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Joanna Jadczak, Joerg Debus, Justyna Olejnik, Ching-Hwa Ho, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Leszek Bryja

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[Biexciton and Singlet Trion Upconvert Exciton Photoluminescence in a MoSe<sub>2</sub> Monolayer Supported by Acoustic and Optical K-Valley Phonons](https://mdr.nims.go.jp/datasets/ec96dda7-59e0-4857-b013-c42c542d8e82)

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Biexciton and Singlet Trion Upconvert Exciton Photoluminescence in a MoSe2 Monolayer Supported by Acoustic and Optical K-Valley PhononsBiexciton and Singlet Trion Upconvert Exciton Photoluminescencein a MoSe2 Monolayer Supported by Acoustic and Optical K‑ValleyPhononsJoanna Jadczak,* Joerg Debus, Justyna Olejnik, Ching-Hwa Ho, Kenji Watanabe, Takashi Taniguchi,and Leszek BryjaCite This: J. Phys. Chem. Lett. 2023, 14, 8702−8708 Read OnlineACCESS Metrics & More Article RecommendationsABSTRACT: Transition metal dichalcogenide monolayers representunique platforms for studying both electronic and phononic interactionsas well as intra- and intervalley exciton complexes. Here, we investigatethe upconversion of exciton photoluminescence in MoSe2 monolayers.Within the nominal transparency window of MoSe2 the exciton emissionis enhanced for resonantly addressing the spin-singlet negative trion andneutral biexciton at a few tens of meV below the neutral excitontransition. We identify that the A′1 optical phonon at the K valleyprovides the energy gain in the upconversion process at the trionresonance, while ZA(K) phonons with their spin- and valley-switchingproperties support the biexciton driven upconversion of the excitonemission. Interestingly, the latter upconversion process yields unpolarized exciton photoluminescence, while the former also leads tocircularly polarized emission. Our study highlights high-order exciton complexes interacting with optical and acoustic K-valleyphonons and upconverting light into the bright exciton.Transition metal dichalcogenide (TMDC) monolayers aredirect band gap semiconductors with unique optical andspin-valley properties.1 Their two-dimensional (2D) natureand the reduced dielectric screening of the Coulombinteraction allow for the formation of excitons with a bindingenergy of hundreds of meV2,3 and high-order excitoniccomplexes, such as trions and biexcitons with binding energiesof tens of meV.4−12 Moreover, due to the strong spin−orbitcoupling in TMDC monolayers and the resulting valley-contrasting spin splitting at the K valleys, the excitoniccomplexes possess both the spin as well as valley degree offreedom.1In optically darkish systems, such as WS2 and WSe2monolayers, the electric-dipole forbidden (optically dark)exciton state is positioned at lower energy than the opticallyactive exciton state. On the contrary, in MoSe2 monolayers thebright exciton state is at the lowest energy. These levelhierarchies as well as exciton−phonon interactions werestudied due to the progress in elaborating high-quality hBN-encapsulated TMDC monolayers.13 In this context, upconver-sion photoluminescence (PL) spectroscopy recently providedthorough insights into exciton−exciton and exciton−phononinteractions and was successfully employed to reveal thecoupling between various excitonic complexes in the opticallydarkish hBN-encapsulated WSe2 and WS2 monolayers. Inparticular, upconversion of light from dark excitons, trions, andbiexcitons to bright excitons was observed.14−16In the n-type MoSe2 monolayer, the lowest energy trionconfiguration is the negative intervalley spin-singlet state (TS).Interestingly, the TS state typically dominates the PL spectra inMoSe2 monolayers at low temperatures but is dramaticallyweakened with increasing temperature. In contrast to that, inMo(SySe1−y)2 alloys with a sulfur mole content up to y = 0.5,the trion emission is also robust at elevated temperatures.8This observation was attributed to a strong increase in theexciton−trion coupling strength and to a rising 2D electron gasconcentration caused by an increasing sulfur content.8 Theenhanced exciton−trion coupling was realized by tuningphonon energies to the trion binding energy in theMo(SySe1−y)2 alloys. Also, the coherent and incoherent natureof the exciton−trion coupling and relevant time scales inMoSe2 monolayers were revealed by optical 2D coherentspectroscopy; it demonstrated an efficient energy transfer viaReceived: July 17, 2023Accepted: September 18, 2023Published: September 21, 2023Letterpubs.acs.org/JPCL© 2023 The Authors. Published byAmerican Chemical Society8702https://doi.org/10.1021/acs.jpclett.3c01982J. Phys. Chem. Lett. 