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[Łucja Kipczak](https://orcid.org/0000-0003-1266-0201), [Natalia Zawadzka](https://orcid.org/0000-0002-3282-9513), [Dipankar Jana](https://orcid.org/0000-0001-9935-4885), [Igor Antoniazzi](https://orcid.org/0000-0002-0803-6011), [Magdalena Grzeszczyk](https://orcid.org/0000-0001-6861-3098), [Małgorzata Zinkiewicz](https://orcid.org/0000-0002-7472-5501), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Marek Potemski](https://orcid.org/0000-0001-8881-6618), [Clément Faugeras](https://orcid.org/0000-0002-9615-8739), [Adam Babiński](https://orcid.org/0000-0002-5591-4825), [Maciej R. Molas](https://orcid.org/0000-0002-5516-9415)

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[Impact of temperature on the brightening of neutral and charged dark excitons in WSe<sub>2</sub> monolayer](https://mdr.nims.go.jp/datasets/c5ecc2fd-bb03-400b-8802-fd18b468d8b2)

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Impact of temperature on the brightening of neutral and charged dark excitons in WSe2 monolayerNanophotonics 2024; 13(26): 4743–4749Research ArticleŁucja Kipczak*, Natalia Zawadzka, Dipankar Jana, Igor Antoniazzi, Magdalena Grzeszczyk,Małgorzata Zinkiewicz, Kenji Watanabe, Takashi Taniguchi, Marek Potemski, Clément Faugeras,Adam Babiński and Maciej R. MolasImpact of temperature on the brighteningof neutral and charged dark excitons in WSe2monolayerhttps://doi.org/10.1515/nanoph-2024-0385Received July 26, 2024; accepted November 7, 2024;published online November 18, 2024Abstract: Optically dark states play an important role inthe electronic and optical properties of monolayers (MLs)of semiconducting transition metal dichalcogenides. Theeffect of temperature on the in-plane-field activation of the*Corresponding author: Łucja Kipczak, Institute of ExperimentalPhysics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland,E-mail: lucja.kipczak@fuw.edu.pl. https://orcid.org/0000-0003-1266-0201Natalia Zawadzka, Igor Antoniazzi, Małgorzata Zinkiewicz, AdamBabiński and Maciej R. Molas, Institute of Experimental Physics, Facultyof Physics, University of Warsaw, 02-093 Warsaw, Poland,E-mail: maciej.molas@fuw.edu.pl (M. R. Molas).https://orcid.org/0000-0002-3282-9513 (N. Zawadzka).https://orcid.org/0000-0002-0803-6011 (I. Antoniazzi).https://orcid.org/0000-0002-7472-5501 (M. Zinkiewicz).https://orcid.org/0000-0002-5591-4825 (A. Babiński).https://orcid.org/0000-0002-5516-9415 (M.R. Molas)Dipankar Jana, Laboratoire National des Champs Magnétiques Intenses,CNRS-UGA-UPS-INSA-EMFL, 25 Avenue des Martrys, 38042 Grenoble,France; and Institute for Functional Intelligent Materials, National Uni-versity of Singapore, Singapore 117544, Singapore.https://orcid.org/0000-0001-9935-4885Magdalena Grzeszczyk, Institute for Functional Intelligent Materials,National University of Singapore, Singapore 117544, Singapore.https://orcid.org/0000-0001-6861-3098Kenji Watanabe, Research Center for Electronic and Optical Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044,Japan. https://orcid.org/0000-0003-3701-8119Takashi Taniguchi, Research Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044,Japan. https://orcid.org/0000-0002-1467-3105Marek Potemski, Institute of Experimental Physics, Faculty of Physics,University of Warsaw, 02-093 Warsaw, Poland; Laboratoire National desChamps Magnétiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 25 Avenuedes Martrys, 38042 Grenoble, France; and CEZAMAT, CENTERA Labs,Warsaw University of Technology, 02-822 Warsaw, Poland.https://orcid.org/0000-0001-8881-6618Clément Faugeras, Laboratoire National des Champs MagnétiquesIntenses, CNRS-UGA-UPS-INSA-EMFL, 25 Avenue des Martrys, 38042Grenoble, France. https://orcid.org/0000-0002-9615-8739neutral and charged dark excitons is investigated in a WSe2ML encapsulated in hexagonal BN flakes. The brighteningrates of the neutral dark (XD) and grey (XG) excitons andthe negative dark trion (TD) differ substantially at partic-ular temperature. More importantly, they weaken consid-erably by about 3–4 orders of magnitude with tempera-ture increased from 4.2 K to 100 K. The quenching of thedark-related