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Phonon-assisted oscillatory exciton dynamics in monolayer MoSe 2 Colin M. Chow,1, Hongyi Yu,2, Aaron M. Jones,1 John R. Schaibley,1 Michael ∗ ∗ Koehler,3 David G. Mandrus,3,4 R. Merlin,5 Wang Yao,2, and Xiaodong Xu1,6, † ‡ 1Department of Physics, University of Washington, Seattle, Washington 98195, USA 2Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China 3Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA 4Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5Center for Photonics and Multiscale Nanomaterials and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA 7 6Department of Materials Science and Engineering, 1 University of Washington, Seattle, Washington 98195, USA 0 (Dated: January 12, 2017) 2 In monolayer semiconductor transition metal dichalcogenides, the exciton-phonon interaction is n expected to strongly affect the photocarrier dynamics. Here, we report on an unusual oscillatory a enhancementoftheneutralexcitonphotoluminescencewiththeexcitationlaserfrequencyinmono- J layerMoSe . ThefrequencyofoscillationmatchesthatoftheM-pointlongitudinalacousticphonon, 2 0 LA(M). Oscillatory behavior is also observed in the steady-state emission linewidth and in time- 1 resolved photoluminescence excitation data, which reveals variation with excitation energy in the excitonlifetime. Theseresultsclearlyexposethekeyroleplayedbyphononsintheexcitonformation ] and relaxation dynamics of two-dimensional van der Waals semiconductors. i c PACS numbers: 78.20.-e, 78.40.Fy, 78.47.jd s - l r t The electron-phonon interaction in solid state systems at the M point, LA(M). Nested within the oscillations m plays a major role in carrier dynamics[1], particularly are fine structures, with linewidths one order of magni- . in the relaxation of photoexcited carriers in semiconduc- tude smaller than that of ordinary PL, originating from t a tor nanostructures, such as quantum wells[2], quantum resonant Raman scattering. Time-resolved PLE shows m wires[3], and quantum dots[4]. Monolayer semiconduct- that exciton dynamics varies with respect to excitation - ingtransitionmetaldichalcogenideshaveattractedmuch energy, where shorter emission lifetime is measured for d n interestlatelyduetointriguingtwo-dimensional(2D)ex- off-phonon-resonanceexcitation,inaccordancetotheos- o citon physics, especially relating to their valley degrees cillations in the natural linewidth of steady-state emis- c of freedom[5, 6]. Reduced Coulomb screening in the sion. This might due to the elevated lattice temperature [ 2Dlimitleadstononhydrogenicexcitonicseries[7–9]and arising from long-wavelength (small k-vector) acoustic 1 strongmany-bodyexcitoninteractions[10,11]. Recently, phonons, which enhances radiative exciton recombina- v signatures of a strong exciton-phonon interaction have tion. Our results show that acoustic LA(M) phonons 0 been observed[12, 13], such as the preservation of val- play an important role in electron-phonon coupling and 7 ley coherence in double-resonant Raman scattering[14], hot-carriercoolinginmonolayerMoSe ,andalsosuggest 7 2 2 triontoexcitonluminescenceupconversioninmonolayer the involvement of intermediate indirect excitonic states 0 WSe assisted by A(cid:48) phonons[15], and exciton enhanced (withQ-valleyelectrons)intheformationofK-valleyex- 2 1 1. anti-Stokes shifts in few-layer MoTe2[16]. Despite a few citons. 0 theoretical proposals on the role of optical phonons[17– 7 19]inexcitondynamics,andseveralexperimentalstudies Inoursteady-statemeasurement, wedetectPLat5K 1 whilescanningtheexcitationenergyofacontinuouswave on phonon-limited exciton relaxation[20–22], the details : (CW) laser, i.e., PLE spectroscopy (see Supplementary v behind how and which phonons impact metrics such as i the formation and relaxation of excitons remains largely Information for experimental details). The PLE inten- X sity plot of Fig. 1(b) shows excitonic emission energies unexplored. Thisknowledgeisimportantforinterpreting r asafunctionoflaserexcitation. Twoluminescencepeaks a a wide range of2D exciton phenomena and forexploring are identified[23]: the neutral exciton (X0), centered at the potential of exciton-based 2D optoelectronics. 