2023, 14, 8702−8708This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on October 6, 2023 at 02:26:08 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Joanna+Jadczak"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Joerg+Debus"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Justyna+Olejnik"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ching-Hwa+Ho"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Leszek+Bryja"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Leszek+Bryja"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.jpclett.3c01982&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/jpclcd/14/39?ref=pdfhttps://pubs.acs.org/toc/jpclcd/14/39?ref=pdfhttps://pubs.acs.org/toc/jpclcd/14/39?ref=pdfhttps://pubs.acs.org/toc/jpclcd/14/39?ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.jpclett.3c01982?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/JPCL?ref=pdfhttps://pubs.acs.org/JPCL?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/phonon-assisted exciton-to-trion downconversion within 2−3ps and trion-to-exciton upconversion in 8 ps.17 The exciton−trion interaction in TMDC monolayers may be alternativelyprobed in upconversion (UPC) PL experiments.14,18 Theexcess energy required for the UPC process may be taken fromphonons or resident electrons in the monolayer.15 Hence, theUPC PL provides information on both the energy spectra ofthe TMDCs as well as the scattering mechanism related toexciton−exciton, exciton−electron, and exciton−phonon in-teractions.Here, we probe the upconversion photoluminescence in anoptically bright hBN-encapsulated MoSe2 monolayer system.UPC PL excitation reveals two pronounced resonances belowthe neutral 1s A-exciton (X). The resonance detected at anenergy of about 25 meV below X coincides with the PL peakand binding energy of the singlet trion TS. The secondresonance at −18 meV with respect to the exciton transition isattributed to the neutral biexciton (XX0), which was previouslyidentified in a MoSe2 monolayer using polarization-resolved2D coherent spectroscopy.10 We propose that the energy gainsrequired in the UPC of the exciton PL originate from differentinteractions, including optical or acoustic phonons at the Kvalley. The upconversion of light from TS and XX0 into X isobserved only for samples with a relatively weak electronconcentration and is enhanced at elevated temperatures. Wealso evaluate the UPC as a function of the incident laser powerand demonstrate specific polarization characteristics of theupconverted exciton emission. In contrast to tungsten-basedstructures, probing of upconverted exciton PL in MoSe2requires a low number of resident electrons and is realizedonly in hBN-encapsulated samples. Moreover, as biexcitons arechallenging to be identified unambiguously using linear opticalspectroscopy methods and were detected only in WS2 andWSe2 monolayers so far in regular PL experiments,upconversion is an alternative route to address, for example,biexcitons in TMDC monolayers, particularly in MoSe2. UPCfurther provides information on the energies of bound carriercomplexes in TMDCs and scattering processes related toexciton−electron and exciton−phonon interactions.In Figure 1a, intensity normalized PL spectra are shown foran uncapped MoSe2 monolayer placed on an hBN substrate(MoSe2/hBN) and for an hBN-encapsulated MoSe2 mono-layer (hBN/MoSe2/hBN). The spectra were measured at 7 Kand were excited nonresonantly by laser light having an energyof 2.33 eV. Since the energy EX of the exciton PL peak changesfrom flake to flake between 1.627 and 1.638 eV, the energyscale of each spectrum is referred to the exciton energy;accordingly, the energy difference E − EX is chosen for thehorizontal axis. The predominant peak which is about 26 or 30meV below the exciton PL peak is attributed to the spin-singletnegative trion TS whose binding energy lies in this energyrange.5 While the neutral exciton recombination in MoSe2yields a symmetric peak, the trion PL is asymmetric with abroad low-energy flank which is attributed to an electron recoileffect for trions.19 The doping level of the samples could beestimated by the intensities and relative energy positionsΔEX−T of the exciton and trion PL peaks. On the one hand, theX emission intensity in the MoSe2/hBN structure issignificantly lower than that in the hBN/MoSe2/hBN sampleand, on the other hand, ΔEX−T amounts to 30 and 26 meV,respectively. These differences indicate a higher electrondensity in the uncapped structure. On the basis of theexciton−trion energy splittings ΔEX−T and gate-dependentoptical characteristics of MoSe2,20 we estimate the electrondensity to be about 2 × 1010 