emissions is accompanied by the two-order-of-magnitude increase in the emissions of their neutral brightcounterparts, i.e. neutral bright exciton (XB) and spin-singlet(TS) and spin-triplet (TT) negative trions, due to the thermalactivations of dark states. Furthermore, the energy split-tings between the dark XD and TD complexes and the corre-sponding bright XB, TS, and TT ones vary with temperaturerises from 4.2 K to 100 K. This is explained in terms of thedifferent exciton–phonon coupling for the bright and darkexcitons stemming from their distinct symmetry properties.Keywords: dark excitons; temperature influence; bright-ening1 IntroductionThe existence of dark neutral and charged (trions) excitonsdetermines the optical response in so-called darkishmono-layers (MLs) of semiconducting transition metal dichalco-genides (S-TMDs), i.e. MoS2, WS2, and WSe2 [1]–[15]. FordarkishMLs, the dark excitons and trions are characterisedby significantly lower energies compared to their brightcounterparts [1]–[15]. Alternatively, the bright S-TMD MLs,i.e. MoSe2 and MoTe2, have the energetically lowest states,which are optically allowed. The dark transitions are opti-cally forbidden or inactive, as the recombining electron-hole (e–h) pairs are characterised by a parallel spin con-figuration for an electron and a hole of the conductionand valence bands, respectively [1], [16]. To date, proper-ties of dark excitons and trions have been investigated inOpen Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License.https://doi.org/10.1515/nanoph-2024-0385mailto:lucja.kipczak@fuw.edu.plhttps://orcid.org/0000-0003-1266-0201mailto:maciej.molas@fuw.edu.plhttps://orcid.org/0000-0002-3282-9513https://orcid.org/0000-0002-0803-6011https://orcid.org/0000-0002-7472-5501https://orcid.org/0000-0002-5591-4825https://orcid.org/0000-0002-5516-9415https://orcid.org/0000-0001-9935-4885https://orcid.org/0000-0001-6861-3098https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0001-8881-6618https://orcid.org/0000-0002-9615-87394744 — Ł. Kipczak et al.: Impact of temperature on the brightening of dark excitons in WSe2 monolayerMLs embeddedwithin several environments (e.g. exfoliatedon Si/SiO2 substrate or encapsulated in hexagonal boronnitride (hBN)flakes) [1], [15], for various levels of free carrierconcentration [5], [11], [12], or due to the Lamb shift [17]. Thebest well-known phenomenon for significantly brighteningof the emission due to dark states in S-TMDMLs is achievedby the in-plane magnetic field (B‖), which leads to mixingthe spin levels of bright and dark excitons [1], [2], [7], [8].In this work, we determine the effect of temperatureon the in-plane-field activation (brightening) of neutral dark(XD) and grey (XG) excitons and negative dark trions (TD)in a high-quality WSe2 ML encapsulated in hBN flakes. Wefound that the brightening of the XD, XG, and TD lines differsubstantially fromeach other at particular temperature, butmore importantly, it weakens considerably by almost 3–4orders of magnitude with temperature increased from 4.2 Kto 100 K. The quenching of the dark-related emissions isaccompanied by the two-order-of-magnitude enlargementof the neutral bright counterparts, i.e. neutral bright exci-ton (XB) and spin-singlet (TS) and spin-triplet (TT) negativetrions, due to the thermal activations of bright states. Inaddition, the extracted dark-bright energy splitting betweenthe neutral and charged complexes is also affected whenthe temperature is increased from 4.2 K to 100 K. This canbe explained in terms of the different exciton-phonon cou-plings for the bright and dark excitons because of theirvarious symmetries.2 Experimental resultsFigure 1(a)–(c) represent the photoluminescence (PL) spec-tra of the WSe2 ML encapsulated in hBN flakes at zero mag-netic field and at 30 T applied in the plane of the ML (B‖)measured at three different temperatures 4.2 K, 50 K, and100 K, respectively. The zero-field spectrum at 4.2 K displaysa set of characteristic emission lines; see Figure 1(a). Thisspectrum, apart from those related to the neutral brightexciton (XB), intravalley spin-singlet (TS) and intervalleyspin-triplet (TT) negative trions, consists