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Ke Xiao, Ruihuan Duan, Zheng Liu, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Wang Yao, Xiaodong Cui

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[Hot exciton effect in photoluminescence of monolayer transition metal dichalcogenide](https://mdr.nims.go.jp/datasets/4c0d3fc6-beef-4f92-ae53-180708dab0c0)

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Hot exciton effect in photoluminescence of monolayer transition metal dichalcogenideReceived: 8 July 2022 Revised: 6 November 2022 Accepted: 7 November 2022DOI: 10.1002/ntls.20220035R E S E A RCH ART I C L EHot exciton effect in photoluminescence ofmonolayertransitionmetal dichalcogenideKeXiao1 RuihuanDuan2 Zheng Liu2 KenjiWatanabe3 Takashi Taniguchi4Wang Yao1 Xiaodong Cui11Department of Physics, The University ofHong Kong, Hong Kong, China2School ofMaterials Science and Engineering,Nanyang Technological University, Singapore,Singapore3Research Center for FunctionalMaterials,National Institute forMaterials Science,Tsukuba, Japan4International Center forMaterialsNanoarchitectonics, National Institute forMaterials Science, Tsukuba, JapanCorrespondenceXiaodong Cui, Department of Physics, TheUniversity of Hong Kong, Hong Kong, China.Email: xdcui@hku.hkFunding informationHong Kong University Grants Council/Research grants council under schemes of,Grant/Award Number: AoE/P-701/20; GRF,Grant/Award Number: 17300520; AoE seedfund of the University of Hong Kong andNational Key R&DProgram of China,Grant/Award Number: 2020YFA0309600;Elemental Strategy Initiative conducted by theMEXT, Japan, Grant/Award Number:JPMXP0112101001; JSPS KAKENHI,Grant/Award Numbers: 19H05790,20H00354, 21H05233; SingaporeMinistry ofEducation Tier 3 Programme “GeometricalQuantumMaterials” AcRF Tier 3, Grant/AwardNumber: MOE2018-T3-1-002; AcRF Tier 2,Grant/Award Number:MOE2019-T2-2-105AbstractHot excitons are usually neglected in optical spectroscopy in two-dimensional semi-conductors for the sake ofmomentum conservation, as themajority of hot excitons areout of light cones. In this letter,weelaborate on the contributionof hot excitons to opti-cal properties of monolayerMolybdenum diselenide (MoSe2) with photoluminescence(PL) and PL excitation (PLE) spectroscopy.With the excitation-intensity-dependent PL,temperature-dependent PL and PLE experiments combined with the simulations, weexperimentally distinguish the influences of the exciton temperature and the latticetemperature in the PL spectrum. It is concluded that the acoustic phonon-assistedPL accounts for the non-Lorentzian high energy tail in the PL spectrum, and the hotexciton effect is significant to linear optical properties of transition metal dichalco-genides. Besides, the effective exciton temperature is found to be several tens ofKelvinhigher than the lattice temperature at non-resonant optical excitation. It indicatesthat the exciton temperature needs to be carefully taken into account when consid-ering the exciton-related quantum phase phenomena such as exciton condensation. Itis experimentally demonstrated that the effective exciton temperature canbe tunedbyexcitation energy.Key points:∙ The acoustic phonon-assisted photoluminescence (PL) accounts for the non-Lorentzian high-energy tail in the PL spectrum.∙ “Hot” excitons play a significant role in optical properties of two-dimensionaltransitionmetal dichalcogenides.∙ The effective exciton temperature could be tuned by excitation energy.KEYWORDS2D semiconductors, exciton-phonon coupling, hot excitonThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, providedthe original work is properly cited.© 2022 The Authors.Natural Sciences published byWiley-VCHGmbH.Nat Sci. 2023;3:e20220035. wileyonlinelibrary.com/journal/ntls 1 of 7https://doi.org/10.1002/ntls.20220035 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttps://orcid.org/0000-0001-5260-7996mailto:xdcui@hku.hkhttp://creativecommons.org/licenses/by/4.0/https://wileyonlinelibrary.com/journal/ntlshttps://doi.org/10.1002/ntls.20220035NATURAL SCIENCES 2 of 7INTRODUCTIONMonolayer transition metal dichalcogenides (TMDs) have been rec-ognized as one of the superior playgrounds for two-dimensional (2D)physics, particularly 2D exciton study. The weak Coulomb screeningand 2D nature lead to prominent excitons with a giant binding energydominating monolayer TMDs’ optical