cm−2 in the encapsulatedmonolayer, whereas in the uncapped monolayer it is in theorder of 1012 cm−2. Additionally, in Figure 1b we compare thereflectance contrast (RC) spectra of both samples excited bywhite light. As clearly seen, only for MoSe2/hBN a weaknegative trion resonance is resolved, which underlines thepresence of a significant electron doping.20 For hBN/MoSe2/hBN, the exciton resonance is sharp and intense due to the lowelectron doping level and the encapsulation, which protects themonolayer from charge transfers and local electric fieldfluctuations.We now focus on the upconversion of the neutral exciton PLin the MoSe2 monolayer, for excitation energies below theneutral exciton in the nominal MoSe2 transparency range, anddemonstrate its dependence on variations of the temperature,laser power, and polarization. In the following, we present thedata for the hBN/MoSe2/hBN heterostructure. For theMoSe2/hBN structure, we observed only negligibly weakupconverted X PL.The regular and upconverted PL of the hBN/MoSe2/hBNstructure recorded at 7 K is demonstrated in Figure 2. InFigure 2a, the PL spectrum and the energy range that isresonantly excited for the UPC PL are shown. The lattermarked by vertical arrows goes from about −15 meV to thelow-energy flank of the trion PL at about −29 meV. For a UPCphotoluminescence excitation (PLE) spectrum, the neutralexciton PL is monitored during the variation of the laserexcitation energy Eexc. The color map in Figure 2b displays theUPC PLE spectra as a function of the excitation energydetuned from EX, while the integrated exciton UPC PL IX,UPCis shown in Figure 2c. The UPC energy gain is given by theenergy difference |Eexc − EX|. Both the color map and theintegrated exciton UPC PL clearly exhibit a prominentresonance at an energy gain of about 25 meV. Thiscorresponds to the binding energy of the spin-singlet negativetrion TS. A second weak resonance is observed at an energygain of about 18 meV. This enhancement of the exciton PLFigure 1. (a) PL spectra of MoSe2/hBN and hBN/MoSe2/hBN vander Waals heterostructures measured at T = 7 K. The energy splittingbetween the exciton and singlet trion PL lines is marked by ahorizontal arrow. (b) RC spectra for both structures measured at 7 K.The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.3c01982J. Phys. Chem. Lett. 2023, 14, 8702−87088703https://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig1&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.3c01982?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asmay originate from the UPC process involving the neutralbiexciton XX0 whose binding energy lies in this range.10In order to gain further insight into the exciton emissionupconverted from the trion TS and biexciton XX0 we performcomparative temperature-dependent PL and UPC PLEmeasurements. In Figures 3a−f the PL spectra, the UPCPLE spectra, and the integrated UPC PL measured at 40 and80 K are presented. At these temperatures, we tune theexcitation energy through the biexciton and singlet trionresonances of the MoSe2 monolayer, as marked by the redarrows in the PL spectra of panels a and b, and detect theresponse of the X emission. The resulting UPC PLE spectraare shown in panels c and d, and the integrated UPC PL IX,UPCof the X is presented in panels e and f. Additionally, Figure 3gprovides an overview about the integrated intensities of the Xand TS PL peaks (black symbols) and the integrated X PLupconverted from the XX0 and TS states (red symbols) as afunction of temperature from 7 to 80 K. Up to 50 K, the PLintensity of the negative trion exceeds that of the exciton, whileboth lines become weaker with increasing temperature. Bycomparison, the upconverted X PL is enhanced with risingtemperature: IX,UPC is maximum at about 50 K, for resonantlyexciting TS, and is reduced by further increasing thetemperature. For exciting XX0, IX,UPC exhibits a maximum atabout 60 K. This thermal behavior differs from that observedin WS2 monolayers,16,18 where the upconverted PL of theexciton becomes significantly intensified with rising temper-ature and even exceeds the regular PL intensity.We further study the dependence of the upconverted X PLon the incident laser power P. It will provide insight into thecharacter of the UPC resonances, in addition to the priorassignment of the resonances according to the binding energiesof the negative trion and neutral biexciton. Typical UPC PLEspectra recorded for 10, 6, and 4 mW are depicted in Figure4a,b,c, respectively. The evolution of the integrated UPCexciton PL as a function of P, for resonantly addressing thenegative trion and biexciton, is given in panel d using a double-logarithmic