Upconversion photoluminescence excitation reveals exciton–trion and exciton–biexciton coupling in hBN/WS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2/hBN van der Waals heterostructures

Monolayers of transition-metal dichalcogenides with direct band gap located at the binary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{-}/K_{+}$$\end{document}K-/K+ points of the Brillouin zone are promising materials for applications in opto- and spin-electronics due to strongly enhanced Coulomb interactions and specific spin-valley properties. They furthermore represent a unique platform to study electron–electron and electron–phonon interactions in diverse exciton complexes. Here, we demonstrate processes in which the neutral biexciton and two negative trions, namely the spin-triplet and spin-singlet trions, upconvert light into a bright intravalley exciton in an hBN-encapsulated WS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document}2 monolayer. We propose that the energy gains required in the polarized upconversion photoluminescence originate from different interactions including resonant optical phonons, a cooling of resident electrons and a non-local and an anisotropic electron–hole exchange, respectively. The temperature dependence (7–120 K) of the excitonic upconversion intensity obtained at excitation energies corresponding to the biexciton and trions provides insight into an increasing phonon population as well as a thermally enhanced electron scattering. Our study sheds new light on the understanding of excitonic spin and valley properties of van der Waals heterostructures and improves the understanding of photonic upconversion mechanisms in two-dimensional quantum materials.

Monolayers of transition-metal dichalcogenides with direct band gap located at the binary K − /K + points of the Brillouin zone are promising materials for applications in opto-and spin-electronics due to strongly enhanced Coulomb interactions and specific spin-valley properties. They furthermore represent a unique platform to study electron-electron and electron-phonon interactions in diverse exciton complexes. Here, we demonstrate processes in which the neutral biexciton and two negative trions, namely the spin-triplet and spin-singlet trions, upconvert light into a bright intravalley exciton in an hBN-encapsulated WS 2 monolayer. We propose that the energy gains required in the polarized upconversion photoluminescence originate from different interactions including resonant optical phonons, a cooling of resident electrons and a non-local and an anisotropic electron-hole exchange, respectively. The temperature dependence (7-120 K) of the excitonic upconversion intensity obtained at excitation energies corresponding to the biexciton and trions provides insight into an increasing phonon population as well as a thermally enhanced electron scattering. Our study sheds new light on the understanding of excitonic spin and valley properties of van der Waals heterostructures and improves the understanding of photonic upconversion mechanisms in two-dimensional quantum materials.
Two-dimensional (2D) materials have attracted considerable scientific attention in the last decade. In particular, transition-metal dichalcogenide (TMDC) monolayers, such as MoS 2 , MoSe 2 , WS 2 and WSe 2 , have emerged as a semiconducting alternative to the zero-band-gap graphene. The atomically thin TMDCs possess direct band gaps in the visible and near-infrared ranges at the K − and K + points of the Brillouin zone 1 . The two-dimensional confinement of charge carriers in TMDC monolayers leads to a reduced dielectric screening of the Coulomb interaction and a formation of excitons with binding energies of hundreds of meV 1,2 . Due to a strong spin-orbit coupling in the TMDC monolayers and a resulting valley-contrasting spin splitting of the energy gap at the K − /K + points, the electrons and holes possess both the spin and valley degree of freedom 3 . Thus, the TMDCs exhibit unique magneto-optical and opto-electronic properties which are very promising for applications in spin-and valleytronics 2,4,5 .
