedingly weak in 5L WSe 2 due to its indirect bandgap. Meanwhile, KK A emission is overwhelmed by the PL signals from Al 2 O 3 substrate noted in grey shadow (see Extended Data Fig. 2 for PL spectrum of 5L WSe 2 on a SiO 2 /Si substrate). Below the KK A emission, we detect a faint PL peak from the lowest-energy momentum-indirect (dark) excitons, labelled as X D , at approximately 1.31 eV, which is attributed to QK or QΓ excitons. 33,34 In the upconversion PL spectrum, we observe a notable emission of UPL around 2.64 eV, which is approximately twice the energy of the X D peak. Intriguing, the UPL intensity is significantly higher than the X D in the typical PL spectrum, suggesting an efficient light upconversion process. A detailed examination of the UPL emission (see the inset in Fig. 1 b) reveals that the line profile can be modelled with two peaks: one at higher energy (coloured in orange) well-described by a Gaussian function and the other at lower energy (coloured in light green) described by a Lorentzian. The Gaussian peak primarily contributes to the UPL and is strongly correlated to X D , which will be analysed in Fig. 2 ; hence, we named it as upconverted excitons (X up ). On the other hand, the Lorentzian is located close to but not directly at the ΓΓ exciton energy seen in the absorbance spectrum. To be clear, we named it as high-lying excitons (HX) instead of ΓΓ excitons. We note that the Lorentzian profile of HX suggests an ultrafast recombination lifetime 35 , consistent with the PL emission from high-lying excitons with a large binding energy of up to 0.6–0.7 eV 36 . The correlation between dark excitons and UPL is further examined with layer-dependent UPL measurements. Figure 2 a presents X D emissions of 2–6 L WSe 2 , exhibiting a red shift in emission energy from 1.553 (2L) to 1.294 eV (6L), consistent with the evolution of the electronic band structure as the layer thickness increases. 37 Fig. 2 b shows the corresponding UPL spectra fitted with two components, HX and X up , as mentioned in the inset of Fig. 1 b. The X up emission is located at 2.857 (3L), 2.712 (4L), 2.642 (5L), and 2.608 eV (6L), and the HX is located at 2.76 (3L) and 2.67 eV (4L) and 2.621 (5L). However, neither X up nor HX emission is detected in 2L WSe 2 . For clarity, we summarise the energies of X up , X D and ΓΓ excitons (extracted from absorbance spectra) as a function of the number of layers in Fig. 2 c. The X up energies (filled blue circles) closely match the red dashed curve, which depicts twice the energy of X D (labelled as 2× E XD ), reinforcing that X up is strongly correlated with X D . Furthermore, the X up energy moves toward ΓΓ excitons (filled green triangles) with the increasing number of layers and overlaps ΓΓ excitons beyond 5L WSe 2 , resulting in a strongly enhanced light upconversion intensity evident in Fig. 2 b and quantified by the open blue triangles in Fig. 2 c. We found that upconversion efficiency Q up (defined in Methods), is greater than unity in 5L WSe 2 and above, which is at least ten times higher than 3L WSe 2 . The Q up > 1 means that UPL emission is larger than X D emission, quantitatively suggesting an efficient light upconversion occurred at the resonance between X up and ΓΓ excitons. We believe that the efficient light conversion is a consequence of the resonant EEA process, as illustrated in Fig. 3 a. Upon optical excitation, photoexcited bright excitons thermally relax to X D via multiple phonon scattering. X D is the momentum-forbidden dark exciton with a finite centre of mass (CoM) momentum, leading to prolonged population lifetime up to tens of nanoseconds. 38,39 The fact that X D has orders of magnitude longer lifetime than bright excitons favours pronounced many-body interactions. 40,41 In our case, the X D is upconverted to a higher energy state X up through EEA, followed by radiative recombination at an energy above the initial excitation. Notably, the UPL emission of X up suggests that the radiative recombination is favoured over phonon scattering as the relaxation pathway, which typically occurs on much shorter timescales of 10–100 fs. 42–44 This indicates that the spontaneous emission holds a competitive edge in the dynamics of upconverted excitons in few-layer WSe 2 . We propose a model wherein a resonant EEA facilitates the light upconversion in few-layer WSe 2 (see more detail in Supplementary note 2) . The resonant EEA process involves the initial state (dark excitons) upconverting to the final state (bright excitons) under a fundamental restriction—both states must follow the conservation of energy and momentum. Figure 3 b illustrates a viable pathway for QΓ dark excitons undergoing the resonant EEA upon the momentum-conserving principle. In the right panel, the final state entails that both electron and hole are at the Γ valley, where bright excitons exhibit zero CoM momentum. For this to occur, two X D in the initial state (left panel) could be momentum-indirect with opposite momenta, a hole at Γ valley and an electron at Q/Q’ valley. The EEA of such dark exciton pairs describes that one dark exciton recombines non-radiatively and transfers its energy and momentum to the other dark exciton, and that the electron of the other dark exciton originally occupying the lowest available conduction band (Q/Q’ valley) is scattered to a high-lying conduction band, forming a bright exciton at Γ valley. We note that the EEA process is also possible by scattering the hole originally occupying the highest available valence band to a lower valence band, forming high-lying bright excitons at Q valley (see Supplementary Fig. 2b). Last, for the resonance to be achieved, the energy of the final state must be approximately twice of that of the initial state. Therefore, the energy conservation allows us to identify possible final states in subsequent calculations. Figure 3 c–e show the calculated exciton energies of dark X D and bright excitons (Γ ex ) with different CoM momentum for 1L, 2L, and 4L WSe 2 , respectively (see Supplementary note 2 for detail). We consider bright exciton states observed in Fig. 1 (KK A , KK B , QQ, and ΓΓ) and dark exciton states (K’K, QK, QΓ, KΓ) that potentially fulfil the valley and band selection rules for the resonant EEA process. In order to identify available final states for involving in the resonant EEA, we depict the energy and the doubled energy of the lowest-lying dark excitons as the grey and light green bars in the figures respectively. For 1L WSe 2 , the lowest energy QK excitons could upconvert to high-lying KK or QQ excitons, but only the high-lying KK excitons fulfil the resonance criterion. Our calculation also supports the recent experimental observation of UPL involving the high-lying KK excitons with negative effective mass and KK A excitons. 45 For 2L WSe 2 , the lowest energy QK excitons upconverting to ΓΓ excitons does not obey the selection rule (The non-resonant process is denoted with a grey arrow with red X in Fig. 3 d; see item 3 of Supplementary Table 1.), which explains the absence of light upconversion in our experiments (See black curve in Fig. 2 b). As the thickness increases, QK and QΓ excitons become the lowest energy and are likely degenerate in 4L WSe 2 , and a cluster of ΓΓ excitons (green solid lines in Fig. 3 e) lies in the vicinity of twice the energy of QΓ/QK excitons, enabling efficient channels for the resonant EEA (denoted with red arrow in Fig. 3 e). In the process of resonant EEA, a QΓ exciton is upconverted into ΓΓ excitons by absorbing the energy and momentum of either a QK or a Q’Γ exciton, which possesses an opposite momentum of the QΓ exciton (see items 4 and 6 of Supplementary Table 1). We note that only a fraction of ΓΓ excitons within the double energy of dark excitons can contribute to the UPL. Our power-dependent measurement further supports the mechanism of EEA-assisted light upconversion in few-layer WSe 2 . UPL spectra in 5L WSe 2 show that the overall intensity increases nonlinearly obtained with power density from 0.03 to 1.02 mW/µm 2 (see Extended Data Fig. 3 a). We integrate the intensity of UPL (including X up and HX) and plot it as a function of excitation power density in Fig. 3 f. Notably, the 5L WSe 2 sample exhibits a superlinear dependence with exponent α = 2 below P = 0.1 mW/µm 2 , suggesting an EEA behaviour. In contrast, bulk WSe 2 exhibits the power law exponent of α = 3, suggesting the conventional Auger recombination (see the corresponding UPL spectra in Extended Data Fig. 3 b). This fundamental difference demonstrates that the light upconversion via resonant EEA is inherently a low-dimensional phenomenon—the dominance of tightly bound excitons in few-layer WSe 2 due to the quantum confinement and the reduced dielectric screening, resulting in much higher exciton binding energies compared to the bulk counterpart. We note that the superlinear dependence of EEA can also be observed in other few-layer WSe 2 (see Extended Data Figs. 3 c–h). Regardless of the layer thickness, we observed a saturation of UPL intensity approaching linear dependence at P > 0.1 mW/µm 2 . The saturation may imply other higher-order nonlinear processes at elevating exciton density, which become significant at the specific power threshold. This highlights rich and intricate many-body dynamics under intense optical excitation. More dynamical studies are required to elucidate the interactions and relaxation of X up , which may be critical for nonlinear optical and optoelectronic applications. The resonant EEA is fundamentally different from other common upconversion mechanisms observed in other 2D materials, such as SHG and phonon-assisted upconversion. Figure 4 a shows the evolution of UPL spectra in a 5L WSe 2 with various excitation energies ( E in ). 