presentation. IX,UPC depends nonlinearly on thelaser power which is evaluated from the slopes α of 2.08 and1.66, for exciting the XX0 and TS resonances, respectively. Thepractically quadratic power dependence (αXX0 = 2.08) of IX,UPC,for Eexc − EX = −18 meV, characterizes a process in which abiexciton is involved. The power-dependent evolution of the XPL intensity upconverted from TS is described by αTdS= 1.66,which reflects the power-dependent slope of the trion regularPL intensity.21Finally, we elucidate the polarization properties of theexciton PL upconverted from the negative trion and neutralbiexciton states, yielding additional details on the UPCmechanisms, which are discussed in the following section. InFigure 4e the UPC PLE spectra are demonstrated for linearlypolarized excitation and unpolarized detection, while in Figure4f,g the incident light and the emission are cocircularly andcross-circularly polarized, respectively. Figure 4h displays IX,UPCas a function of the polarization configurations for excitationenergies ranging from −28 to −14 meV in proximity to the X.The upconverted X PL is predominantly unpolarized, forFigure 2. (a) PL spectrum of the hBN/MoSe2/hBN structuredetected at 7 K, for nonresonant laser excitation at 2.33 eV. (b) Colormap of the UPC PLE spectra with a detection range of ±6 meV atexciton resonance EX; T = 7 K. (c) Integrated UPC PL of the neutralexciton for excitation energies ranging from −29 to about −15 meVwith respect to the X resonance.Figure 3. PL spectra of the hBN-encapsulated MoSe2 monolayer recorded at (a) 40 and (b) 80 K. Color maps of the UPC PLE spectra for varyingenergy gain measured at (c) 40 and (d) 80 K. (e and f) Integrated UPC PL of X as a function of the energy gain given at 40 and 80 K, respectively.(g) Temperature dependence of (left scale) integrated PL intensities and (right scale) IX,UPC excited at TS and XX0.The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.3c01982J. Phys. Chem. Lett. 2023, 14, 8702−87088704https://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig3&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.3c01982?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-astuning the excitation energy to the biexciton resonance, whilein the circularly polarized spectra IX,UPC is negligibly weak. Bycomparison, the exciton PL upconverted from the negativetrion TS is slightly polarized (+10%) with regard to the laserlight polarization, while its intensity is also high in theunpolarized configuration. It is worthwhile to mention thatIX,UPC becomes significantly polarized (+50%) for reducing theenergy gain to 14 meV. It is consistent with results obtained forthe regular exciton PL whose circular polarization is rather lowcompared to other TMDCs22 and is enhanced for approachingthe excitation energy of the A-exciton resonance.23,24The experimental observations performed in the nominaltransparency window of MoSe2 are summarized in thefollowing: (a) only the hBN-encapsulated MoSe2 monolayerexhibits pronounced UPC PL of the neutral exciton (1s A-exciton); (b) the X PL is enhanced for resonantly addressingthe spin-singlet negative trion at an energy gain of about 25meV and the neutral biexciton at about 18 meV; (c) the UPCPL possesses intensity maxima at elevated temperatures; (d)the UPC PL intensity is scaled nonlinearly with the incidentlaser power; and (e) the UPC PL of the exciton is clearlyunpolarized at the XX0 resonance and exhibits a slightlypositive circular polarization at the TS resonance.In contrast to WSe2 and WS2 monolayers in which thelowest exciton state is optically forbidden (spin-dark)25 at theK valleys, MoSe2 monolayers are characterized by spin-allowedFigure 4. UPC PLE spectra as color maps obtained at (a) 10 mW, (b) 6 mW, and (c) 4 mW laser power. (d) The integrated UPC PL of theexciton is shown as a function of the laser power, for addressing the XX0 (red circles) and TS (black circles). (e−g) Unpolarized and circular-polarization resolved UPC PLE spectra measured at 7 K and P = 8 mW. The color scale at the top right belongs to panel e; the bottom-right scalerefers to panels f and g. (h) Integrated UPC PL of X as a function of the energy gain, for the different polarization configurations. The black coloreddata points represent the unpolarized case, while the red (blue) symbols display the copolarized (cross-polarized) configuration.Figure 5. Schematic presentation of the mechanisms for upconverting the exciton PL by the (a) neutral biexciton and (b) spin-singlet trion. EachUPC process is sequentially sketched by going from the left to the right side. The single-particle picture is chosen where an electron (a hole) isillustrated by a blue (green) sphere. Only the energetically lowest conduction subband and highest valence subband are shown.The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.3c01982J. Phys. Chem. Lett. 2023, 14, 8702−87088705https://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpclett.3c01982?fig=fig5&ref=pdfpubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.3c01982?