of several emissionlines on its lower energy side. These additional lines havebeen attributed in the literature to charged excitons (tri-ons), neutral and charged biexcitons, dark excitons and tri-ons, their phonon replicas, etc. [4]–[6], [10]–[15], [18]–[24],described in detail in the Supplementary Material (SM). The02426281021040246810120123456781.64 1.66 1.68 1.70 1.72 1.740204060801001201401.64 1.66 1.68 1.70 1.72 1.740.00.51.01.52.02.53.03.54.01.64 1.66 1.68 1.70 1.72 1.740.000.010.020.030.04Intensity(arb.units)0 T30 TT = 4.2 KTDXG/DXB(a)TTTSXG/DTDXBT = 50 K(b)TTTST = 100 KXG/DTDXB(c)TTTSRelativeIntensity(arb.units)Energy (eV)XG/DTD(d)Energy (eV)XG/DTD(e)Energy (eV)XG/DTD(f)1.686 1.689050100150Energy (eV)XDXG1.680 1.686024Energy (eV)XG/D1.668 1.6740.000.020.04Energy (eV)XG/DFigure 1: Photoluminescence spectra of the investigated WSe2 ML at different temperatures: (a) 4.2 T, (b) 50 K, and (c) 100 K, measured at zero field(orange curves) and at B‖ = 30 T (blue curves) applied in the plane of the ML. The PL spectra were normalised to the intensity of the bright XB line.(d)–(f) Corresponding relative spectra (red curves) defined as PLB‖=30T − PLB‖=0T. Insets in the panels (d)–(f) shows the XG∕D emission lines with theircorresponding Lorentzian fits.Ł. Kipczak et al.: Impact of temperature on the brightening of dark excitons in WSe2 monolayer — 4745application of the external B‖ field results in the appear-ance of the new signal at energies below the XB, see Figure1(a)–(c). These new field-induced emission lines were asso-ciated with the recombination processes of neutral darkexciton (XD) and negative dark trion (TD). The sign of theTD trion is determined from the PL lineshape at T = 4.2 Kin which two lines due to negative TS and TT trions areapparent [18].To better visualise the effect of the in-plane magneticfield on dark complexes and compare the results obtained atdifferent temperatures, we define the relative spectrum asPLB‖=30T − PLB‖=0T intensity. The relative spectra obtainedforB‖= 30 T are shown in Figure 1(d)–(f). For dark excitons,the exchange interaction lifts their valley degeneracy, whichgives rise to afine structure splittingwith two types of states,termed grey and dark excitons [3], [4], [25]. These two statesare qualitatively different. The XG has an optically activerecombination channel with photons emittedwithin theMLplane [26], which can be observed only in a standard out-of-plane experimental setupwhen using objectives with a highnumerical aperture [3], [4]. TheXD state is truly optically for-bidden, and its activation requires external magnetic fields[3], [4]. The detailed analysis of the emission line, shown inthe inset to Figure 1(d), reveals its fine structure, i.e. XD andXG, which is in line with previous studies on WSe2 MLs [3],[4]. The dark exciton emission was deconvoluted up to T =40 K, using two Lorentz functions, which allowed us to inde-pendently investigate the intensities of the contributions ofthe XG and XD transitions.As seen in Figure 1, three lines, i.e. TD, XD, and XG, sig-nificantly brightened at T = 4.2 K. The temperature increaseto 50 K results in the forty and thirty five times decreaseof the maximum intensity of the TD and XD emissions,respectively. The further temperature increase results in theintensity reduction by more than an order of magnitudefor both emission lines. This demonstrates that temperaturecan drastically modify the brightening effect of in-planemagnetic fields on the dark states.To analyse in detail the influence of temperature on thebrightening of dark complexes, we deconvoluted the rela-tive spectra using Lorentz functions. The extracted evolu-tion of the integrated intensities (I) of the studiedTD,XD, andXG complexes as a function of the in-plane magnetic fieldfor three selected temperatures are presented in Figure 2.The dependencies are expected to be quadratic and can bedescribed by the formula: I = 𝛼B2‖, where 𝛼 correspondsto the brightening coefficient (see Refs. [1], [2], [4], [25]).The 𝛼 parameter is proportional to the population of darkexcitons and the emission intensity of the bright exciton[4], [15]. As can be seen in Figure 2, the experimental datacan be nicely reproduced by the fitted intensity evolution(a)(b)(c)Figure 2: Magnetic field evolution of the integrated intensities ofthe neutral grey (XG) and dark (XD) excitons and the dark trion (TD)extracted at different temperatures: (a) 4.2 K, (b) 50 K, and (c) 100 K.Black curves represent the fits of the function I = 𝛼B2‖.given by the formula. The complete analysis of the mag-netic field dependences of the integrated intensities of theinvestigated lines are given in the SM. The 𝛼 is substan-tially different for the XD and XG excitons at T = 4.2 K,i.e. 