5L WSe 2 has no inversion symmetry, allowing us to compare the EEA and SHG. We utilised a tuneable pulsed laser to selectively excite near resonantly with X D at E in from 1.24 to 1.33 eV. Emission energies in the spectra are fitted with two Gaussians (see Methods), as displayed in Fig. 4 b. In Fig. 4 a, across all the excitation energies, we observed an emission peak (yellow) strongly correlating with the E in . The extracted peak energies show a good agreement with doubled excitation energy, 2× E in (depicted as the grey solid line in Fig. 4 b), indicating a SHG characteristic. Remarkably, when the excitation energy was tuned closely to the energy of X D peak (1.301–1.326 eV), an additional emission peak (blue) appears at 2.575 eV, which we identified as UPL, is nearly independent of E in (denoted as X up in Fig. 4 b). This independence is distinct from the SHG peaks because the UPL is only present at E in near the dark exciton energy, whereas SHG signal is observed throughout the excitation energies. We further depict normalised UPL intensity as a function of the excitation energy in Fig. 4 c. The intensity is significant at 1.28 eV but negligible at both 1.24 and 1.33 eV, indicating the correlation between the UPL intensity and the population of dark excitons. Second, Fig. 4 d shows the UPL peaks in both HH (co-polarisation) and HV (cross-polarisation) configurations 46 (see Methods for more detail). The UPL intensity is identical in different polarisation configurations, in contrast to the SHG in which the inherently polarisation-dependent process is described by the tensor of second-order nonlinear optical susceptibility. 47 Third, SHG often necessitates a femtosecond pulsed laser to achieve high photon density. Our experiments, however, have demonstrated the pronounced UPL signal simply using a CW laser, suggesting a low threshold of photon density in the upconversion process. Fourth, in contrast to SHG which only present in odd-layer samples due to the broken inversion symmetry, UPL is persistently present for WSe 2 thickness beyond 3 layers without any evident odd/even layer dependence, as we already demonstrated in Fig. 2 . All the above observations point to the importance of the dark exciton in UPL and ruling out SHG as the primary mechanism for light upconversion. The phonon-assisted upconversion is a mechanism through which extra energy is provided to excitons through exciton-phonon interactions, resulting in a transition to higher excitonic states. 28,48 As a result, the increasing temperature tends to increase the phonon population and thus enhance upconversion process. Figure 4 e shows UPL intensity of 5L WSe 2 sample as a function of temperature. The UPL remains detectable up to room temperature while the intensity exponentially decreases as the temperature increases, which cannot be explained by the phonon-assisted process. Moreover, the energy difference between UPL emission and excitation energy is significantly higher than the energy of optical phonons in 5L WSe 2 , which is about 50 meV (see Extended Data Fig. 4 ). These observations support the unlikelihood of phonon-assisted upconversion playing a role in our observations. The light upconversion is not exclusive to few-layer WSe 2 , but seen in few-layer WS 2 , MoS 2 , and MoSe 2 . Figure 5 a shows that the UPL emission (2.875 eV for 5L WS 2 , 2.77 eV for 3L MoS 2 , and 2.49 eV for 3L MoSe 2 ) closely matches the double energy of the dark exciton emissions (1.43 eV for 5L WS 2 , 1.4 eV for 3L MoS 2 , and 1.28 eV for 3L MoSe 2 ,), signifying the important role of dark excitons in the light upconversion. Figure 5 b shows that UPL intensity is strongly enhanced as the layer thickness increases, suggesting a shared characteristic of the resonant EEA process within the few-layer (Mo, W)(S, Se) 2 . Moreover, we highlight that the UPL emission is tuneable, offering a significant advantage for applications requiring specific wavelengths. Figure 5 c summarises the peak energy of UPL in few-layer WSe 2 , WS 2 , MoS 2 , and MoSe 2 . The UPL emission energies span a broad spectrum, ranging from green light (2.34 eV) to ultraviolet light (3.1 eV). Such tunability illustrates the potential of these materials in enhancing optoelectronic and photocatalytic applications through engineered light-matter interactions. In summary, our research has showcased efficient light upconversion in atomically thin TMDs. The UPL is driven by the resonant EEA of momentum-indirect dark excitons. The demonstrated many-body interaction provides a universal route for harnessing the energy of the lowest-lying momentum-indirect excitons to generate green to ultraviolet light, featuring a broad scope of tunability. The process of exciton-mediated light conversion underlines the intricate many-body excitonic physics within TMDs and opens a door to promising advancements in the fields of optoelectronics and photocatalysis, where control over such fundamental interactions is essential. REFERENCES (UP TO 50) (1) DaCosta, M. 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METHODS Samples preparation Bulk WSe 2 and MoSe 2 crystals with ultra-low defects were grown by a two-step self-flux method. 49 The bulk WS 2 and MoS 2 crystals were purchased from HQ Graphene and SPI supplies, respectively. Thin TMD flakes were mechanically exfoliated onto polydimethylsiloxane (PDMS) and subsequently dry-transferred onto Al 2 O 3 or SiO 2 /Si substrates. The layer thickness of the samples was determined by analysing optical contrast and ultra-low frequency Raman spectroscopy, as shown in Extended Data Fig. 1 . Upconversion Photoluminescence Spectroscopy The fresh-made samples are transferred to a cryostat with optical access (Janis ST-500) under a high-vacuum environment (base pressure < 5 × 10 − 6 Torr) to ensure reliable results. The sample can be cooled down to 80 K by continuous flowing liquid nitrogen. A diode-pump solid-state continuous-wave laser at an excitation energy of 2.33 and 1.96 eV was employed for excitation. The spectroscopy was set up in a back-scattering configuration. A 40× objective lens (numerical aperture, 0.6) was applied to focus the laser to the diffraction limit. The PL signal was filtered by three cascaded Bragg notch filters (OptiGrate), dispersed by a grating-based monochromator (Horiba, iHR-550 with 150 gr/mm grating), and detected by a nitrogen-cooled charge-coupled device (Horiba, Symphony II). In addition, two linear polarisers are placed in incident and scattered light, which enable us to select polarisation of incident/scattered light and the relative polarisation between them. In Fig. 4 d, the 0° and 90° of relative polarisation is defined as parallel (HH) and perpendicular (HV) mode, respectively. Note that all experimental figures are executed at a temperature of 80 K and incident power of 0.34 mW/µm 2 unless stated. Ultrafast Photoluminescence Spectroscopy The ultrafast photoluminescence spectroscopy with tuneable fs pulses was executed with samples at T = 9 K in a closed-cycle cryostat (Montana Instruments, Cryostation). A 20× objective lens (numerical aperture, 0.38) was used both to focus the excitation laser and collect the PL emission. The tuneable excitation came from a non-collinear optical parametric amplifier (Light Conversion, Orpheus-N-3H) pumped by the third harmonic of a Nd:YAG amplified femtosecond laser system (Light Conversion, Pharos). The spectrum of each excitation pulse was measured before the sample by a Thorlabs CCS200 spectrometer. The PL emission was separated from the pump by a 600 nm short-pass dichroic beam splitter, and measured using an Andor Kymera 328i spectrometer with an Andor Zyla sCMOS camera. The recorded spectra were processed using a custom written python script. Each peak was fit by two Gaussian functions: one for the PL emission component and the other for the SHG component. The fits were completed using the SciPy Curve Fit module. The peak energy and full-width at half-maximum (FWHM) of the SHG component were fixed, based on the parameters from a Gaussian fit of the excitation spectrum. Specifically, the peak energy was determined by doubling the energy and the FWHM was scaled by a factor of √2 from the values obtained for the excitation spectrum. The integrated peak amplitude of the PL emission was determined from the Gaussian fit parameters. Normalisation of photoluminescence spectra and calculation of upconversion efficiency ( Q up ) The PL spectra of 2–6L WSe 2 in Fig. 2 a,b are normalised to 3L WSe 2 and the calculation of upconversion efficiency ( Q