properties.1–6 The attributes ofexcitons in monolayer TMDs featuring strong oscillator strength, rich-ness of degrees of freedom, that is, spin and valley, and spin-valleylocking7,8 have been stimulating intriguing experiments in many-bodyphysics.9,10 Especially, the strong spin–orbit coupling of the transi-tion metal atoms gives rise to the large spin splitting in the valenceband, resulting in the two families of optical accessible bright excitons,namely, A excitons (lower energy) and B excitons (higher energy).11,12As yet, not much attention has been paid to the influence of hotexcitons whose kinetic energy is significantly higher than lattice tem-perature. Unlike hot electrons that affect physics properties in manyaspects,13–15 hot excitons areusually neglected in optical spectroscopyexcept in dynamics study16 for the sake of momentum conservation,as the majority of hot excitons are out of light cone. Figure 1 depictsthe photoluminescence (PL) process in TMDs. The excited electronsand holes immediately form excitons in a highly non-equilibrium stateoncepumpedasFigure1aelaborates.After a time 𝜏th(∼sub-100fs),17,18a thermalization among excitons themselves is reached, and excitonsfollow the Boson/Boltzmann distribution characterized by the excitontemperature Texciton (Figure 1b). Note that the exciton temperature isstill much higher than the lattice temperature Tlattice at this time. Theexcitons further cool down accompanying with an energy transfer tolattice via exciton-phonon scattering or some other process19–21 untilachieving thermal equilibrium ( Texciton = Tlattice ), characterized by atime scale 𝜏ex−ph (∼tens of picosecond; Figure 1c).16,22–25It is widely assumed that excitons and lattices share the same tem-perature in optical spectroscopy. Given that the excitons’ radiativelifetime of sub-picosecond26 is much shorter than 𝜏ex−ph, the exci-tons could radiate before thermalizing with the lattice. Meanwhile,only the excitons inside the light cone can realize direct radiativerecombination for the requirement of in-plane momentum conserva-tion (Figure 1d). Intuitively, the temperature of excitons seems not asimportant as that of electrons since these radiation-active excitons aremuch less influenced by the exciton temperature. The homogeneouslinewidth broadening (∼several meV) can also relax to some extentthe energy-momentum conservation requirement in the exciton’s lightemission.27 We calculate the PL spectra at various exciton tempera-tures (Texciton) and conclude this homogeneous linewidth broadeningeffect is considerably minor and has a negligible contribution to thePL linewidth (more specifically in the Supporting Information). Theothermechanismaccounting for the linewidth broadening is the acous-tic phonon-assisted exciton PL.28–30 The hot excitons (green circlein Figure 1d) could be scattered into the light cone by absorbing oremitting acoustic phonons.In this letter, we elaborate the contribution of hot excitons to opticalproperties of monolayer MoSe2. With the intensity- and temperature-dependent PL and PL excitation (PLE) experiments combined with thesimulations, we experimentally distinguish the influences of the exci-ton temperature and the lattice temperature in the PL spectrum. It isconcluded that the acoustic phonon assisted PL (APAPL) accounts forthe non-Lorentzian high-energy tail in the PL spectrum, and the hotexciton effect is significant to optical properties of TMDs. Besides, theF IGURE 1 Schematic of the exciton distribution dynamics. (a) at t = 0, excitons are in a highly non-equilibrium state after a pulse excitation.(b) at t = 𝜏th , the excitons reach thermalization of themselves at Texciton > Tlattice. (c) at= 𝜏ex−ph , the exciton temperature cools down and achievesa thermal equilibriumwith lattice. g(E) and f(E) represent the density of states and Boltzmann distribution respectively. Q is the center of massmomentum of excitons. The line-thickness of the exciton dispersion (in red) represents the effective occupation. (d) Zoom-in of the dashed area in(b) sketches acoustic phonon-assisted exciton photoluminescence (PL) 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License3 of 7 HOT EXCITON EFFECT IN PHOTOLUMINESCENCEF IGURE 2 (a) PL excitation (PLE) spectral map ofMoSe2 with the excitation energy ranging from 2.3 to 2.75 eV. Lorentz fitting results: PLintensity (c), PL peak