𝛼XD = 24 × 10−2 T−2 and 𝛼XG = 39 × 10−3 T−2. Thislarge variation can be explained by the difference in thepopulations of these two states at 4.2 K. The population ratioe−𝛿∕kT = 0.161 (𝛿 = 660 μeV [4]) is in excellent agreementwith the measured ratio 𝛼XG∕𝛼XD = 0.161. This suggests thatthe relative population of the neutral grey and dark exci-tons is controlled by the Boltzmann distribution. The 𝛼TD =4746 — Ł. Kipczak et al.: Impact of temperature on the brightening of dark excitons in WSe2 monolayer16 × 10−2 T−2 confirms that the free-electron density in thestudied WSe2 ML is not negligible, leading to the formationof a significant number of dark trions. From T = 50 K, asingle emission line can be resolved in the energy range ofthe neutral grey and dark excitons, which is denoted asXG∕Din the following (see Figure 3). By analysing the temperaturevariation of the 𝛼 parameters of the XG and XD lines, we canpropose the attribution of the aforementioned single line attemperatures higher than 40 K. Although the 𝛼XD parameterdecreases by about one order of magnitude from 4.2 K to50 K and simultaneously the variation of 𝛼XG is only a fewtimes, we tentatively ascribe this line to the grey exciton.The neutral and charged dark exciton intensities also followthe aforementioned quadratic evolutions at higher temper-atures, see Figure 2(b)–(c) and the SM for details. However,themagnitude ofmagnetic activation of dark complexes, i.e.𝛼 parameter, is greatly reduced by more than 3 orders ofmagnitude with increasing temperature from 4.2 K to 100 K.The temperature dependence of the integrated intensi-ties of the TD, XD, and XG complexes obtained in magneticfield B‖ = 30 T is shown in Figure 3(a). Note that the corre-sponding evolution of the extracted 𝛼 parameters displaysanalogous trends and is shown in the SM. The XD inten-sity reduces dramatically 7 times in the temperature range4.2 K–20 K, while the XG counterpart intensity stays almostat the same level. At higher temperatures, the intensities ofboth neutral dark excitons show similar intensities up to(a)(b)Figure 3: The integrated intensities of the (a) dark (XG, XD, and TD)and (b) bright (XB, TT, and TS) complexes, obtained in magnetic fieldB‖ = 30 T, as a function of temperature. The vertical axes are givenin logarithmic scale for clarity.40 K, which is followed by the exponential decay of the XDintensity. For the TD, its intensity stays at the same level upto 20 K, and then a significant drop of TD intensity is appar-ent. In summary, the increase at temperature from 4.2 K to100 K leads to the reduction of the integrated intensities ofthe dark complexes by more than 3 orders of magnitude.Figure 3(b) shows the integrated intensities of the XB, TT,and TS lines. The evolution of the XB intensity describes asimilar evolution to theXG andXB ones, which are, however,inverted. This means that up to around 40 K–50 K, a smallincrease of the XB intensity is observed, which is followedby its rapid exponential growth, as previously reported [27].The analogous inverted evolution can be seen for the TTand TS lines compared to the dark trion. These results showthat the intensities of the bright and neutral complexes for agiven family (neutral and charged) are associated with eachother. However, for the bright complexes, only a 2 ordersof magnitude increase is observed in the range from 4.2 Kto 100 K, as compared to the aforementioned 3 orders ofmagnitude reduction for the dark features.Although the difference in the 𝛼 parameter of the XGand XD lines can be explained by the difference in the popu-lation of