up ) is based on the normalisation. Specifically, in Fig. 2 a, we first calculated the integrated PL intensity of dark excitons for each layer thickness. The intensity ratio of each layer thickness to 3L WSe 2 can be calculated using I XD,n / I XD,3 , where I XD,n is the integrated PL intensity of dark excitons in n -layer WSe 2 ( n = 2–6). The spectrum of 2–6L WSe 2 is then scaled according to the intensity ratio. In Fig. 2 b, the same intensity ratio is applied to the UPL spectrum of 2–6L WSe 2 . After the normalisation, we define the Q up by counting the intensity ratio of UPL to the dark exciton PL, ( I Xup + I HX )/ I XD , where I Xup , I HX , and I XD are integrated PL intensities of upconverted, high-lying, and dark excitons, respectively. Declarations Notes The authors declare no competing interest. Extended Data Fig. 1. Low-wavenumber Raman spectra of few-layer WSe 2 obtained with polarisation-resolved Raman spectroscopy. a – b Evolution of perpendicular mode (HV, including only shear mode) ( a ) and parallel mode (HH, including shear and breathing modes) ( b ) with layer thickness from 2L to 11L. In ( a ), the black dash line guides to the eyes. c Extracted frequencies of shear modes (S 1 , S 2 , S 3 ) as a function of the layer thickness. Extended Data Fig. 2. Photoluminescence spectrum of a 5L WSe 2 on a SiO 2 /Si substrate obtained at T = 80 K. Extended Data Fig. 3. Power-dependent characteristics of light upconversion in layered WSe 2 at T = 80 K and excitation energy of 2.33 eV (wavelength 532 nm). a,b Evolution of upconversion photoluminescence in 5L ( a ) bulk WSe 2 ( b ) with power density from 0.03 to 1.02 mW/µm 2 . Each spectrum is normalised by the power density. The black dashed lines are guides to the eyes. c – h Upconversion photoluminescence intensity as a function of incident power density P for 3L ( c ), 4L ( d ), 5L ( e ), 6L ( f ), 7L ( g ), and 11L WSe 2 ( h ). The black solid line in each figure represents a power-law exponent α = 2. Extended Data Fig. 4. Optical phonons and photoluminescence spectrum of 5L WSe 2 at T = 80 K and excited with excitation energy of 2.33 eV. Author Contributions Y. H. C. and P. Y. L. contribute equally to this work. Y. H. C. and S. Y. C. conceived and designed this project. Y. H. C. and S. Y. C. conducted device fabrication, optical measurement, and data analysis. J. H., L. N. H., and K. B. from Columbia University provided bulk WSe 2 and MoSe 2 crystals. M. H. contributed towards confirming the quality of TMD crystals. K. B. from Swinburne University of Technology conducted ultrafast optical measurement. P. Y. L., G. H. P., C. J. H., C. E. H., Y. N. H., P. H., H. C. H., and S. J. C. contributed theoretical calculations. W. H. W. provided resources for conducting optical measurements. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT Tungsten diselenide and molybdenum diselenide crystal growth was supported under the United States National Science Foundation Materials Research Science and Engineering Center through grants DMR-1420634 and DMR-2011738. Y. H. Chen, K.W. Boschen, J. A. Davis, M. S. Fuhrer, and S.-Y. Chen acknowledge support from the ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET; CE170100039). S.-Y. Chen acknowledges support from the National Science and Technology Council of Taiwan through Grant 111-2112-M-002-047 and 112-2628-M-002-008-, and the Center of Atomic Initiative for New Materials, National Taiwan University (grant nos. 112 L9008 and 113 L9008), from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education of Taiwan. S.-Y. Chen thanks the experimental support from Dr. Wei-Hua Wang in the Institute of Atomic and Molecular Sciences, Academia Sinica. S. J. Cheng acknowledges that this study is supported by the National Science and Technology Council of Taiwan under the contract, 112-2112-M-A49-028-, and by National Center for High-Performance Computing of Taiwan. P Y. Lo acknowledges support from the National Science and Technology Council of Taiwan, under the contract NSTC 112-2112-M-A49-019-MY3. H. C. Hsueh, C. E. Hsu, and Y. N. Hsu acknowledge the support from National Science and Technology Council, Taiwan, under Grant: 110-2112-M-032-014-MY3, and thank the National Center for High-Performance Computing in Taiwan for providing computational resources. P. H. work was supported by the Quantum Sensors QSP078 and On-Chip Integrated Photonic Circuits Based on 2D Materials HTSN341 Challenge Programs at the National Research Council of Canada, NSERC Discovery Grant No. RGPIN-2019-05714, and University of Ottawa Research Chair in Quantum Theory of Materials, Nanostructures, and Devices. Unsectioned Paragraphs Additional Declarations There is NO Competing Interest. Supplementary Files SIEEAinTMD20240609.docx Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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upconverted excitons in 5L WSe\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003e(a)\u003c/strong\u003e Absorbance spectrum at \u003cem\u003eT\u003c/em\u003e = 80 K with bright excitons indicated by arrows; labels discussed in text.\u003cstrong\u003e (b)\u003c/strong\u003e PL spectrum at \u003cem\u003eT\u003c/em\u003e = 80 K excited with excitation energy 2.33 eV (wavelength 532 nm). The spectrum is divided into typical (blue) and upconversion PL (ruby) regimes. The inset in upconversion PL regime: The peak fittings of UPL from upconverted excitons X\u003csub\u003eup\u003c/sub\u003e and high-lying excitons (HX). The low-energy PL is also shown magnified 60× to better show the dark exciton X\u003csub\u003eD\u003c/sub\u003e emission at 1.31 eV. The grey shadow area indicates photoluminescence from the Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e substrate. \u003cstrong\u003e(c)\u003c/strong\u003e The schematic of electronic band structure and corresponding bright/dark excitons observed in \u003cstrong\u003e(a,b)\u003c/strong\u003e.\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"Fig15LPLAandbandstrcuture.png","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/4f42a00af25059536f422c72.png"},{"id":63951483,"identity":"dd0a5730-078d-41ed-a029-9567182d279d","added_by":"auto","created_at":"2024-09-04 07:03:42","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":846476,"visible":true,"origin":"","legend":"\u003cp\u003eLayer-dependent characteristics of UPL in few-layer WSe\u003csub\u003e2\u003c/sub\u003e at \u003cem\u003eT\u003c/em\u003e = 80 K. Evolution of \u003cstrong\u003e(a) \u003c/strong\u003edark excitons X\u003csub\u003eD\u003c/sub\u003e and \u003cstrong\u003e(b)\u003c/strong\u003e UPL spectra with the number of layers from 2L to 6L. The UPL emission of 3–6L WSe\u003csub\u003e2\u003c/sub\u003e can be deconvoluted into upconverted X\u003csub\u003eup\u003c/sub\u003e (short dash line; peak denoted by circles) and high-lying excitons HX (long dash line; peak denoted by pentagons). The spectrum of each thickness is vertically shifted for clarity. \u003cstrong\u003e(c)\u003c/strong\u003e Emission energy of X\u003csub\u003eD\u003c/sub\u003e and X\u003csub\u003eup\u003c/sub\u003e, and absorption energy of ΓΓ excitons \u003cem\u003eE\u003c/em\u003e\u003csub\u003eΓΓ\u003c/sub\u003e, and extracted upconversion efficiency \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eup\u003c/sub\u003e as a function of layer thickness. In \u003cstrong\u003e(a\u003c/strong\u003e–\u003cstrong\u003ec)\u003c/strong\u003e, the photoluminescence intensity is normalised to X\u003csub\u003eD\u003c/sub\u003e emission of 3L WSe\u003csub\u003e2\u003c/sub\u003e (see Method for further details).\u003c/p\u003e","description":"","filename":"Fig2LdepWSe2.png","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/f65367f2cb6f98dfa4f954bc.png"},{"id":63951482,"identity":"5900cfca-5cea-4392-a322-35d18867b990","added_by":"auto","created_at":"2024-09-04 07:03:42","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1471722,"visible":true,"origin":"","legend":"\u003cp\u003eResonant exciton-exciton annihilation of dark excitons in few-layer WSe\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003e(a)\u003c/strong\u003e The schematic of upconversion process in few-layer WSe\u003csub\u003e2\u003c/sub\u003e. Light-excited bright excitons thermally relax to dark exciton states at the lowest energy X\u003csub\u003eD\u003c/sub\u003e through multiple phonon scattering. The resonant EEA process upconverts two excitons X\u003csub\u003eD\u003c/sub\u003e to a single high-energy exciton X\u003csub\u003eup\u003c/sub\u003e, followed by a radiative combination, resulting in the light upconversion emission. \u003cstrong\u003e(b)\u003c/strong\u003e A schematic representation of excitonic upconversion before (left panel) and after the electron-scattering process (right panel). \u003cstrong\u003e(c\u003c/strong\u003e–\u003cstrong\u003ee)\u003c/strong\u003e Exciton energy as a function of exciton centre of mass (CoM) momentum in 1L \u003cstrong\u003e(c)\u003c/strong\u003e, 2L \u003cstrong\u003e(d)\u003c/strong\u003e, and 4L WSe\u003csub\u003e2\u003c/sub\u003e \u003cstrong\u003e(e)\u003c/strong\u003e. Black arrows denote the energy of the lowest energy dark exciton \u003cem\u003eE\u003c/em\u003e\u003csub\u003eXD\u003c/sub\u003e and the corresponding twice energy 2×\u003cem\u003eE\u003c/em\u003e\u003csub\u003eXD\u003c/sub\u003e, respectively.