In addition to neutral excitons, a manifold of exciton complexes may be formed with binding energies of tens of meV [6][7][8] ; however, their identification in optical spectra was beyond the reach of simple structures exfoliated directly on standard SiO 2 /Si substrates 9 . Recent progress in elaborating high-quality van der Waals (vdW) heterostructures based on hBN-encapsulated TMDC monolayers allows for observing the subtle optical properties of the exciton complexes thus offering the exploration of many-body effects including electron-electron and electron-phonon interactions [10][11][12][13][14][15][16][17] . For W-based vdW structures, electron-electron interactions manifest themselves in a trion photoluminescence (PL) line splitting into an inter-valley triplet and intra-valley singlet whose energies  6,7,18 . Alternatively, the electron-electron coupling may yield the observation of the biexciton fine structure 19 . Instead, electron-phonon interactions give rise to a coupling between the ground and excited states of the neutral exciton realized by an exchange of phonons in a Raman scattering process 20 . Moreover, photonic upconversion (UPC) is a highly relevant phenomenon of light-matter interaction which not only is studied in fundamental sciences like physics and chemistry, but also finds application in fluorescence UPC in optical fibers 21,22 . The optical UPC is a fundamental light-matter interaction, an anti-Stokes-like process, in which an absorbed photon receives energy from the environment and is re-emitted at an energy higher than the excitation energy. Different mechanisms are known for describing UPC in different material systems; however, the mechanisms of exciton UPC in particularly 2D quantum materials are not well understood 23 . In that context, an open question is related to the exciton emission upconverted from three-or four particle states which are addressed in the transparency window of the TMDC monolayer. Additionally, hitherto, only in WS 2 monolayers without encapsulating hBN layers, excitonic UPC processes were studied 11,14 . In the current manuscript, we demonstrate the UPC of the exciton emission, for the first time, in hBNencapsulated WS 2 monolayers which are characterized by narrow spectral properties (about 2-4 meV) compared to that of uncapped monolayers or monolayers placed on SiO 2 . This spectral line narrowing allows us to unambiguously reveal the nature of the upconverting states and mechanisms. For resonantly addressing the coupling between different exciton complexes in the hBN-encapsulated WS 2 monolayer with low electron doping, we tune the laser excitation energy below the neutral exciton. This UPC photoluminescence excitation (PLE) measured at cryogenic temperatures reveals emission of the neutral intravalley exciton X upconverted from the neutral biexciton (XX 0 ) as well as the spin-triplet (T T ) and spin-singlet (T S ) trions. While the exciton emission upconverted from the trions is mainly based on spin-conserving electron-phonon and electron-electron scattering, the biexciton-mediated UPC is attributed to a non-local electron-hole exchange and an anisotropic (flip-stop) interaction. Furthermore, we evaluate the UPC dependence on changes in the temperature and the polarization degree of the exciting laser light. The polarization-resolved experiments indicate that the UPC PL is more efficient, for resonant excitation of the K + valley. Our study enhances the understanding of fundamental upconversion processes in vdW heterostructures and contributes to their application as opto-electronic newgeneration devices.

Results
Photoluminescence and reflectivity of WS 2 /hBN and hBN/WS 2 /hBN heterostructures.  and (c) the corresponding spectra of an hBN-encapsulated WS 2 monolayer with a d = 15-nm-thick (s 2 ) and, respectively, d = 240-nm-thick (s 3 ) hBN bottom-layer are presented. The PL spectra are excited non-resonantly with laser light of 2.33 eV energy. For all structures, we observe the PL lines of the neutral exciton X and the triplet T T and singlet T S trion, as reported in previous publications on WS 2 monolayers 7,18,24 . Since the exciton energy E X changes from flake to flake between 2.058 and 2.080 eV, the energy scale of each spectrum is referred to the X energy so that the energy difference E − E X is shown. The PL spectra in Fig. 1a-c demonstrate that the emission intensity of the X line differs for the samples s 1 , s 2 , and s 3 . It is lowest for the uncapped WS 2 /hBN structure (s 1 ) and increases for the hBN-encapsulated W 2 monolayers gradually with the hBN bottom-layer thickness. This indicates a decreasing electron density in the structures s 1 , s 2 , and s 3 , which in turn is consistent with a decreasing exciton-trion energy splitting in the respective samples.