1.650 eV, and the negative trion (X ), centered at 1.624 − Inthisletter,weinvestigatetheroleofexciton-phonon eV. Evidently, the intensity of X0 emission oscillates as interaction in exciton dynamics using the model system a function of excitation laser frequency, while the behav- of monolayer MoSe (Fig. 1(a)). Performing photolumi- ior of X is monotonic. Fig. 1(c) shows PL spectra 2 − nescence excitation (PLE) spectroscopy, we observe that takenattheexcitationenergies1.699eV(red)and1.686 the neutral exciton PL intensity, as well as its linewidth, eV (green), which exemplify the contrasting excitation- oscillates as a function of excitation energy with a pe- energy dependencies of X0 and X PL. Within our laser − riod matching that of the longitudinal acoustic phonon scanrange,whichhasahigh-energylimitof1.77eV(700 2 FIG. 1. (a) Optical micrograph of an MoSe monolayer on 2 285-nm-thick SiO on silicon. (b) PLE intensity map of the 2 monolayer shown in (a), indicating neutral exciton (X0) and trion (X−) emission centered at 1.650 eV and 1.624 eV, respectively. ArrowsindicateregionsofPLenhancement. Color bar: counts per second. (c) PL spectra at two distinct excitation energies showing the variation of X0 (but not X−) PL with excitation energy. FIG.2. (a)Magnifiedviewoftheregionenclosedbythewhite nm),fiveequallyspacedregionsofluminescenceenhance- square in Fig. 1(b), showing narrow resonance peaks with ment,indicatedbywhitearrows,canbeseeninX0,with correspondingphononmodesindicated. (b)PLspectrumfor 1.678 eV excitation, showing a narrow resonance associated an average energy separation of 18.5 meV. Such oscillation of X0 emission intensity in PLE, first reported in with the A(cid:48)1 phonon superimposed on the broader X0 emission. (c)VerticallinecutofthePLEmapattheX0resonance, CdS[24] for longitudinal optical phonon modes, is a hall- plotted in terms of excess energy. Selected phonon-enhanced mark of resonant excitation of phonon modes. peaksarelabeledwithexcessesenergyinparenthesis(inmeV, A closer look at Fig. 1(b) shows that each PLE reso- with 1 meV uncertainty), along with possible assignments. nanceregioncontainsseveralnarrowpeaks. Fig. 2(a)of- fers an expanded view of the spectral regime highlighted by the white square in Fig. 1(b). Three narrow lines phonon coupling to qualitatively resemble those of these shift in parallel with the excitation laser detuning, im- compounds[29]. Therefore, we assign the oscillation in plying a Raman-scattering origin of these lines. Their PLE as overtones (harmonic series) of the LA(M). This sub-meV linewidths are consistent with “conventional” assignment is corroborated by plotting the PL intensity Ramanspectra[25–27]measuredonadifferentmonolayer at the exciton resonance as a function of excess energy MoSe sample (Supplementary Information). The com- (Fig. 2(c)),wheretheexcessenergyisdefinedasthesep- 2 bined spectral features of PL emission and Raman scat- aration of laser excitation energy from the exciton reso- teringgiverisetotheoverallemissionspectrum,asshown nance. ComparedtothephononassignmentinRef. [27], in the example of Fig. 2(b). As with earlier studies in weidentifythe38-meVpeakastheresonantRamanscat- monolayer WSe [14], on top of the spectrally broad fea- tering of the 2LA(M) mode. The other higher overtones 2 tures (conventional X0 PL) sits a narrow peak arising from3LA(M)to6LA(M)arealsoidentifiedandindicated from resonant Raman scattering. in Fig. 2(c) with their respective excess energies. Like- Nowweturntotheassignmentoftheobservedphonon wise, we assign the 30-meV and 35 meV peaks to A(cid:48)(Γ) 1 modes. ThedominantfeatureintheX0 PLEistheaver- and E(cid:48)(Γ), respectively. Additional higher-order phonon ageoscillationperiodof18.5meV.Fromrecentmeasure- modeassignmentscanbefoundintheSupplementaryIn- ments of Raman scattering on monolayer MoSe [25, 27], formation. Similar PLE features with identical phonon 2 this period matches that of the M-point longitudinal modes are also observed in another sample (Supplemen- acoustic phonon, LA(M). Fig. 3(a) shows the loca- tary Information). tions of M points in the Brillouin zone. According to As required by momentum conservation during the ab initio calculations reported on monolayer MoS and Raman process, the total phonon wavevector of each 2 WS [28, 29], the electron-phonon interaction strength is phonon-enhanced PLE peak indicated in Fig. 2(c) must 2 largestforLAphononsinthevicinityofMpoints. Since be zero. This requirement is easily fulfilled by A(cid:48)(Γ) 1 monolayer MoSe is structurally similar to MoS and andE(cid:48)(Γ)modes,butnotthefundamentalLA(M)mode. 2 2 WS ,weexpectmodespecificcharacteristicsofelectron- However, for the LA(M) overtones, the requirement can 2 3 valley[31] might result in a larger exciton binding energy ofX0(M)thanthatofX0. Thisbindingenergydifference can partially cancel the electron band energy difference