\u003cstrong\u003e (f)\u003c/strong\u003e UPL intensity as a function of power density for 5L and bulk WSe\u003csub\u003e2\u003c/sub\u003e obtained at \u003cem\u003eT\u003c/em\u003e = 80 K. The blue and red dash lines represent a power-law exponent α = 2 and α = 3, respectively.\u003c/p\u003e","description":"","filename":"Fig3EEAschematicpdepandtheory.png","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/0852f7b6aea66eb7fabe4aa3.png"},{"id":63952906,"identity":"957ca7d1-4fbf-4368-9036-84829705e836","added_by":"auto","created_at":"2024-09-04 07:19:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1174055,"visible":true,"origin":"","legend":"\u003cp\u003eExcitation energy, polarisation, and temperature dependence of light upconversion in 5L WSe\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003e(a)\u003c/strong\u003e Evolution of UPL spectrum at \u003cem\u003eT\u003c/em\u003e = 9 K with excitation energy from 1.246 to 1.333 eV. The excitation energy for each spectrum is labelled accordingly. Blue and orange peaks represent UPL emission from upconverted excitons X\u003csub\u003eup\u003c/sub\u003e at 2.575 eV and SHG, respectively. \u003cstrong\u003e(b)\u003c/strong\u003e Extracted energy of X\u003csub\u003eup\u003c/sub\u003e and SHG as a function of excitation energy. The grey solid line indicates the double of the excitation energy. \u003cstrong\u003e(c)\u003c/strong\u003e Normalised UPL intensity as a function of excitation energy obtained. The intensity is normalised by the square of incident power. \u003cstrong\u003e(d)\u003c/strong\u003e UPL spectra at \u003cem\u003eT\u003c/em\u003e = 80 K obtained in perpendicular (HV) and parallel (HH) scattering configuration. \u003cstrong\u003e(e)\u003c/strong\u003e UPL intensity as a function of temperature ranging from 80 to 300 K.\u003c/p\u003e","description":"","filename":"Fig45LPdepkyleSwinburne.png","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/95c3bceac4b9951fdb70f143.png"},{"id":63951485,"identity":"823428cd-51d7-4267-964b-ee7f6d8e34d9","added_by":"auto","created_at":"2024-09-04 07:03:43","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":907669,"visible":true,"origin":"","legend":"\u003cp\u003eLight upconversion in few-layer MoS\u003csub\u003e2\u003c/sub\u003e, MoSe\u003csub\u003e2\u003c/sub\u003e, WS\u003csub\u003e2\u003c/sub\u003e, and WSe\u003csub\u003e2\u003c/sub\u003e at \u003cem\u003eT\u003c/em\u003e = 80 K. \u003cstrong\u003e(a)\u003c/strong\u003e Photoluminescence spectrum of 5L WS\u003csub\u003e2\u003c/sub\u003e, 3L MoS\u003csub\u003e2\u003c/sub\u003e, and 3L MoSe\u003csub\u003e2\u003c/sub\u003e at emission energy ranging from 1.2 to 3.1 eV. \u0026nbsp;The excitation energy (2.33 eV) is denoted as the green arrow. \u003cstrong\u003e(b)\u003c/strong\u003e The UPL spectrum of 6L WS\u003csub\u003e2\u003c/sub\u003e, MoS\u003csub\u003e2\u003c/sub\u003e, and MoSe\u003csub\u003e2\u003c/sub\u003e in contrast to thinner counterparts (3L WS\u003csub\u003e2\u003c/sub\u003e, 3L MoS\u003csub\u003e2\u003c/sub\u003e, and 4L MoSe\u003csub\u003e2\u003c/sub\u003e). The spectra are normalised to the incident power. The excitation energy for each spectrum (2.33 eV for WS\u003csub\u003e2\u003c/sub\u003e and MoS\u003csub\u003e2\u003c/sub\u003e, 1.96 eV for MoSe\u003csub\u003e2\u003c/sub\u003e) is denoted as the green arrow. \u003cstrong\u003e(c)\u003c/strong\u003e Peak energy of upconversion photoluminescence in MoS\u003csub\u003e2\u003c/sub\u003e (open), MoSe\u003csub\u003e2\u003c/sub\u003e (solid), WS\u003csub\u003e2\u003c/sub\u003e (half left), and WSe\u003csub\u003e2\u003c/sub\u003e (half up) with the layer thickness ranging from 3L to 7L, and thicker than 7L.\u003c/p\u003e","description":"","filename":"Fig5materialdep.png","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/66fd3008d39e46506e841ae0.png"},{"id":63952907,"identity":"ec056d79-f0da-465d-9e6c-8c94f1b855f3","added_by":"auto","created_at":"2024-09-04 07:19:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5738158,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/86fe9b16-8845-4823-8876-97c71399f648.pdf"},{"id":63952005,"identity":"46b1f6fe-0c5d-4a80-8445-b89b49744ee3","added_by":"auto","created_at":"2024-09-04 07:11:43","extension":"docx","order_by":11,"title":"","display":"","copyAsset":false,"role":"supplement","size":518747,"visible":true,"origin":"","legend":"","description":"","filename":"SIEEAinTMD20240609.docx","url":"https://assets-eu.researchsquare.com/files/rs-4643091/v1/088c598535b734fa50eacaa0.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eUpconversion photoluminescence (UPL) is an anti-Stokes phenomenon of light-matter interactions in which a material radiatively emits photons at an energy higher than the excitation energy. Since the process is able to generate high-energy photons, UPL is of interest in a wide range of applications across various fields such as biology\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e, medicine\u003csup\u003e4,5\u003c/sup\u003e, and energy\u003csup\u003e6\u0026ndash;8\u003c/sup\u003e. Starting from the very first rare-earth doped nanomaterials\u003csup\u003e9\u003c/sup\u003e, the demonstration of UPL has been reported in inorganic\u003csup\u003e10,11\u003c/sup\u003e, organic\u003csup\u003e12,13\u003c/sup\u003e, and organic-inorganic hybrid\u003csup\u003e14,15\u003c/sup\u003e semiconductors. Recent advancements, particularly in molecular systems employing triplet\u0026thinsp;\u0026minus;\u0026thinsp;triplet annihilation, have achieved high-quantum efficiency and/or low excitation density in the upconversion process.\u003csup\u003e16,17\u003c/sup\u003e However, there is still a growing demand for solid-state alternatives due to their enhanced durability and compatibility with existing semiconductor manufacturing technologies, which could open doors for broader applications.\u003c/p\u003e \u003cp\u003eExciton-exciton annihilation (EEA) has a fundamental advantage over other upconversion mechanisms for spontaneous light upconversion in solid-state materials. EEA is a two-body process in which one exciton transfers its energy and momentum to another, effectively doubling the energy of the resulting exciton.\u003csup\u003e18\u003c/sup\u003e The rate of EEA exhibits a quadratic dependence on exciton density\u003csup\u003e19\u003c/sup\u003e, which is more efficient than the cubic dependence in three-body processes, such as Auger recombination\u003csup\u003e20\u003c/sup\u003e, especially in the low-density regime. Despite its potential, EEA phenomena require a dominance of excitonic effects in materials, a condition challenging to achieve in bulk semiconductors due to their small exciton binding energies. Atomically thin 2D semiconducting materials, on the other hand, possess excitons with binding energies reaching several hundreds of meV because of the reduced dielectric screening.\u003csup\u003e21\u003c/sup\u003e Moreover, they host a rich exciton landscape from the intriguing electronic band structures within the Brillouin zone, making them ideal candidates for exploring EEA-driven light upconversion. Indeed, EEA has been demonstrated in low-dimensional materials such as carbon nanotubes\u003csup\u003e19,22\u003c/sup\u003e, graphene nanoribbons\u003csup\u003e23\u003c/sup\u003e, quantum wells\u003csup\u003e24\u003c/sup\u003e, quantum dots\u003csup\u003e25\u003c/sup\u003e, and even 2D semiconductors\u003csup\u003e26\u0026ndash;28\u003c/sup\u003e. However, the UPL under the EEA principle has rarely been reported.\u003c/p\u003e \u003cp\u003eIn this work, we report light upconversion in few-layer transition metal dichalcogenides (TMDs) via a resonant EEA of dark excitons. The resonant EEA involves two momentum-indirect dark excitons with opposite momenta upconverting to higher-energy zero-momentum excitons at Γ valley, supported by layer-dependent dark/bright exciton energies observed in both experiments and theoretical calculations. The quadratic power dependence is characterised in WSe\u003csub\u003e2\u003c/sub\u003e atomic layers by using power dependent measurements, indicating EEA as the mechanism for the upconversion process. We also show that the UPL, initiated by using the continuous-wave laser with a fairly low-power density, is fundamentally different from second harmonic generation (SHG), which often necessitates high-power density through a pulsed laser. Lastly, our study showcases that UPL is remarkably tuneable through material choice (WSe\u003csub\u003e2\u003c/sub\u003e, WS\u003csub\u003e2\u003c/sub\u003e, MoS\u003csub\u003e2\u003c/sub\u003e, and MoSe\u003csub\u003e2\u003c/sub\u003e) and layer number, with upconversion photon energy ranging from 2.34 to 3.1 eV. Such tunability underscores the strong layer-dependent energy of dark excitons, originating from significant interlayer Coulomb interactions and quantum confinement effects inherent in atomically thin TMDs.\u003c/p\u003e"},{"header":"RESULTS AND DISCUSSION","content":"\u003cp\u003eThe initial investigation focuses on identifying excitonic species and UPL in few-layer WSe\u003csub\u003e2\u003c/sub\u003e. The fabrication of WSe\u003csub\u003e2\u003c/sub\u003e samples is described in Methods. The thickness of the samples is identified using optical contrast and low-wavenumber Raman spectroscopy (see Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea,b compare the absorbance and UPL spectra, respectively, of a 5L WSe\u003csub\u003e2\u003c/sub\u003e sample at 80 K. The absorbance spectrum (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) reveals four pronounced peaks attributed to bright excitons, which are labelled according to their electron/hole configurations, denoted as MN\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, where M and N represent the momentum of the electron and hole in the hexagonal Brillouin zone, respectively, and \u003cem\u003ei\u003c/em\u003e indicates the index in ascending energy order for identical configurations. The corresponding electron/hole configurations are schematically illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. From low to high energy, the first and second peaks, labelled KK\u003csub\u003eA\u003c/sub\u003e and KK\u003csub\u003eB\u003c/sub\u003e, correspond to the traditionally known A and B excitons respectively. At higher energy, we assigned the peaks to QQ and ΓΓ excitons based on our theoretical analysis of excitonic band structures (further details in \u003cb\u003eSupplementary note 1\u003c/b\u003e) and the prior experiments\u003csup\u003e29\u003c/sup\u003e. Notably, ΓΓ excitons are composed of electrons with negative effective mass and holes with positive effective mass. Such atypical conduction and valence bands may result in a nesting of excitonic bands with a high joint density of states.\u003csup\u003e30\u0026ndash;32\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the UPL spectroscopy, we collect luminescence signals spanning energies both below and above the excitation energy (2.33 eV), yielding a typical PL (upconversion PL) spectrum represented by the blue (ruby) curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb. Sharp features adjacent to 2.33 eV are attributed to Raman scattering by WSe\u003csub\u003e2\u003c/sub\u003e. The PL emission from KK\u003csub\u003eA\u003c/sub\u003e and KK\u003csub\u003eB\u003c/sub\u003e excitons becomes exceedingly weak in 5L WSe\u003csub\u003e2\u003c/sub\u003e due to its indirect bandgap. Meanwhile, KK\u003csub\u003eA\u003c/sub\u003e emission is overwhelmed by the PL signals from Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e substrate noted in grey shadow (see Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for PL spectrum of 5L WSe\u003csub\u003e2\u003c/sub\u003e on a SiO\u003csub\u003e2\u003c/sub\u003e/Si substrate). Below the KK\u003csub\u003eA\u003c/sub\u003e emission, we detect a faint PL peak from the lowest-energy momentum-indirect (dark) excitons, labelled as X\u003csub\u003eD\u003c/sub\u003e, at approximately 1.31 eV, which is attributed to QK or QΓ excitons.\u003csup\u003e33,34\u003c/sup\u003e In the upconversion PL spectrum, we observe a notable emission of UPL around 2.64 eV, which is approximately twice the energy of the X\u003csub\u003eD\u003c/sub\u003e peak. Intriguing, the UPL intensity is significantly higher than the X\u003csub\u003eD\u003c/sub\u003e in the typical PL spectrum, suggesting an efficient light upconversion process. A detailed examination of the UPL emission (see the inset in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb) reveals that the line profile can be modelled with two peaks: one at higher energy (coloured in orange) well-described by a Gaussian function and the other at lower energy (coloured in light green) described by a Lorentzian. The Gaussian peak primarily contributes to the UPL and is strongly correlated to X\u003csub\u003eD\u003c/sub\u003e, which will be analysed in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e; hence, we named it as upconverted excitons (X\u003csub\u003eup\u003c/sub\u003e). On the other hand, the Lorentzian is located close to but not directly at the ΓΓ exciton energy seen in the absorbance spectrum. To be clear, we named it as high-lying excitons (HX) instead of ΓΓ excitons. We note that the Lorentzian profile of HX suggests an ultrafast recombination lifetime\u003csup\u003e35\u003c/sup\u003e, consistent with the PL emission from high-lying excitons with a large binding energy of up to 0.6\u0026ndash;0.7 eV\u003csup\u003e36\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe correlation between dark excitons and UPL is further examined with layer-dependent UPL measurements. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea presents X\u003csub\u003eD\u003c/sub\u003e emissions of 2\u0026ndash;6 L WSe\u003csub\u003e2\u003c/sub\u003e, exhibiting a red shift in emission energy from 1.553 (2L) to 1.294 eV (6L), consistent with the evolution of the electronic band structure as the layer thickness increases.\u003csup\u003e37\u003c/sup\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb shows the corresponding UPL spectra fitted with two components, HX and X\u003csub\u003eup\u003c/sub\u003e, as mentioned in the inset of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb. The X\u003csub\u003eup\u003c/sub\u003e emission is located at 2.857 (3L), 2.712 (4L), 2.642 (5L), and 2.608 eV (6L), and the HX is located at 2.76 (3L) and 2.67 eV (4L) and 2.621 (5L). However, neither X\u003csub\u003eup\u003c/sub\u003e nor HX emission is detected in 2L WSe\u003csub\u003e2\u003c/sub\u003e. For clarity, we summarise the energies of X\u003csub\u003eup\u003c/sub\u003e, X\u003csub\u003eD\u003c/sub\u003e and ΓΓ excitons (extracted from absorbance spectra) as a function of the number of layers in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. The X\u003csub\u003eup\u003c/sub\u003e energies (filled blue circles) closely match the red dashed curve, which depicts twice the energy of X\u003csub\u003eD\u003c/sub\u003e (labelled as 2\u0026times;\u003cem\u003eE\u003c/em\u003e\u003csub\u003eXD\u003c/sub\u003e), reinforcing that X\u003csub\u003eup\u003c/sub\u003e is strongly correlated with X\u003csub\u003eD\u003c/sub\u003e. Furthermore, the X\u003csub\u003eup\u003c/sub\u003e energy moves toward ΓΓ excitons (filled green triangles) with the increasing number of layers and overlaps ΓΓ excitons beyond 5L WSe\u003csub\u003e2\u003c/sub\u003e, resulting in a strongly enhanced light upconversion intensity evident in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and quantified by the open blue triangles in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. We found that upconversion efficiency \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eup\u003c/sub\u003e (defined in Methods), is greater than unity in 5L WSe\u003csub\u003e2\u003c/sub\u003e and above, which is at least ten times higher than 3L WSe\u003csub\u003e2\u003c/sub\u003e. The \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eup\u003c/sub\u003e \u0026gt; 1 means that UPL emission is larger than X\u003csub\u003eD\u003c/sub\u003e emission, quantitatively suggesting an efficient light upconversion occurred at the resonance between X\u003csub\u003eup\u003c/sub\u003e and ΓΓ excitons.\u003c/p\u003e \u003cp\u003eWe believe that the efficient light conversion is a consequence of the resonant EEA process, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. Upon optical excitation, photoexcited bright excitons thermally relax to X\u003csub\u003eD\u003c/sub\u003e via multiple phonon scattering. X\u003csub\u003eD\u003c/sub\u003e is the momentum-forbidden dark exciton with a finite centre of mass (CoM) momentum, leading to prolonged population lifetime up to tens of nanoseconds.\u003csup\u003e38,39\u003c/sup\u003e The fact that X\u003csub\u003eD\u003c/sub\u003e has orders of magnitude longer lifetime than bright excitons favours pronounced many-body interactions.\u003csup\u003e40,41\u003c/sup\u003e In our case, the X\u003csub\u003eD\u003c/sub\u003e is upconverted to a higher energy state X\u003csub\u003eup\u003c/sub\u003e through EEA, followed by radiative recombination at an energy above the initial excitation. Notably, the UPL emission of X\u003csub\u003eup\u003c/sub\u003e suggests that the radiative recombination is favoured over phonon scattering as the relaxation pathway, which typically occurs on much shorter timescales of 10\u0026ndash;100 fs.\u003csup\u003e42\u0026ndash;44\u003c/sup\u003e This indicates that the spontaneous emission holds a competitive edge in the dynamics of upconverted excitons in few-layer WSe\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe propose a model wherein a resonant EEA facilitates the light upconversion in few-layer WSe\u003csub\u003e2\u003c/sub\u003e (see more detail in \u003cb\u003eSupplementary note 2)\u003c/b\u003e. The resonant EEA process involves the initial state (dark excitons) upconverting to the final state (bright excitons) under a fundamental restriction\u0026mdash;both states must follow the conservation of energy and momentum. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb illustrates a viable pathway for QΓ dark excitons undergoing the resonant EEA upon the momentum-conserving principle. In the right panel, the final state entails that both electron and hole are at the Γ valley, where bright excitons exhibit zero CoM momentum. For this to occur, two X\u003csub\u003eD\u003c/sub\u003e in the initial state (left panel) could be momentum-indirect with opposite momenta, a hole at Γ valley and an electron at Q/Q\u0026rsquo; valley. The EEA of such dark exciton pairs describes that one dark exciton recombines non-radiatively and transfers its energy and momentum to the other dark exciton, and that the electron of the other dark exciton originally occupying the lowest available conduction band (Q/Q\u0026rsquo; valley) is scattered to a high-lying conduction band, forming a bright exciton at Γ valley. We note that the EEA process is also possible by scattering the hole originally occupying the highest available valence band to a lower valence band, forming high-lying bright excitons at Q valley (see Supplementary Fig.\u0026nbsp;2b). Last, for the resonance to be achieved, the energy of the final state must be approximately twice of that of the initial state. Therefore, the energy conservation allows us to identify possible final states in subsequent calculations.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec\u0026ndash;e show the calculated exciton energies of dark X\u003csub\u003eD\u003c/sub\u003e and bright excitons (Γ\u003csub\u003eex\u003c/sub\u003e) with different CoM momentum for 1L, 2L, and 4L WSe\u003csub\u003e2\u003c/sub\u003e, respectively (see \u003cb\u003eSupplementary note 2\u003c/b\u003e for detail). We consider bright exciton states observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (KK\u003csub\u003eA\u003c/sub\u003e, KK\u003csub\u003eB\u003c/sub\u003e, QQ, and ΓΓ) and dark exciton states (K\u0026rsquo;K, QK, QΓ, KΓ) that potentially fulfil the valley and band selection rules for the resonant EEA process. In order to identify available final states for involving in the resonant EEA, we depict the energy and the doubled energy of the lowest-lying dark excitons as the grey and light green bars in the figures respectively. For 1L WSe\u003csub\u003e2\u003c/sub\u003e, the lowest energy QK excitons could upconvert to high-lying KK or QQ excitons, but only the high-lying KK excitons fulfil the resonance criterion. Our calculation also supports the recent experimental observation of UPL involving the high-lying KK excitons with negative effective mass and KK\u003csub\u003eA\u003c/sub\u003e excitons.\u003csup\u003e45\u003c/sup\u003e For 2L WSe\u003csub\u003e2\u003c/sub\u003e, the lowest energy QK excitons upconverting to ΓΓ excitons does not obey the selection rule (The non-resonant process is denoted with a grey arrow with red X in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed; see item 3 of Supplementary Table\u0026nbsp;1.), which explains the absence of light upconversion in our experiments (See black curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). As the thickness increases, QK and QΓ excitons become the lowest energy and are likely degenerate in 4L WSe\u003csub\u003e2\u003c/sub\u003e, and a cluster of ΓΓ excitons (green solid lines in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee) lies in the vicinity of twice the energy of QΓ/QK excitons, enabling efficient channels for the resonant EEA (denoted with red arrow in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee). In the process of resonant EEA, a QΓ exciton is upconverted into ΓΓ excitons by absorbing the energy and momentum of either a QK or a Q\u0026rsquo;Γ exciton, which possesses an opposite momentum of the QΓ exciton (see items 4 and 6 of Supplementary Table\u0026nbsp;1). We note that only a fraction of ΓΓ excitons within the double energy of dark excitons can contribute to the UPL.\u003c/p\u003e \u003cp\u003eOur power-dependent measurement further supports the mechanism of EEA-assisted light upconversion in few-layer WSe\u003csub\u003e2\u003c/sub\u003e. UPL spectra in 5L WSe\u003csub\u003e2\u003c/sub\u003e show that the overall intensity increases nonlinearly obtained with power density from 0.03 to 1.02 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e (see Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). We integrate the intensity of UPL (including X\u003csub\u003eup\u003c/sub\u003e and HX) and plot it as a function of excitation power density in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef. Notably, the 5L WSe\u003csub\u003e2\u003c/sub\u003e sample exhibits a superlinear dependence with exponent α\u0026thinsp;=\u0026thinsp;2 below \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e, suggesting an EEA behaviour. In contrast, bulk WSe\u003csub\u003e2\u003c/sub\u003e exhibits the power law exponent of α\u0026thinsp;=\u0026thinsp;3, suggesting the conventional Auger recombination (see the corresponding UPL spectra in Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). This fundamental difference demonstrates that the light upconversion via resonant EEA is inherently a low-dimensional phenomenon\u0026mdash;the dominance of tightly bound excitons in few-layer WSe\u003csub\u003e2\u003c/sub\u003e due to the quantum confinement and the reduced dielectric screening, resulting in much higher exciton binding energies compared to the bulk counterpart. We note that the superlinear dependence of EEA can also be observed in other few-layer WSe\u003csub\u003e2\u003c/sub\u003e (see Extended Data Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec\u0026ndash;h). Regardless of the layer thickness, we observed a saturation of UPL intensity approaching linear dependence at \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.1 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e. The saturation may imply other higher-order nonlinear processes at elevating exciton density, which become significant at the specific power threshold. This highlights rich and intricate many-body dynamics under intense optical excitation. More dynamical studies are required to elucidate the interactions and relaxation of X\u003csub\u003eup\u003c/sub\u003e, which may be critical for nonlinear optical and optoelectronic applications.\u003c/p\u003e \u003cp\u003eThe resonant EEA is fundamentally different from other common upconversion mechanisms observed in other 2D materials, such as SHG and phonon-assisted upconversion. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea shows the evolution of UPL spectra in a 5L WSe\u003csub\u003e2\u003c/sub\u003e with various excitation energies (\u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e). 5L WSe\u003csub\u003e2\u003c/sub\u003e has no inversion symmetry, allowing us to compare the EEA and SHG. We utilised a tuneable pulsed laser to selectively excite near resonantly with X\u003csub\u003eD\u003c/sub\u003e at \u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e from 1.24 to 1.33 eV. Emission energies in the spectra are fitted with two Gaussians (see Methods), as displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, across all the excitation energies, we observed an emission peak (yellow) strongly correlating with the \u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e. The extracted peak energies show a good agreement with doubled excitation energy, 2\u0026times;\u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e (depicted as the grey solid line in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), indicating a SHG characteristic. Remarkably, when the excitation energy was tuned closely to the energy of X\u003csub\u003eD\u003c/sub\u003e peak (1.301\u0026ndash;1.326 eV), an additional emission peak (blue) appears at 2.575 eV, which we identified as UPL, is nearly independent of \u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e (denoted as X\u003csub\u003eup\u003c/sub\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). This independence is distinct from the SHG peaks because the UPL is only present at \u003cem\u003eE\u003c/em\u003e\u003csub\u003ein\u003c/sub\u003e near the dark exciton energy, whereas SHG signal is observed throughout the excitation energies. We further depict normalised UPL intensity as a function of the excitation energy in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. The intensity is significant at 1.28 eV but negligible at both 1.24 and 1.33 eV, indicating the correlation between the UPL intensity and the population of dark excitons. Second, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed shows the UPL peaks in both HH (co-polarisation) and HV (cross-polarisation) configurations\u003csup\u003e46\u003c/sup\u003e (see Methods for more detail). The UPL intensity is identical in different polarisation configurations, in contrast to the SHG in which the inherently polarisation-dependent process is described by the tensor of second-order nonlinear optical susceptibility.