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asneutral excitons as energetically lowest states at the K+ and K−valleys. The bright exciton at the K+ (K−) valley is excited byσ+ (σ−) circularly polarized light in accordance with a valleyindex of either +1 or −1. Here, the upconversion of the excitonemission is initiated by optically creating either the neutralbiexciton XX0 or the negative trion TS. The difference betweenthe neutral exciton energy and the incident laser light energycorresponds to the binding energy of the excitonic complexinvolved in the UPC process. An individual number ofinteractions is followed by the final exciton annihilation. Theoverall efficiency of the UPC is governed by the order of theprocess, whereby spin- and momentum-conserving scatteringor exchange interaction processes are favored.We first consider the exciton PL UPC involving the neutralbiexciton which is observed at an optical excitation energy ofabout ΔEXX0 = 18 meV below the X transition (correspondingto the XX0 binding energy) and in the presence of only a lownumber of resident electrons (close to the neutrality point).Moreover, the energy difference (energy gain) lies within therange of phonon energies, and the UPC is particularlypronounced at elevated temperatures. These aspects indicatethe significance of phonon contributions without a disturbingimpact of additional electrons (due to, e.g., exchangeinteraction). Additionally, the quadratic power dependence isalso characteristic for neutral biexcitons. Besides the specifictemperature dependence and low energy gain, the strongnonlinear power dependence rules out a potential two-photonabsorption with a real biexciton state and an Auger-likeprocess, as demonstrated by ref 26. As shown in Figure 5a, wethus propose that initially (1) a neutral biexciton with spin-upelectron and hole at the K+ and spin-down electron and hole atthe K− valley are excited, whereby the net angular momentumtransfer is zero, in agreement with the linearly polarizedincident light. Afterward, (2) each electron interacts with thezone-corner flexural acoustic ZA(K) phonon mode of aboutEZA = 17.5 meV (4.2 THz) energy.27 Hence, each electron isscattered to the opposite valley (K+ → K−, K+ → K−),28 underreversal of its spin so that in total the spin angular momentumis not changed and the crystal momentum is conserved. Inaccordance with the Elliot−Yafet mechanism the phonon inthe spin-flip process must possess an odd parity under mirror-symmetry operation.29 In contrast to the longitudinal andtransversal acoustic phonon modes, the ZA(K) phonon fulfillsthis criterion.27 The phonon absorption provides the energy2EZA to the carrier complex which is about twice the bindingenergy (2ΔEXX0). Therefore, we propose that after theelectron−phonon interaction, the electrons relax to theminimum of their conduction sub-bands, as sketched in theright scheme of Figure 5a. The electron−phonon interactionwith the subsequent electron relaxation adds dispersion to theresonance energy so that from about Eexc − EX = −20 meVuntil −16 meV the XX0 resonance is observed. Finally, (3)both excitons recombine, giving rise to emission which isunpolarized. Since the upconverted X PL is not observed inany circular polarization setting of the detection path, forlinearly polarized excitation, we conclude that the final statecomposed of two bright excitons residing at the K+ and K−valleys is a coherent intervalley (superposition) state.We take into account the neutral biexciton in MoSe2composed of two spin-allowed intravalley excitons residing atthe K+ and K− valley, respectively. This intervalley XX0configuration is, due to Pauli blocking, energetically favoredagainst an intravalley configuration in which a bright and darkexciton are both excited in the same valley.11For the exciton emission upconverted from the spin-singlettrion, we propose the following spin-conserving process. Asshown in Figure 5b, for σ+ polarized excitation and detection,(1) the TS state is excited with a spin-up electron and hole atthe K+ valley as well as a spin-down resident electron at the K−valley. (2) As only for low electron concentration the X PL isupconverted from TS, we propose that the spin-up photo-electron is scattered by the A′1 phonon to the energeticallylowest