energy and PL linewidth (d) are summarized as a function of excitation energy. (c) and (d) are further divided into two regionsbased on the PL intensity. (b) The PL linewidth and PL energy peak (determined by Lorentz fitting) as a function of excitation intensity. The insetshows the two-dimensional map of excitation-intensity-dependent PL spectra. The excitation-intensity-dependent PL is measured under anexcitation of 2.33 eV at 15 Kcontrasting linewidth broadening behaviors owing to exciton tem-perature increase or lattice temperature increase are discussed. It isexperimentally demonstrated that the effective exciton temperaturecan be tuned by excitation energy.RESULTSFigure 2 summarizes our PLE and excitation-intensity-dependent PLdata. Theexcitationenergy ranging from2.3 to2.75eV is set far beyondthe A and B exciton energies to avoid resonant absorption. The exci-tation intensity is kept below 100 —W to minimize the local heating.The PL intensity across the excitation range primarily results fromthe corresponding excitation intensity profile (blue ball in Figure 2c)and the absorption coefficient (details in the Supporting Informa-tion). At region I, the PL intensity decreases as the excitation energyincreases primarily owing to the reduction of laser intensity (blue ballsin Figure 2c). At region II, thePL intensity remains unchanged relativelyandeven slightly increases though theexcitation intensity reduceswiththe increase energy,whichmay result from the boosted absorption inCband (more details in the Supporting Information). The energy shift ofA-1s exciton shows a consistent trend with PL intensity or exciton den-sity, which also agrees well with our excitation-intensity-dependentPL result (Figure 2b). In Figure 2b, the A-1s peak energy undergoesa slight redshift with the increase of exciton density under the exci-tation of 2.33 eV accompanying the linewidth broadening, which isconsistent with the previous results.31 The redshift is attributed to thebandgap renormalization andCoulomb screening effect. Usually, as theexcitation intensity increases, the electronic bandgap decreases owingto the bandgap renormalization from photocarriers,32–35 whereas theCoulomb screening effect is enhanced owing to the increased exci-ton density, leading to the decrease of the exciton binding energy, andconsequently results in the PL peak energy blueshift.35 In monolayerMoSe2, the bandgap renormalization effect is larger than the Coulombscreening effect, and therefore the PL peak undergoes a redshift asa function of excitation intensity. Figure 2d indicates that the excita-tion energy plays amore prominent role at low exciton density. Usually,a low-intensity excitation leads to narrower exciton PL linewidth onaccount of the less Auger-like exciton–exciton interaction26,36 as elab-orated in Figure 2b. In region I, although the PL intensity or exciton 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseNATURAL SCIENCES 4 of 7F IGURE 3 (a) Representative PL spectra under different excitation energies at 15 K base temperature. The PL spectra are renormalized andshifted with respect to the spectral peak for comparison. The upper halves of the PL lineshape (normalized PL> 0.5) are nearly the same, and thelower parts of PL lineshape expand at the higher excitation energy. The expansion weighs heavily at the higher energy tails as magnified in theinset. (b) Representative PL spectra at various cryostat temperature. The linewidth broadening owing to the lattice temperature displays differentpatterns against that of exciton temperature. The inset shows the linewidth from Lorentz fitting as a function of the lattice temperature (c)Simulated PL spectra with themechanism of acoustic phonon-assisted exciton emission, where the lattice temperature is kept constant(Tlattice = 15K) and the exciton temperature is the sole variable. The high-energy side tail expands obviously accompanying with the linewidthbroadening. The inset shows the linewidth broadening as a function of the exciton temperature. Simulation result of PL spectra with excitationenergy of 2.31 eV (d) and 2.75 eV (e), the exciton temperature is estimated to be 39 and 55 K (∼24 and 40 K higher than the lattice temperature)under the excitation energies of 2.31 eV and 2.75 eV, respectivelydensitymonotonically decreaseswith the increasing excitation energy,the PL linewidth almost