\u003csup\u003e47\u003c/sup\u003e Third, SHG often necessitates a femtosecond pulsed laser to achieve high photon density. Our experiments, however, have demonstrated the pronounced UPL signal simply using a CW laser, suggesting a low threshold of photon density in the upconversion process. Fourth, in contrast to SHG which only present in odd-layer samples due to the broken inversion symmetry, UPL is persistently present for WSe\u003csub\u003e2\u003c/sub\u003e thickness beyond 3 layers without any evident odd/even layer dependence, as we already demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. All the above observations point to the importance of the dark exciton in UPL and ruling out SHG as the primary mechanism for light upconversion.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe phonon-assisted upconversion is a mechanism through which extra energy is provided to excitons through exciton-phonon interactions, resulting in a transition to higher excitonic states.\u003csup\u003e28,48\u003c/sup\u003e As a result, the increasing temperature tends to increase the phonon population and thus enhance upconversion process. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee shows UPL intensity of 5L WSe\u003csub\u003e2\u003c/sub\u003e sample as a function of temperature. The UPL remains detectable up to room temperature while the intensity exponentially decreases as the temperature increases, which cannot be explained by the phonon-assisted process. Moreover, the energy difference between UPL emission and excitation energy is significantly higher than the energy of optical phonons in 5L WSe\u003csub\u003e2\u003c/sub\u003e, which is about 50 meV (see Extended Data Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). These observations support the unlikelihood of phonon-assisted upconversion playing a role in our observations.\u003c/p\u003e \u003cp\u003eThe light upconversion is not exclusive to few-layer WSe\u003csub\u003e2\u003c/sub\u003e, but seen in few-layer WS\u003csub\u003e2\u003c/sub\u003e, MoS\u003csub\u003e2\u003c/sub\u003e, and MoSe\u003csub\u003e2\u003c/sub\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea shows that the UPL emission (2.875 eV for 5L WS\u003csub\u003e2\u003c/sub\u003e, 2.77 eV for 3L MoS\u003csub\u003e2\u003c/sub\u003e, and 2.49 eV for 3L MoSe\u003csub\u003e2\u003c/sub\u003e) closely matches the double energy of the dark exciton emissions (1.43 eV for 5L WS\u003csub\u003e2\u003c/sub\u003e, 1.4 eV for 3L MoS\u003csub\u003e2\u003c/sub\u003e, and 1.28 eV for 3L MoSe\u003csub\u003e2\u003c/sub\u003e,), signifying the important role of dark excitons in the light upconversion. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb shows that UPL intensity is strongly enhanced as the layer thickness increases, suggesting a shared characteristic of the resonant EEA process within the few-layer (Mo, W)(S, Se)\u003csub\u003e2\u003c/sub\u003e. Moreover, we highlight that the UPL emission is tuneable, offering a significant advantage for applications requiring specific wavelengths. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec summarises the peak energy of UPL in few-layer WSe\u003csub\u003e2\u003c/sub\u003e, WS\u003csub\u003e2\u003c/sub\u003e, MoS\u003csub\u003e2\u003c/sub\u003e, and MoSe\u003csub\u003e2\u003c/sub\u003e. The UPL emission energies span a broad spectrum, ranging from green light (2.34 eV) to ultraviolet light (3.1 eV). Such tunability illustrates the potential of these materials in enhancing optoelectronic and photocatalytic applications through engineered light-matter interactions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn summary, our research has showcased efficient light upconversion in atomically thin TMDs. The UPL is driven by the resonant EEA of momentum-indirect dark excitons. The demonstrated many-body interaction provides a universal route for harnessing the energy of the lowest-lying momentum-indirect excitons to generate green to ultraviolet light, featuring a broad scope of tunability. 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Two-Step Flux Synthesis of Ultrapure Transition-Metal Dichalcogenides. \u003cem\u003eACS Nano\u003c/em\u003e \u003cb\u003e2023\u003c/b\u003e, \u003cem\u003e17\u003c/em\u003e (17), 16587\u0026ndash;16596. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acsnano.3c02511\u003c/span\u003e\u003cspan address=\"10.1021/acsnano.3c02511\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eSamples preparation\u003c/h2\u003e \u003cp\u003eBulk WSe\u003csub\u003e2\u003c/sub\u003e and MoSe\u003csub\u003e2\u003c/sub\u003e crystals with ultra-low defects were grown by a two-step self-flux method.\u003csup\u003e49\u003c/sup\u003e The bulk WS\u003csub\u003e2\u003c/sub\u003e and MoS\u003csub\u003e2\u003c/sub\u003e crystals were purchased from HQ Graphene and SPI supplies, respectively. Thin TMD flakes were mechanically exfoliated onto polydimethylsiloxane (PDMS) and subsequently dry-transferred onto Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e or SiO\u003csub\u003e2\u003c/sub\u003e/Si substrates. The layer thickness of the samples was determined by analysing optical contrast and ultra-low frequency Raman spectroscopy, as shown in \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eUpconversion Photoluminescence Spectroscopy\u003c/h2\u003e \u003cp\u003eThe fresh-made samples are transferred to a cryostat with optical access (Janis ST-500) under a high-vacuum environment (base pressure\u0026thinsp;\u0026lt;\u0026thinsp;5 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e Torr) to ensure reliable results. The sample can be cooled down to 80 K by continuous flowing liquid nitrogen. A diode-pump solid-state continuous-wave laser at an excitation energy of 2.33 and 1.96 eV was employed for excitation. The spectroscopy was set up in a back-scattering configuration. A 40\u0026times; objective lens (numerical aperture, 0.6) was applied to focus the laser to the diffraction limit. The PL signal was filtered by three cascaded Bragg notch filters (OptiGrate), dispersed by a grating-based monochromator (Horiba, iHR-550 with 150 gr/mm grating), and detected by a nitrogen-cooled charge-coupled device (Horiba, Symphony II). In addition, two linear polarisers are placed in incident and scattered light, which enable us to select polarisation of incident/scattered light and the relative polarisation between them. In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed, the 0\u0026deg; and 90\u0026deg; of relative polarisation is defined as parallel (HH) and perpendicular (HV) mode, respectively. Note that all experimental figures are executed at a temperature of 80 K and incident power of 0.34 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e unless stated.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eUltrafast Photoluminescence Spectroscopy\u003c/h2\u003e \u003cp\u003eThe ultrafast photoluminescence spectroscopy with tuneable fs pulses was executed with samples at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9 K in a closed-cycle cryostat (Montana Instruments, Cryostation). A 20\u0026times; objective lens (numerical aperture, 0.38) was used both to focus the excitation laser and collect the PL emission. The tuneable excitation came from a non-collinear optical parametric amplifier (Light Conversion, Orpheus-N-3H) pumped by the third harmonic of a Nd:YAG amplified femtosecond laser system (Light Conversion, Pharos). The spectrum of each excitation pulse was measured before the sample by a Thorlabs CCS200 spectrometer. The PL emission was separated from the pump by a 600 nm short-pass dichroic beam splitter, and measured using an Andor Kymera 328i spectrometer with an Andor Zyla sCMOS camera.\u003c/p\u003e \u003cp\u003eThe recorded spectra were processed using a custom written python script. Each peak was fit by two Gaussian functions: one for the PL emission component and the other for the SHG component. The fits were completed using the SciPy Curve Fit module. The peak energy and full-width at half-maximum (FWHM) of the SHG component were fixed, based on the parameters from a Gaussian fit of the excitation spectrum. Specifically, the peak energy was determined by doubling the energy and the FWHM was scaled by a factor of \u0026radic;2 from the values obtained for the excitation spectrum. The integrated peak amplitude of the PL emission was determined from the Gaussian fit parameters.