subband at the K+ valley. The A′1 optical phonon at theK valleys has an energy of about 25 meV (6 THz),27 whichwell fits to the TS binding energy. While the resident electronremains at the spin-down subband of the K− valley, the spin-upphotoelectron as well as the hole at the K+ valley recombine,resulting in σ+ polarized exciton emission. The X PLupconverted from the negative trion is both copolarized aswell as slightly cross-polarized. The cross-polarization may hintat a stimulated exciton (boson) scattering.26 Alternatively, dueto intervalley scattering of the hole including a spin reversal,23the recombination of the electron and hole at the K− valleyleads to σ− polarized exciton emission which also explains theemission in the cross-polarized configuration.The contribution of phonon modes to UPC processes inTMDCs strongly depends on temperature.18,30 Recenttheoretical calculations have shown that in MoSe2 theupconversion rate is significantly higher than that in WSe2.30It results in a stronger electron−phonon interaction and ashorter thermal average upconversion time, which is abouteight times faster in MoSe2 than in WSe2.30 Moreover, in aMoSe2 monolayer the thermal average upconversion timedecreases strongly with increasing temperature; at 60 K it isabout 10 times smaller than at 7 K.30 This thermal behaviorsupports the explanation of the temperature dependencesobserved in our experiments and the UPC mechanisms,including optical and zone-edge acoustic phonons. Thetemperature-dependent growth of the exciton UPC PL islikely governed by an increased phonon population, leading toa more probable phonon-mediated scattering of the electrons.By comparison, the thermally induced PL decrease in theMoSe2 monolayer may be caused by an intravalley scatteringwith acoustic phonons.31,32For an hBN-encapsulated MoSe2 monolayer with a relativelylow concentration of resident electrons (2 × 1010 cm−2), wehave demonstrated the upconversion of the 1s A-exciton PL bythe neutral biexciton and singlet trion, respectively. In thenominal transparency window of MoSe2 the X PL is observedfor resonantly addressing TS (XX0) at an energy of about 25meV (18 meV) below the neutral exciton resonance. Theupconverted X PL is enhanced nonlinearly with the incidentlaser power and also at elevated temperatures of 50−60 K. Thelatter is attributed to an increased phonon population givingrise to a high phonon-mediated scattering rate of the electrons.Additionally, the UPC PL of the exciton is unpolarized at theXX0 resonance and displays a slight circular polarization at theTS resonance. The mechanism of the exciton PL upconvertedby the neutral biexciton is attributed to the interaction of thephotocreated electrons at the K+ and K− valleys with zone-corner flexural acoustic ZA(K) phonons. They scatter theelectrons to opposite valleys under reversal of their spins.Finally, two bright excitons residing at the K+ and K− valleysrecombine leading to unpolarized emission at the neutralexciton energy. The UPC of the X PL via the spin-singletThe Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letterhttps://doi.org/10.1021/acs.jpclett.3c01982J. Phys. Chem. Lett. 2023, 14, 8702−87088706pubs.acs.org/JPCL?ref=pdfhttps://doi.org/10.1021/acs.jpclett.3c01982?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asnegative trion is assigned to a spin- and valley-conservingscattering process of the photocreated electron with the opticalA′1 phonon mode whose energy at the K valleys matches theenergy difference between the singlet trion and the neutralexciton.Our results extend the current discussion about interactionsof electrons with both optical and acoustic phonons at the Kvalleys and their role in the upconversion of exciton emissionin MoSe2 monolayers. We also provide further insights intoresonant exciton−trion and exciton−biexciton couplings foroptically exciting a 2D material within its nominal transparencyrange.■ MATERIALS AND METHODSMoSe2 crystals were grown by a chemical vapor transporttechnique. Prior to the crystal growth, the powderedcompounds were prepared from the elements Mo (purity:99.99%) and Se (99.999%) by reaction at 1000 °C for 10 daysin quartz ampules. The mixture was slowly heated to 1000 °C.The chemical transport was achieved with I2 as transport agenthaving a concentration of about 5 mg/cm3. The growthtemperature was gradually changed from 1030° to 980 °C,with a temperature gradient of 3 °C/cm and a growth time of20 days. The crystals had the shape of thin-layered plates withthicknesses and surface areas ranging from 20 to 1000 μm andfrom 20 to 100 mm2, respectively.We prepared van der Waals hBN-encapsulated MoSe2heterostructures using