As depicted in Fig. 1a, both trions T T and T S in the sample s 1 are red-shifted with respect to X by 35 meV and 41 meV, respectively. In s 2 and s 3 these values are reduced relatively by 3 meV and about 5 meV, respectively. The comparison of the exciton-trion peak separation with results recently presented for hBN/WS 2 /hBN heterostructures 24 allows us to assume that the electron concentration in s 1 and s 2 is higher than in s 3 , in which it ranges about (1-1.3) ×10 11 cm −2 being closely to a charge neutrality. Also, the appearance of the neutral biexciton XX 0 about 18 meV below X in the PL spectra 25 attributes the lowest electron density to the sample s 3 . Similar conclusions can be drawn from the complementary RC spectra. The neutral exciton resonance is dominant for all structures; however, as the electron concentration increases, for s 2 and s 3 , the trion resonances start to emerge in the RC spectra. The significantly higher electron doping in uncapped WS 2 /hBN structures in comparison to hBN-encapsulated (isolated) monolayers may result from laser induced doping effects 7 . Also, defects randomly distributed in the monolayer may act as donors or acceptors leading to a significant p-or n-doping 26 .
It is worthwhile to emphasize that vdW heterostructures assembled from an hBN-encapsulated WS 2 monolayer with a relatively low electron doping (close to charge neutrality) allow for observing subtle optical properties of exciton complexes. Hence, they offer the exploration of many-body effects including electron-electron and electron-phonon interactions. Our experiments on exciton upconversion thus focus on sample s 3 .
Upconverted exciton photoluminescence of hBN/WS 2 /hBN heterostructure. The regular and upconverted PL of the hBN/WS 2 /hBN vdW heterostructure exhibiting the lowest electron doping (s 3 ) recorded at 7 K is demonstrated in Fig. 2. The spectrum shown in Fig. 2a shows the PL lines of different excitonic complexes relative to the X line. The respective energy difference E − E X is indicated by the x-axis.
The UPC PL is excited resonantly by scanning the laser energy from the low-energy flank of the T S peak to the high-energy flank of the XX 0 peak; these limits of the excitation energy E exc are marked by the red arrows in Fig. 2a  For the exciton emission upconverted from the trion states, we propose the following spin-conserving scattering processes, where we consider a σ + polarized excitation and detection. Initially, for the intravalley singlet trion T S , a spin-down resident electron is at the K − valley. After creating a virtual exciton within the band gap at the K + valley, the spin-up photo-electron is scattered by coupling with the resident electron to the energetically lowest subband at the K − valley, as shown in Fig. 3. The resident electron is in turn scattered to the K + valley under spin conservation. This second stage could also be described in terms of a cooling of the resident electron gas allowing for the electronic scattering. The third stage of the UPC mechanism is established by an electron-phonon coupling shifting the photo-electron to the spin-up subband at the K + valley yielding a carrier configuration similar to that of the intra-valley spin-singlet trion. Finally, the photo-electron recombines with the hole giving rise to σ + polarized bright exciton emission.
The UPC of the exciton emission based on addressing the intervalley triplet trion T T is likely based on the interaction with a single phonon. The A ′ 1 phonon energy fits well with the energy gain of 29.5 meV 11,14,17 . In this resonant phonon scattering process the spin as well as the valley momentum are conserved. At the final stage, one resident electron remains at the spin-up subband of the K − valley, while the spin-up photo-electron as well as the hole at the K + valley recombine resulting in the bright exciton emission.
Interestingly, it has been recently discussed by Ayari et al. 17 that the contribution of different phonon modes to UPC processes in TMDCs strongly depends on the temperature, dielectric environment and carrier density. The UPC rate of the homopolar mode A ′ 1 is independent of the dielectric environment, while for the longitudinal optical phonon E ′ the strength of the Fröhlich interaction depends on the polarization properties of the encapsulating materials 17,27,28 . The theoretical analysis has also shown 17 that UPC rates due to E ′ and A ′ 1 phonons become comparable, for a large screening length in hBN-encapsulated W-based monolayers.