betweenQandKvalleys,leadingtoasmallerenergysep- aration between X0(M) and X0, which enhances the role of X0(M) as an intermediate state. A seemingly related intervalley exciton-phonon scattering is proposed to ex- plain the strong 2LA(M) peak in excitation-dependent RamanspectroscopyofWS [32],althoughtheexcitation 2 thereiniswellabovebandedgeandinvolveshigherlying conduction bands. We note that while oscillations due to phonon resonance feature prominently in the X0 transition, the X − emission intensity is relatively constant, except for excitation below 1.68 eV, close to the X0 resonance of 1.65 eV. The lack of oscillatory enhancement in X is possi- − bly due to its distinct radiative properties compared to X0, together with the availability of multiple formation pathways[33] (e. g. via the exciton-electron interaction following exciton relaxation[34]). For X0, only those inside the light cone (k ω /c) can radiate. In contrast, X0 FIG. 3. (a) Wavevectors of M-point phonons in a hexagonal ≤ X with a much larger range of momentum can radi- Brillouin zone. (b) Phonon mediated transitions of an elec- − tronbetweenKandQ¯ valleyswithintheBrillouinzone. Here, ate due to the electron recoil effect[23]. As a result, X0 three M-point phonons are involved, with zero net change of PL intensity depends strongly on its momentum distri- electron k-vector. Blue- and red-shaded regions correspond bution, as determined by the resonance condition of the toQ¯ andQvalleys,respectively. (c)Lowestconductionband excitationenergy,whilesuchdependencyisweakforX . − and top valence band of monolayer MoSe2, with the Q¯ val- Moreover, the X− formation process is largely indepen- ley indicated. Upon the LA(M)-phonon-mediated intervalley dentoftheexcitationenergy,becauseevenforexcitation scattering of an electron between Q¯ and K valleys, the opti- away from the phonon resonances, optically dark exci- callydarkindirectexcitonX0(M)canbeinterconvertedwith the optically bright exciton X0. Red and blue curves corre- tons can still be generated at large momentum (outside spond to different spins. thelightcone),whichcaninteractwithelectronstoform trions. The lack of sensitivity to the excitation energy in both trion formation and relaxation processes dimin- be satisfied through the following scenarios. In the case ishesanyoscillatoryfeaturesintheX− emission. Amore of 2LA(M), a combination of M and M¯ wavevectors con- detailed analysis can be found in the Supplementary In- serves momentum. In 3LA(M), this requirement is met formation. following the scheme shown in Fig. 3(b), where an equi- Asidefromspectralinformation,thePLEmapalsoof- lateral triangle is formed by three M vectors, also re- fers insights into the exciton dynamics. From the fit to sulting in a zero vector sum. In monolayer MoSe , in the spectrum taken at each excitation energy, we found 2 addition to the K and K¯ valleys (band edges), the con- that both X− and X0 lineshapes are well-described by duction band also has Q and Q¯ valleys located close to Voigt profiles, from which one can infer the homoge- halfwaybetweenΓandtheK/K¯ points. Themomentum neous linewidths of the excitonic transitions, as well as carried by an LA(M) phonon therefore matches the mo- the widths of the Gaussian-broadened spectral distribu- mentum separation between the K/K¯ and Q¯/Q valleys tions of their resonances (Supplementary Information). (Fig. 3(a) and (b)). Thus, following the involvement of The latter is associated with the inhomogeneous broad- M-point phonons, conservation of momentum stipulates ening of the excitonic transitions. Oscillatory behavior that the electron be scattered between K and Q¯ valleys; is found in the homogeneous linewidth, γ , of X0, which 0 see Fig. 3(c). In other words, phonon-assisted scattering issmallerforexcitationresonantwithphononharmonics occursbetweentheopticallybrightexcitonX0 withboth (Fig. 4(a)). Its inhomogeneous (Gaussian) width re- the electron and hole in K valley, and the optically dark mains relatively constant, consistent with the expecta- indirect exciton X0(M) with an electron in Q¯ and a hole tionthatinhomogeneousbroadeningshoulddependonly in K valley (Fig. 3(c)). Here, X0(M) can be a virtual weakly on excitation energy. Since γ is associated with 0 intermediate state such that its energy is not required the relaxation rate, this suggests that resonant excita- to match that of X0 + LA(M). Nonetheless, despite the tion of LA(M) phonons correlates with the subsequent estimated 0.2-eV[30] electron band energy difference be- X0 dynamics. tweenKandQvalleys, thelargereffectivemassoftheQ To explore the phonon-assisted dynamics directly, we 4 FIG. 4. (a) Oscillation in the best-fit homogeneous linewidth, γ , of the X0 resonance with excitation energy. Error bars 0 represent 99% confidence intervals of the fits. (b) An example of raw streak camera data for excitation centered at 1.732 eV. The trion (X−) and neutral exciton (X0) resonances are marked by dashed lines A—A’ and B—B’, respectively. Color bar: signalintensityinlog-scale,arbitraryunit. (c),(d)Time-tracesoftheX− andX0 resonances,respectively,afterdeconvolution (Supplementary Information), in log-scale. The 10%—90% rise-times are indicated, along with the best-fit exponential decay lifetime,τ. Circlesandredsolidlinesrepresentdatapointsandlinearfitstothe90%—10%decay,respectively. (e)Excitation frequency-dependentrisetimesofX− (crosses)andX0 (circles)emissionextractedfromaseriesofstreakcamerameasurements in varying excitation energy. (f) Excitation frequency-dependent lifetimes, τ, of X− (crosses) and X0 (circles). Error bars representthefitstandarddeviationsinboth(e)and(f),whilethedashedlinein(e)servesasguidetotheeye. Shadedregions indicate phonon resonances as obtained from Fig. 1(b). measure time-resolved emission of X0 and X with a times oscillate in accordance to the phonon modes seen − streak camera. (Method detailed in Supplementary In- in Fig. 1(b). Nonetheless, in Fig. 4(f) showing the formation.) Fig. 4(b) presents an example of the mea- emission lifetimes, despite the noise caused by excita- suredspectrawiththepulsedexcitationcenteredat1.732 tion pulse leakthrough at energies below 1.73 eV, the eV. The time evolution of the emission is characterized remaining data shows clear oscillations of the X0 emis- by a rapid onset within a few picoseconds, followed by sion lifetime. Remarkably, it agrees with the oscilla- an exponential decay. This is exemplified by extracting tions of γ as plotted in Fig. 4(a), where the emission 0 time traces along A—A’ and B—B’ from Fig. 4(b) for decay rate, proportional to γ , is higher for excitation 0 X and X0 and plotted in Figs. 4(c) and (d), respec- away from phonon resonances. To understand this ef- − tively, from which the 10%—90% rise time and lifetime fect, we propose a framework using rate equations to (τ) can be obtained. By stepping the center frequency modelphonon-assistedinterconversionsbetweenexcitons ofthepulses,excitationenergy-dependentrisetimesand inside and outside the light cone (Supplementary Infor- lifetimes are obtained and plotted in Figs. 4(e) and 4(f), mation). In brief, a thermalized population of excitons respectively, where shaded regions indicate energies of both inside and outside the light cone is formed shortly phonon-enhanced PL seen in the PLE map in Fig. 1(b). after excitation. The bright (inside the light cone) exci- Fig. 4(e) shows that measured rise times of X0 and tons quickly recombine[35, 36], leaving behind the dark X emissionfluctuatewiththeexcitationenergy. Unfor- excitons, which are then scattered into the light cone − tunately,duetomeasurementnoiseandtheresolutionof by phonons and recombine (Fig. 5(a)), producing the the streak camera, we are unable to observe an unam- observed exponential decay. When the excitation is off- biguous systematic variation with the excitation energy. resonant, excitonic relaxation results in the emission of Afurtherstudywithimprovedexperimentalmethodand many long-wavelength phonons (Fig. 5(b)), forming a cleaner data is needed to determine whether the rise phonon bath that increases the scattering rate. On the 5 Grant No. DMR-1120923. XX acknowledges a Cottrell Scholar Award, support from the State of Washington fundedCleanEnergyInstitute,andBoeingDistinguished Professorship. ∗ These authors contributed equally to this work. † [email protected] ‡ [email protected] FIG.5. (a)Schematicshowinginwardandoutwardscattering [1] M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa, and of the excitons across the light cone due to long-wavelength E. Hanamura, Excitonic Processes in Solids, 1st ed. phonons. (b) Energy level scheme showing optical excita- (Springer-Verlag Berlin Heidelberg, Berlin, 1986). tion (blue arrow) away from a phonon resonance, intervalley [2] A. Seilmeier, H. Hu¨bner, G. Abstreiter, G. Weimann, relaxations accompanied by the emission of LA(M) phonons and W. Schlapp, Phys. Rev. Lett. 59, 1345 (1987). (purplewavyarrows)andtheeventualfluorescence-producing [3] J. Bellessa, V. Voliotis, R. Grousson, X. L. Wang, radiative decay of X0 (red arrow). The laser generates X0 M. Ogura, and H. Matsuhata, Phys. Rev. 