these two states (the Boltzmann distribution) from4.2 K to 40 K, the difference in the temperature evolutionbetween the dark and bright excitons and trions is morecomplex. For bright neutral excitons in WSe2 ML, a strongquenching of their emission was referred to the presence oftheir dark counterparts with decreasing temperature [27],[28]. In our case, we observe directly that the reductionsmentioned above in the XB, TT, and TS emissions occursimultaneously with substantial brightening of the darkcomplexes (XD, XG, and TD). Due to the substantial suppres-sion of the thermal activation of dark excitons at low tem-peratures (T < 50 K and <30 K for the neutral and chargedexcitons, respectively), bright emissions are also reduced inthis temperature range.When the temperature is increased,the efficiency of thermal activation from the dark to brightstates increases, which leads to a shrinkage of the bright-ening of dark states as the population of the bright statesgrows. The competition between the thermal activation ofthe bright states and the in-plane magnetic activation of thedark states suppresses the brightening of dark complexes attemperatures higher than 100 K. An analogous quenching ofthe brightening, i.e. above 100 K, was reported for WSe2 MLexfoliated on the Si/SiO2 substrate [2].Figure 4 presents the energy splitting between bright(XB, TT, and TS) and dark (XD, XG, and TD) complexes asa function of temperature. The temperature evolution ofgiven excitonic complexes is shown in the SM. The neutralbright-dark splitting (XB and XD) stays constant at 60 K, andfurther a blueshift of about 3 meV is observed at higherŁ. Kipczak et al.: Impact of temperature on the brightening of dark excitons in WSe2 monolayer — 47470 20 40 60 80 10020222428304446Dark-brightenergysplitting(meV)Temperature (K)B|| = 30 TTS - TDTT - TDXB - XDFigure 4: The temperature evolution of the energy splitting betweenbright (XB, TT, and TS) and dark (XD, XG, and TD) complexes extracted fromdata measured in B‖ = 30 T.temperatures. This behaviour can be understood in termsof different properties of the symmetries of the bright andgrey (dark) excitons. The XB exciton is characterised bythe in-plane dipole moment, whereas the zero and out-of-plane dipole momenta determine the XD and XG com-plexes. The typical redshifts of excitonic resonances underincreased temperature are associated with the shrinkage ofthe bandgap energy [29]. However, for excitonic complexes,the interaction of bound electron-hole pairs with latticephonons needs to be taken into account, which results inslightly different temperature evolutions of particular exci-tonic transitions [1], [28]. Due to the different orientationsof excitonic dipole moments, they can couple to phononsof several symmetries, e.g. described by in-plane or out-of-plane vibrations, andhence affect the excitonic temperaturedependences. The bright-dark splittings for the negative tri-ons (TT and TS vs. TD) are almost constant up to 80 K, andare followed by redshifts of about 2 meV. In this case, unfor-tunately, the extracted dependences are a consequence ofa peculiar temperature evolution of the TD lines (see theSM for details), which needs to be further developed. Thepresented analysis of the bright-dark splitting sheds newlight on the temperature activation of the bright complexes.So far, its modelling relies on a constant value of energysplitting [10], [27], while our results demonstrate its clearvariation at higher temperature. We believe that our workwould trigger more theoretical studies on this issue.3 SummaryIn conclusion, we described the in-plane-field optical activa-tion of the neutral dark/grey excitons and the negative darktrions in aWSe2 ML as a function of temperature from 4.2 Kto 100 K. The brightening ratios of the dark complexes differsubstantially from each other at a particular temperature,but more importantly, it vanishes considerably by about3–4 orders of magnitude with the temperature increasedfrom 4.2 K to 100 K. The quenching of the dark-related emis-sions is found to be accompanied by enlargement of theneutral bright counterparts, neutral bright exciton and spin-singlet and