Considering the neutral biexciton as real intermediate state for the upconverted X emission, we propose the initial excitation of two virtual excitons at the K + valley; see Fig. 3. Due to a non-local exchange interaction in accordance with Ref. 29 , the electrons and holes are scattered so that an electron-hole pair is located both at the K + (with spin-up configuration) and K − valley (with spin-down alignment). In addition to that non-local exchange, we consider an anisotropic electron-hole exchange interaction which changes the electron spin while keeping the hole spin unchanged 30 . This anisotropic flip-stop-like exchange interaction is caused by spatially shifted probability densities of the electron and hole at the K − valley. When the centers of their in-plane localization areas do not coincide, the symmetry of this carrier complex is lowered and, in turn, a projection of the angular momentum on the axis defined by the vector linking both centers is not preserved. This symmetry reduction allows for flipping the spin of the electron while leaving that of the hole unchanged. Consequently, a spin-forbidden exciton is given at the K − valley, as illustrated in Fig. 3. The combination of the bright (spin-allowed) and dark (spin-forbidden) excitons residing at the K + and K − valleys, respectively 19,31 , represents the XX 0 . Finally, from this biexcitonic state the electron-hole pair at the K + valley annihilates and causes the experimentally observed enhancement of the exciton emission.
Temperature and polarization dependence of the regular and upconverted photoluminescence. The temperature-dependent UPC PLE shall provide insight into an increasing phonon population as well as a thermally enhanced electron scattering. In Fig. 4 the PL spectra, the UPC PLE spectra and the integrated UPC PL of the exciton are shown for the temperatures 60 K, 90 K, and 120 K. For scanning the laser excitation energy between the low-energy flank of the T S PL line and the high-energy flank of the T T PL line and detecting the response of the X PL, as marked by the red arrows and dashed rectangle in the panels (a), (b), and (c), we obtain UPC PLE spectra which are presented in the panels (d), (e), and (f). The integrated UPC  Figure 5a summarizes these results showing the temperature dependence of the integrated PL intensity of X, XX 0 , T T , and T S , while in Fig. 5b the integrated PL upconverted from the biexciton and trions to the neutral exciton is demonstrated. As seen in Fig. 5a the integrated X PL intensity (black points) is enhanced with increasing temperature, whereas the integrated XX 0 emission (blue points) remains nearly constant. The integrated PL intensity of T T (green points) and T S (pink points) also increases for rising T, whereby the T S line is dominant up to 90 K. At 120 K the T S PL weakens and both trion features are broadened. The UPC PL intensities integrated for all initial excitonic states are clearly enhanced with increasing temperature; see Fig. 5b. The most intense upconverted exciton PL I UPC T T is obtained for exciting the triplet trion T T , also in comparison to the upconverted PL I UPC T S for T S excitation. The latter is presented in the inset of  The intensities of the regular and upconverted exciton PL in hBN-encapsulated WS 2 exhibit a similar temperature-dependent behavior. This is contradictory to the behavior observed in uncapped WS 2 /hBN monolayers 14 , where the UPC PL of the exciton becomes intensified at 120 K and even exceeds the regular PL which practically remains constant with increasing temperature. The thermally induced PL enhancement in the vdW heterostructure studied may be caused by a more efficient non-radiative relaxation of the carriers to the band minima, a thermally induced brightening of dark states and a dissociation of carriers from defects contributing to the excitonic emission. The temperature-dependent growth observed in the exciton UPC efficiency is governed by an increasing phonon population leading to more probable phonon-mediated scattering of the electrons 11,14 . Moreover, at high temperatures the electron-electron scattering within the UPC from the singlet trion is more likely to take place. This thermally more efficient scattering channel explains the enhanced contribution of I UPC T S to α with rising temperature.