linearly increases. It seems contradictory toour excitation-intensity-dependent PL results (Figure 2b) if only theexciton density-induced linewidth variation is taken into account. Weattribute this linewidth broadening to the APAPL, which we elaboratein the following section. In region II, the PL intensity remains flat, whichimplies theexcitondensity is nearly constant in region II and theexcitondensity-induced linewidth broadening could be excluded. Therefore,the APAPL plays a sole role in broadening the linewidth. Hence, thePL linewidth in region II increases faster than in region I (the two redlines in Figure 2d). Meanwhile, the Raman scattering is exploited tomonitor the lattice temperature under the excitation (below 100 —W),showing that the local heating is negligible and the local latticetemperature remains a constant in the excitation range (details in theSupporting Information). The anomalous linewidth broadening in bothregions I and II and thenon-Lorentzian line shapeofPL spectra are thenattributed to the effective exciton temperature rise, which activatesthe APAPL process as demonstrated in Figure 3.Figure 3a shows the representative PL spectra under different exci-tation energies. These PL spectra are renormalized and shifted withrespect to the PL energy peak for better comparison. Note that thetop halves of the PL spectra where the normalized intensity > 0.5are nearly the same across the excitation energy range. Contrarily,the tail at the high energy side expands with the elevating excita-tion energy as illustrated in the inset. This linewidth broadening hasa contrasting manner to the lattice temperature-induced line shape 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License5 of 7 HOT EXCITON EFFECT IN PHOTOLUMINESCENCEF IGURE 4 (a) Sketch of the relation between the effective exciton temperature and the excitation energy. The exciton excited by higherenergy photon has a higher initial kinetic energy. After a time scale (∼𝜏rad), the excitons reach different effective exciton temperatures. (b) Theeffective exciton temperature as a function of the excitation energybroadening (Figure 3b), which displays a whole line shape broadeningother than just an expansion in the tail. To simulate the phonon-assisted PL, we set the exciton temperature as the single variableand keep the lattice temperature as a constant (∼15K). Figure 3cshows the simulated PL spectrum of A-1s exciton under the APAPLmechanism with all defined parameters from Glazov and Urbaszek’swork28 (detailed in the Supporting Information). The expansion atthe higher energy edge leads to the effective linewidth broaden-ing (inset of Figure 3c), remarkably reproducing the experimentalfeatures in Figure 2d. The simulation perfectly describes our experi-mental results, and it clearly indicates that the APAPL process makessignificant contribution to the whole PL spectrum in high-qualitysamples. Comparing our experimental (Figure 3a) with simulationresults (Figure 3c), we conclude that the higher excitation energyleads to the higher exciton temperature and finally raises non-Lorentzhigh-energy tail. As demonstrated in Figure 3d,e, the effective exci-ton temperature (Texciton) is 24K higher than the lattice temperature(Tlattice) when the excitation is at 2.31 eV and 40 K higher at 2.75 eV,respectively.Under higher energy excitation, excitons will have higher initialkinetic energy.17 Within a typical exciton radiative lifetime 𝜏rad, theexciton reaches an effective exciton temperature (Texciton), which issignificantly different from the lattice temperature as sketched inFigure 4a. In Figure 4b, the effective exciton temperature is retrievedfrom the fitting of our PL spectra based on our model, which incor-porates two components: one is the Lorentz function that describesthe PL from the exciton inside the light cone; the other is the high-energy tail as elaborated in the Supporting Information, Note 6, whichdescribes the APAPL (Texciton as a fitting parameter) from excitons out-side the light cone. The latter contributes more weight as the Texcitonincreases.OurPLEexperiments indicate that the effective exciton tem-perature can be tuned continuously by the excitation energy as shownin Figure 4b.In summary, our PL and PLE spectroscopic experiments reveal thatthe effect of hot excitons and the effective exciton temperature can beremarkably extracted