high-purity hexagonal boron nitride(hBN) and Si substrates (300 nm SiO2). The monolayers weremechanically exfoliated from the MoSe2 bulk crystals using thedeterministic all-dry stamping method, similar to Castellanos-Gomez et al.33 A MoSe2 monolayer and hBN crystals were firstexfoliated on a flexible PDMS gel-film stamp rigidly attached toa glass slide. The thicknesses of the hBN flakes were about 200nm for the bottom layer in MoSe2/hBN structures and about100 nm for the bottom layer and about 2 nm for the top layer,respectively, in hBN-encapsulated structures. During thetransfer process, the substrate and the stamp were placedbelow an optical microscope equipped with an XYZ position-ing stage. A long-working distance microscope objectiveenabled us to locate and deterministically transfer selectedflakes to the substrate. After each transfer step the sample washeated to about 180 °C for 20 min in air. After the last layerwas added to the sample, a final thermal annealing wasperformed in air for 2 h at about 200 °C.For the PL and UPC PLE experiments, the samples weremounted on the coldfinger of a nonvibrating closed-cyclehelium cryostat, in which the temperature could be varied from7 to 350 K. The PL was excited by the second harmonic 532nm (2.33 eV) of a continuous-wave single-mode Nd:YAGlaser. The UPC PLE was excited by a continuous-waveTi:sapphire laser whose emission was tunable in the range from760 to 780 nm. The laser beam was focused on the sampleunder normal incidence using a high-resolution, long-workingdistance (WD = 10 mm, NA = 0.65) 50× microscopeobjective. The diameter of the excitation spot was about 1 μm.The emission from the sample was collected by the samemicroscope objective and was analyzed with a 0.5-m-focallength spectrometer equipped with a 600 lines/mm grating anda Peltier-cooled charged-coupled-device Si camera. The RCspectrum was measured at the same setup using a filamentlamp as a light source. To eliminate the scattered laser light, aset of short- and long-pass edged filters was used. For thepolarization-resolved experiments, a Glan-Thompson prismcombined with a quarter-wave retardation plate was introducedin the excitation and detection path.■ AUTHOR INFORMATIONCorresponding AuthorJoanna Jadczak − Department of Experimental Physics,Wrocław University of Science and Technology, 50-370Wrocław, Poland; orcid.org/0000-0003-2953-1203;Email: joanna.jadczak@pwr.edu.plAuthorsJoerg Debus − Department of Physics, TU DortmundUniversity, 44227 Dortmund, Germany; orcid.org/0000-0002-8678-4402Justyna Olejnik − Department of Experimental Physics,Wrocław University of Science and Technology, 50-370Wrocław, Poland; orcid.org/0009-0007-4948-4789Ching-Hwa Ho − Graduate Institute of Applied Science andTechnology, National Taiwan University of Science andTechnology, Taipei 106, Taiwan; orcid.org/0000-0002-7195-208XKenji Watanabe − National Institute for Materials Science,Tsukuba, Ibaraki 305-0044, Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − National Institute for Materials Science,Tsukuba, Ibaraki 305-0044, Japan; orcid.org/0000-0002-1467-3105Leszek Bryja − Department of Experimental Physics, WrocławUniversity of Science and Technology, 50-370 Wrocław,PolandComplete contact information is available at:https://pubs.acs.org/10.1021/acs.jpclett.3c01982NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThe project was funded by the QuanterERA II EuropeanUnion’s Horizon 2020 research and innovation programmeunder the EQUAISE project, Grant Agreement No.101017733, under the supervision of the National Center forResearch and Development in Poland within the projectQuantERA II ERA-Net Cofund in Quantum Technologies(QUANTERAII/1/74/EQUAISE/2022). J.D. acknowledgesthe support by the DFG-funded TRR 160 (Project B4, No.249492093).■ REFERENCES(1) Xiao, D.; Liu, G.-B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin andValley Physics in Monolayers of MoS2 and Other Group-VIDichalcogenides. Phys. Rev. Lett. 2012, 108, 196802.(2) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. AtomicallyThin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010,105, 136805.(3) Wang, G.; Chernikov, A.; Glazov, M. M.; Heinz, T. F.; Marie, X.;Amand, T.; Urbaszek, B. Colloquium: Excitons in Atomically ThinTransition Metal Dichalcogenides. Rev. Mod. Phys. 2018, 90, 021001.(4) Drüppel, M.; Deilmann, T.; Krüger, P.; Rohlfing, M. Diversity oftrion states and substrate effects in the optical properties of an MoS2monolayer. Nat. Commun. 2017, 8, 2117.(5) Mostaani, E.; Szyniszewski, M.; Price, C. H.; Maezono, R.;Danovich, M.; Hunt, R. J.; Drummond, N. D.; Fal’ko, V. I. 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