Finally, we elucidate the circular polarization properties of the regular and upconverted PL as well as Raman scattering lines performing quasi-resonant and circularly polarized PL and UPC PL experiments. Figure 6a shows PL spectra excited at 2.096 eV and measured at 7 K, for co-and cross-circular polarized configurations. To estimate the circular polarization or, respectively, helicity preservation in the trion PL with respect to the polarization of the exciting laser light, we determine the polarization degree by P deg = (I σ + σ + − I σ + σ − )/(I σ + σ + + I σ + σ − ) , where σ + σ + and σ + σ − indicate the co-circularly and cross-circularly polarized configurations, respectively. The PL of the triplet trion exhibits a polarization degree of almost 59% , while, for the T S line, we obtain P deg ≈ 22% . This is in line with previous results obtained for a WS 2 monolayer 18,32 . However, it is worth noting that the circular polarization degree of trions varies in different monolayers, since it results from the interplay between different effects, such as scattering processes (radiative and non-radiative types), photo-doping, and free carrier redistribution among the two K-valleys 32 . High positive values of the circular polarization degree of the triplet trion are associated with an efficient spin-valley pumping of the resident electrons in a WS 2 monolayer using circularly polarized laser light 32 .
In the PL spectra we also distinguish Raman scattering features in the energy range of 2.044-2.062 eV. They are presented in Fig. 6b and are attributed to first-and second-order scattering processes including the A ′ , E ′ , E ′′ modes and 2LA(M) and 2ZA(M) bands, respectively 33 . Figure 6c depicts circularly polarized UPC PL spectra with a resonance at an energy gain of about 28 meV; the excitation energy was tuned from the T S peak to the high-energy flank of the T T peak, as marked by the red arrows in Fig. 6a. The resonance coincides with the spectral position of the intervalley triplet trion T T ; compare the upper energy scale in Fig. 6a. The exciton PL upconverted from T T is slightly co-polarized ( P deg = 12% ) with the laser light polarization. The high intensities in the co-polarization configuration imply that the UPC is more efficient for resonantly addressing the K + valley. Moreover, the circular polarization degree of the upconverted X emission is decreasing with increasing energy gain from 18% for E = 24 meV to 11% for 37 meV, as seen in Fig. 6d. This falling trend, for energetically departing from the trion resonances, corresponds to an increasing www.nature.com/scientificreports/ probability of scattering processes which change the valley momentum of the carriers. Besides that, P deg for the UPC PL is slightly lower than values ( 21% ) obtained for regular PL under nearly resonant excitation 34 . This discrepancy is likely caused by a possible scattering of bright excitons into momentum-dark states due to the interaction with K-point phonons or electrons. It is also worthwhile to mention that the preservation of the exciton valley polarization, for T T excitation, is consistent with the polarization properties of the A ′ 1 phonon 11 ; see also Fig. 6b.

Discussion
We present temperature-dependent and polarization-resolved PL of the bright neutral exciton upconverted from singlet and triplet negative trions and the neutral biexciton, for a hBN-encapsulated WS 2 monolayer possessing a relatively low electron doping in the range of (1-1.3) ×10 11 cm −2 . The resonant tuning of the excitation energy through the XX 0 , T T and T S states, lying below the neutral exciton, leads to characteristic energy gains of 18.0, 29.5 and 36.0 meV, respectively. These energy gains in the UPC processes are attributed to interactions with resonant optical phonons and, respectively, to a cooling of resident electrons. In the exciton emission upconverted from the trions, spin-conserving electron-phonon and electron-electron scatterings are involved, while the biexciton-mediated UPC is related to a non-local electron-hole exchange followed by an anisotropic electron-hole interaction. The temperature dependence of the upconverted exciton PL intensity demonstrates significant enhancements up to 120 K. They underline both an increasing phonon population giving rise to a high phonon-mediated scattering rate of the electrons as well as a more efficient electron-electron scattering within the UPC involving the singlet trion. Both trions and the neutral biexciton act as real states in the particularly electron-and/or phonon-mediated UPC processes whose circular polarization properties imply that the UPC occurs more efficiently at the K + valley, as the UPC PL has predominantly the same helicity as the exciting laser light. Our results extend the current discussion on exciton-trion and exciton-biexciton couplings in WS 2 monolayers as well as the understanding of optical UPC mechanisms in 2D materials.