from the PL spectrum of monolayer TMDs. Weelaborate the roles of effective exciton temperature and lattice tem-perature in PL spectra and the linewidth broadening mechanism. Thethermal equilibrium between the excitons and the lattice is not neces-sarily achieved in linear optical properties of 2D TMDs. The effectiveexciton temperature could be tuned by excitation energy.METHODSCrystal growthBulk MoSe2 crystals are grown by the chemical vapor transportmethod.Mo powder (99.9%), slightly excessive Se ingot (99.999%), anda bit of iodine as transport agents are loaded in silica tubes, whichare evacuated and sealed. Then, the silicon tubes are put in the reac-tion zone of 950◦C and the growth zone of 900◦C. After 15 days, bulkMoSe2 with large sizes are obtained in the cold zone. The monolayerMoSe2 is mechanically exfoliated onto Si substrate with 285nm SiO2film.Sample preparationMonolayer MoSe2 and thin hexagonal boron nitride (hBN) were firstexfoliated frombulkMoSe2 crystal onto the different Si/SiO2 (300 nm)substrates. Afterward, dry-transfer technique was used to stack themtogether. Figure S1 shows the optical image of our hBN-encapsulatedMoSe2 under bright and dark fields.PLE measurementIn our PLE measurement, the light source (SuperK EXTREME EXB-3,NKT photonics) is a picosecond laser (80MHz, 5 ps) pumped supercon-tinuum photonic crystal fiber going through a motorized continuousband-pass filter. The PL is collected through a long working distance 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseNATURAL SCIENCES 6 of 7objective (Olympus, 50x) with a spectrometer (Shamrock 193i) and anelectron-multiplying charge-couple-device (EMCCD, Andor).AUTHOR CONTRIBUTIONSConceptualization, formal analysis, investigation, software, project admin-istration, visualization, writing-original draft: Ke Xiao. Resources: RuihuanDuan. Resources: Zheng Liu. Resources: Kenji Watanabe. Resources:Takashi Taniguchi.Writing-review and editing: Wang Yao. Conceptualiza-tion, funding acquisition, project administration, supervision, writing-reviewand editing: Xiaodong Cui.ACKNOWLEDGMENTSThe work was supported by the Hong Kong University Grants Coun-cil/ Research grants council under schemes of (AoE/P-701/20), GRF(17300520) and AoE seed fund of the University of Hong Kong andNational Key R&DProgram of China (2020YFA0309600). K.W. and T.T.acknowledge support from theElemental Strategy Initiative conductedby the MEXT, Japan (Grant Number JPMXP0112101001) and JSPSKAKENHI (Grant Numbers 19H05790, 20H00354, and 21H05233).R.D and Z.L. acknowledge support from the Singapore Ministry ofEducation Tier 3 Programme “Geometrical Quantum Materials” AcRFTier 3 (MOE2018-T3-1-002), AcRF Tier 2 (MOE2019-T2-2-105). Theauthors thank Dr. Fengren Fan, Dr. Tengfei Yan, and Dr. Bairen Zhu forthe fruitful discussion.CONFLICT OF INTERESTWangYao is a co-author of themanuscript and an editor of Natural Sci-ences and was not involved in the handling of the peer-review processof this submission.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from thecorresponding author upon reasonable request.ETHICS STATEMENTThe authors confirmed that they have followed the ethical policies ofthe journal.ORCIDKeXiao https://orcid.org/0000-0001-5260-7996PEER REVIEWThe peer review history for this article is available at https://publons.com/publon/10.1002/ntls.20220035REFERENCES1. Chernikov A, Berkelbach TC, Hill HM, et al. Exciton binding energyand nonhydrogenic Rydberg series in monolayer WS 2. Phys Rev Lett.2014;113:076802.2. Ye Z, Cao T, O’Brien K, et al. Probing excitonic dark states in single-layer tungsten disulphide.Nature. 2014;513: 214-218.3. 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Hotexciton effect in photoluminescence of monolayer transitionmetal dichalcogenide.Nat Sci. 2023;3:e20220035.https://doi.org/10.1002/ntls.20220035 26986248, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/ntls.20220035 by Cochrane Japan, Wiley Online Library on [13/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttps://doi.org/10.1002/ntls.20220035 Hot exciton effect in photoluminescence of monolayer transition metal dichalcogenide Abstract INTRODUCTION RESULTS METHODS Crystal growth Sample preparation PLE measurement AUTHOR CONTRIBUTIONS ACKNOWLEDGMENTS CONFLICT OF INTEREST DATA AVAILABILITY STATEMENT ETHICS STATEMENT ORCID PEER REVIEW REFERENCES SUPPORTING INFORMATION