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNormalisation of photoluminescence spectra and calculation of upconversion efficiency (\u003c/b\u003e \u003cb\u003eQ\u003c/b\u003e \u003csub\u003e \u003cb\u003eup\u003c/b\u003e \u003c/sub\u003e \u003cb\u003e)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe PL spectra of 2\u0026ndash;6L WSe\u003csub\u003e2\u003c/sub\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea,b are normalised to 3L WSe\u003csub\u003e2\u003c/sub\u003e and the calculation of upconversion efficiency (\u003cem\u003eQ\u003c/em\u003e\u003csub\u003eup\u003c/sub\u003e) is based on the normalisation. Specifically, in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, we first calculated the integrated PL intensity of dark excitons for each layer thickness. The intensity ratio of each layer thickness to 3L WSe\u003csub\u003e2\u003c/sub\u003e can be calculated using \u003cem\u003eI\u003c/em\u003e\u003csub\u003eXD,n\u003c/sub\u003e/\u003cem\u003eI\u003c/em\u003e\u003csub\u003eXD,3\u003c/sub\u003e, where \u003cem\u003eI\u003c/em\u003e\u003csub\u003eXD,n\u003c/sub\u003e is the integrated PL intensity of dark excitons in \u003cem\u003en\u003c/em\u003e-layer WSe\u003csub\u003e2\u003c/sub\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2\u0026ndash;6). The spectrum of 2\u0026ndash;6L WSe\u003csub\u003e2\u003c/sub\u003e is then scaled according to the intensity ratio. In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, the same intensity ratio is applied to the UPL spectrum of 2\u0026ndash;6L WSe\u003csub\u003e2\u003c/sub\u003e. After the normalisation, we define the \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eup\u003c/sub\u003e by counting the intensity ratio of UPL to the dark exciton PL, (\u003cem\u003eI\u003c/em\u003e\u003csub\u003eXup\u003c/sub\u003e+\u003cem\u003eI\u003c/em\u003e\u003csub\u003eHX\u003c/sub\u003e)/\u003cem\u003eI\u003c/em\u003e\u003csub\u003eXD\u003c/sub\u003e, where \u003cem\u003eI\u003c/em\u003e\u003csub\u003eXup\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003eHX\u003c/sub\u003e, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003eXD\u003c/sub\u003e are integrated PL intensities of upconverted, high-lying, and dark excitons, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eNotes\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interest.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eExtended Data Fig.\u0026nbsp;1.\u003c/h2\u003e \u003cp\u003e Low-wavenumber Raman spectra of few-layer WSe\u003csub\u003e2\u003c/sub\u003e obtained with polarisation-resolved Raman spectroscopy. \u003cb\u003ea\u003c/b\u003e\u0026ndash;\u003cb\u003eb\u003c/b\u003e Evolution of perpendicular mode (HV, including only shear mode) (\u003cb\u003ea\u003c/b\u003e) and parallel mode (HH, including shear and breathing modes) (\u003cb\u003eb\u003c/b\u003e) with layer thickness from 2L to 11L. In (\u003cb\u003ea\u003c/b\u003e), the black dash line guides to the eyes. \u003cb\u003ec\u003c/b\u003e Extracted frequencies of shear modes (S\u003csub\u003e1\u003c/sub\u003e, S\u003csub\u003e2\u003c/sub\u003e, S\u003csub\u003e3\u003c/sub\u003e) as a function of the layer thickness.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eExtended Data Fig.\u0026nbsp;2.\u003c/h2\u003e \u003cp\u003e Photoluminescence spectrum of a 5L WSe\u003csub\u003e2\u003c/sub\u003e on a SiO\u003csub\u003e2\u003c/sub\u003e/Si substrate obtained at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 K.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eExtended Data Fig.\u0026nbsp;3.\u003c/h2\u003e \u003cp\u003e Power-dependent characteristics of light upconversion in layered WSe\u003csub\u003e2\u003c/sub\u003e at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 K and excitation energy of 2.33 eV (wavelength 532 nm). \u003cb\u003ea,b\u003c/b\u003e Evolution of upconversion photoluminescence in 5L (\u003cb\u003ea\u003c/b\u003e) bulk WSe\u003csub\u003e2\u003c/sub\u003e (\u003cb\u003eb\u003c/b\u003e) with power density from 0.03 to 1.02 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e. Each spectrum is normalised by the power density. The black dashed lines are guides to the eyes. \u003cb\u003ec\u003c/b\u003e\u0026ndash;\u003cb\u003eh\u003c/b\u003e Upconversion photoluminescence intensity as a function of incident power density \u003cem\u003eP\u003c/em\u003e for 3L (\u003cb\u003ec\u003c/b\u003e), 4L (\u003cb\u003ed\u003c/b\u003e), 5L (\u003cb\u003ee\u003c/b\u003e), 6L (\u003cb\u003ef\u003c/b\u003e), 7L (\u003cb\u003eg\u003c/b\u003e), and 11L WSe\u003csub\u003e2\u003c/sub\u003e (\u003cb\u003eh\u003c/b\u003e). The black solid line in each figure represents a power-law exponent α\u0026thinsp;=\u0026thinsp;2.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eExtended Data Fig.\u0026nbsp;4.\u003c/h2\u003e \u003cp\u003e Optical phonons and photoluminescence spectrum of 5L WSe\u003csub\u003e2\u003c/sub\u003e at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;80 K and excited with excitation energy of 2.33 eV.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eY. H. C. and P. Y. L. contribute equally to this work. Y. H. C. and S. Y. C. conceived and designed this project. Y. H. C. and S. Y. C. conducted device fabrication, optical measurement, and data analysis. J. H., L. N. H., and K. B. from Columbia University provided bulk WSe\u003csub\u003e2\u003c/sub\u003e and MoSe\u003csub\u003e2\u003c/sub\u003e crystals. M. H. contributed towards confirming the quality of TMD crystals. K. B. from Swinburne University of Technology conducted ultrafast optical measurement. P. Y. L., G. H. P., C. J. H., C. E. H., Y. N. H., P. H., H. C. H., and S. J. C. contributed theoretical calculations. W. H. W. provided resources for conducting optical measurements. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eACKNOWLEDGMENT\u003c/h2\u003e \u003cp\u003eTungsten diselenide and molybdenum diselenide crystal growth was supported under the United States National Science Foundation Materials Research Science and Engineering Center through grants DMR-1420634 and DMR-2011738. Y. H. Chen, K.W. Boschen, J. A. Davis, M. S. Fuhrer, and S.-Y. Chen acknowledge support from the ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET; CE170100039). S.-Y. Chen acknowledges support from the National Science and Technology Council of Taiwan through Grant 111-2112-M-002-047 and 112-2628-M-002-008-, and the Center of Atomic Initiative for New Materials, National Taiwan University (grant nos. 112 L9008 and 113 L9008), from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education of Taiwan. S.-Y. Chen thanks the experimental support from Dr. Wei-Hua Wang in the Institute of Atomic and Molecular Sciences, Academia Sinica. S. J. Cheng acknowledges that this study is supported by the National Science and Technology Council of Taiwan under the contract, 112-2112-M-A49-028-, and by National Center for High-Performance Computing of Taiwan. P Y. Lo acknowledges support from the National Science and Technology Council of Taiwan, under the contract NSTC 112-2112-M-A49-019-MY3. H. C. Hsueh, C. E. Hsu, and Y. N. Hsu acknowledge the support from National Science and Technology Council, Taiwan, under Grant: 110-2112-M-032-014-MY3, and thank the National Center for High-Performance Computing in Taiwan for providing computational resources. P. H. work was supported by the Quantum Sensors QSP078 and On-Chip Integrated Photonic Circuits Based on 2D Materials HTSN341 Challenge Programs at the National Research Council of Canada, NSERC Discovery Grant No. RGPIN-2019-05714, and University of Ottawa Research Chair in Quantum Theory of Materials, Nanostructures, and Devices.\u003c/p\u003e"},{"header":"Unsectioned Paragraphs","content":"\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"light upconversion, exciton-exciton annihilation, dark excitons, transition metal dichalcogenides, 2D materials","lastPublishedDoi":"10.21203/rs.3.rs-4643091/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4643091/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMaterials capable of light upconversion\u0026mdash;transforming low-energy photons into higher-energy ones\u0026mdash;are pivotal in advancing optoelectronics, energy solutions, and photocatalysis. However, the discovery in various materials pays little attention on few-layer transition metal dichalcogenides, primarily due to their indirect bandgaps and weaker light-mater interactions. Here, we report a pronounced light upconversion in few-layer transition metal dichalcogenides through upconversion photoluminescence spectroscopy. Our joint theory-experiment study attributes the upconversion photoluminescence to a resonant exciton-exciton annihilation involving a pair of dark excitons with opposite momenta, followed by the spontaneous emission of upconverted bright excitons, which can have a high upconversion efficiency. Additionally, the upconversion photoluminescence is generic in MoS\u003csub\u003e2\u003c/sub\u003e, MoSe\u003csub\u003e2\u003c/sub\u003e, WS\u003csub\u003e2\u003c/sub\u003e, and WSe\u003csub\u003e2\u003c/sub\u003e, showing a high tuneability from green to ultraviolet light (2.34\u0026ndash;3.1 eV). The findings pave the way for further exploration of light upconversion regarding fundamental properties and device applications in two-dimensional semiconductors.\u003c/p\u003e","manuscriptTitle":"Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-04 07:03:37","doi":"10.21203/rs.3.rs-4643091/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"ca5e87ff-eff9-4359-b6a7-04f377afcbe2","owner":[],"postedDate":"September 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":35786298,"name":"Physical sciences/Physics/Optical physics/Nonlinear optics"},{"id":35786299,"name":"Physical sciences/Materials science/Nanoscale materials/Graphene/Optical properties and devices"},{"id":35786300,"name":"Physical sciences/Nanoscience and technology/Nanoscale materials/Graphene/Optical properties and devices"}],"tags":[],"updatedAt":"2024-09-04T07:03:38+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-04 07:03:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4643091","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4643091","identity":"rs-4643091","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}