Methods
Bulk WS 2 . The WS 2 crystals were grown by the chemical vapor transport (CVT) technique. Prior to the crystal growth, the powdered compounds were prepared from the elements (W: 99.99% , S: 99.999% ) by reaction at 1000 • C, for 10 days in quartz ampules. The mixture was slowly heated to 1000 • C. The chemical transport was achieved with I 2 as a transport agent in the amount of about 5 mg/cm 3 . The growth temperature was changed from 1030 to 980 • C with a temperature gradient of 3 • C/cm and a growth time of 20 days. The crystals had the shape of thin layered plates with thicknesses and surface areas ranging from 20 to 1000 µ m and 20 to 100 mm 2 , respectively.
Monolayer WS 2 . We prepared hBN-encapsulated WS 2 and uncapped WS 2 /hBN heterostructures using high-purity hexagonal boron nitride (hBN) and a target Si substrate with 300-nm-thin SiO 2 . The WS 2 monolayers were mechanically exfoliated from the aforedescribed bulk crystals. For this purpose, the deterministic all-dry stamping method was applied 35 . The WS 2 monolayer and the hBN crystals were first exfoliated on a flexible polydimethylsiloxane gel-film stamp which was rigidly attached to a glass slide. The thicknesses of the hBN flakes were ∼ 15 nm and ∼ 240 nm, for the bottom layer, and up to ∼ 5 nm, for the top layer. During the transfer process the substrate and the stamp were inspected using an optical microscope equipped with an xyz stage. The application of a long-working distance objective enables us to locate and deterministically transfer selected flakes to the substrate by carefully bringing the stamp in contact with the substrate. After each transfer step, the samples were heated to ∼ 180 • C in air for 20 minutes. After adding the last layer to the stacked samples, an annealing at ∼ 200 • C was performed in air for 2 h. Figure 7a presents an optical microscope contrast image of the hBN/WS 2 /hBN/SiO 2 /Si heterostructure with the thickness of the hBN bottom-layer d = 240 nm. The monolayer character of the WS 2 flake was confirmed by PL and Raman scattering experiments performed at room temperature under ambient conditions. Figure 7b shows a PL intensity map of the WS 2 monolayer recorded at the neutral exciton energy of 1.995 eV. A typical PL spectrum including the exciton line is demonstrated in Fig. 7c. Linearly polarized Raman scattering spectra depicted in Fig. 7d clearly identify the E ′ and A ′ optical phonons located at 357.5 cm −1 (44 meV) and 418 cm −1 (52 meV), respectively. Experimental setup. The samples were mounted on the cold finger of a vibration-isolated closed-circle cryostat which allowed for temperature variations between 7 and 300 K. The PL was excited by the second harmonic (532 nm, 2.33 eV) of a continuous-wave single-mode Nd:YAG laser. The UPC PLE was excited by a continuous-wave dye laser equipped with DCM whose emission was tuned in the range from 602 (2.06 eV) to 650 (1.91 eV). The laser beam was focused on the sample under normal incidence using a long-working distance microscope objective with 50× magnification. The diameter of the excitation spot was about 1 µ m. The emission was collected by the same microscope objective, was dispersed by a monochromator with 0.5 m focal length and 600 lines/mm grating and was detected by a Peltier-cooled charged couple device Si-camera. The Raman spectra were measured in the backscattering geometry using either 1800 or 600 lines/mm gratings. The impact of elastically scattered light on the spectra was reduced by a set of spectrally appropriate edge filters.

Data availability
The data sets used and/or analyzed during the current study are available from the corresponding author on reasonable request.