spin-triplet negative trions, due to their thermalactivations. Furthermore, the extracted dark-bright energysplittings between the neutral and charged complexes wereshown to be a function of temperature with nonmonotonicchanges of about 2 meV when temperature is increase from4.2 K to 100 K. This was explained in terms of the differentexciton-phonon couplings for the bright and dark excitonsbecause of their various symmetry properties. Our resultsindicate that the population of dark excitons and dark trionsplays a very important role in theWSe2 ML emission spectrain the temperature range below 100 K, but also affect thespectra at higher temperatures due to increased thermalactivation.4 MethodsThe investigated sample is composed of a WSe2 MLand hBN layers that were fabricated by two-stage PDMS(polydimethylsiloxane)-based mechanical exfoliation [30].TheWSe2 MLflakewas placed on the thick bottomhBNflake(with thickness of about 39 nm), which was directly exfo-liated on the SiO2(90 nm)/Si substrate. Finally, the ML wascappedwith a thinner top hBNflake (with thickness of about29 nm) and then the complete hBN/WSe2 ML/hBN/SiO2/Sistructure was obtained.Low-temperature micro-magneto-PL experimentswere performed in the Voigt geometry, i.e. magneticfield orientated parallel with respect to ML’s plane.Measurements (spatial resolution 1 μm) were carried outwith the aid of a resistive magnetic coil that producesfields up to 30 T using a free-beam-optics arrangement. Thesample was placed on top of an x–y–z piezo-stage kept at T= 4.2 K and was excited using a CW laser diode with 515 nmwavelength (2.41 eV photon energy).Laser light was focused to the sample and the signalwas collected using the long-working distance objective (NA= 0.35). The emitted light was dispersed with a 0.5 m focallength monochromator and detected with a CCD camera.Acknowledgments: We are grateful to Artur Slobodeniukfor fruitful discussions.Research funding: The work has been supportedby the National Science Centre, Poland (Grant No.2018/31/B/ST3/02111) and the CNRS via IRP ‘2DM’ project. Weacknowledge the support of the LNCMI-CNRS, member of4748 — Ł. Kipczak et al.: Impact of temperature on the brightening of dark excitons in WSe2 monolayerthe EuropeanMagnetic Field Laboratory (EMFL). The Polishparticipation in EMFLwas supported by theDIR/WK/2018/07Grant from the Polish Ministry of Education and Science.KW and TT acknowledge support from the JSPS KAKENHI(Grant Numbers 21H05233 and 23H02052) and the WorldPremier International Research Center Initiative (WPI),MEXT, Japan. MP acknowledges the support from theFoundation for Polish Science (MAB/2018/9 Grant within theIRA Program financed by EU within SG OP Program).Author contributions: ŁK, NZ, DJ, IA, andMZ performed themeasurements of the PL spectra in the in-plane magneticfield. MG fabricated the sample withWSe2 ML encapsulatedin hBN. TT and KW grew the hBN crystals. CF and MP par-ticipated in the measurements. AB participated in the dis-cussions. MRM initiated and supervised the project. ŁK andMRM analysed the data. ŁK andMRMwrote the manuscriptwith the input of all coauthors. All authors have acceptedresponsibility for the entire content of this manuscript andapproved its submission.Conflict of interest: Authors state no conflicts of interest.Informed consent: Informed consent was obtained from allindividuals included in this study.Ethical approval: The conducted research is not related toeither human or animals use.Data availability: The datasets obtained during the experi-ments and analysed for the current study are available fromthe corresponding author on reasonable request.References[1] M. R. Molas, et al., “Brightening of dark excitons in monolayers ofsemiconducting transition metal dichalcogenides,” 2D Mater.,vol. 4, no. 2, p. 021003, 2017..[2] X.-X. Zhang, et al., “Magnetic brightening and control of darkexcitons in monolayer WSe2,” Nat. Nanotechnol., vol. 12, no. 9,p. 883, 2017..[3] C. Robert, et al., “Fine structure and lifetime of dark excitons intransition metal dichalcogenide monolayers,” Phys. Rev. B, vol. 96,no. 15, p. 155423, 2017..[4] M. 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