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Amand, A. Balocchi, P. Renucci, S. Tongay, B. Ur- baszek, and X. Marie, Phys. Rev. B 93, 205423 (2016). Phonon-Assisted Oscillatory Exciton Dynamics in Monolayer MoSe : Supplementary 2 Information Colin M. Chow,1, Hongyi Yu,2, Aaron M. Jones,1 John R. Schaibley,1 Michael ∗ ∗ Koehler,3 David G. Mandrus,3,4 R. Merlin,5 Wang Yao,2, and Xiaodong Xu1,6, † ‡ 1Department of Physics, University of Washington, Seattle, Washington 98195, USA 2Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China 3Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA 4Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5Center for Photonics and Multiscale Nanomaterials and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA 6Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, USA (Dated: January 10, 2017) This supplementary document is comprised of seven sections: (i) Sample preparation and experimental procedures, (ii) PL lineshape fitting, (iii) exciton rise time and lifetime extraction, (iv) exciton and trion decay rates in time-resolved luminescence, (v) exciton and trion steady-state dynamics, (vi) data from a second monolayer MoSe sample, and (vii) Raman spectrum of a third 2 monolayer MoSe sample. To simplify referencing, all labels for figures and tables in the supple- 2 mentary information begin with the letter “S”. I. SAMPLE PREPARATION AND a translational stage is used to block the frequency com- EXPERIMENTAL PROCEDURES ponentbelongingtotheexcitationlaser. Finally,fluores- cencespectraaremeasuredwithaliquid-nitrogen-cooled CCDcameraattachedtotheoutputportofaspectrome- Undoped MoSe crystals are synthesized using chem- 2 ter (Princeton Acton SP2500). The final spectral resolu- ical vapor transport technique with iodine as transport tion is 0.027 nm ( 0.06 meV at 755 nm), limited by the agent. To obtain monolayer MoSe samples, thin MoSe 2 2 ∼ pixel size of the CCD camera. Each spectrum is taken flakesaremechanicallyexfoliatedfrombulkcrystalsonto with an accumulation time of 5 seconds. SiO substrates thermally grown on Si wafers. Monolay- 2 ers are first identified visually by their optical contrast under a microscope and then confirmed by measuring theirthickness( 0.7nm)usingatomicforcemicroscopy. ∼ Throughouttheexperiments,thesamplesaremaintained at a temperature of 5 K in a cold finger cryostat. In time-resolved fluorescence measurements, the exci- All optical studies are made in reflection geometry, tationbeamisproducedbyawavelength-tunable,mode- where the incident beam and reflected fluorescence tra- locked Ti-Sapphire laser with a pulse repetition rate of verse the same microscope objective mounted on a mi- 80 MHz, and a pulse duration less than 100 fs. The crometer stage assembly. The use of a high-power mi- bandwidth of the output pulses, of about 17 meV, is un- croscope objective with cover-slip correction results in a suitable for resolving the oscillatory behavior which is focal spot size of less than 1 µm in diameter. For PLE expected to have a period of about 18.5 meV. The pulse measurements, a Ti-Sapphire tunable CW laser (Solstis bandwidth is therefore reduced to about 5 meV with the from M-Squared Lasers, LTD) is used to produce the aid of the spectral filter described above, only with the excitation beam. The incident power is held at 20 µW, graphite rod now replaced by a slit. This introduces a belowthePLsaturationthresholdofabout100µW.This chirp to the pulses, which is then compensated by pass- corresponds roughly to a typical exciton density[1, 2] on ing the beam through a single mode fiber with a specific the order of 1011 – 1012 cm 2. The excitation frequency length. The fiber serves a secondary purpose of produc- − isscannedatarateof5secondsperstepandwithastep ing a clean Gaussian beam profile to help achieving the size of 1 meV ( 0.42 nm at 721 nm). Rejection of the best beam spot on the sample. The central wavelength ∼ reflected excitation laser is accomplished first by an an- ofthepulsesistunedwith1-nmsteps( 2.4meVat721 ∼ alyzer and then by spectral filtering. The spectral filter nm), and the average power is held constant at 50 µW. consists of a pair of achromatic doublets forming a 1:1 A streak camera (Hamamatsu C10910-05) with a nomi- telescope, and a pair of gratings positioned at the out- nalresolutionof1psisusedtoregisterthetime-resolved ward conjugate focal planes. At the central focal plane, fluorescence spectra. The streak camera is operated at the spectral distribution of the fluorescence is mapped a moderate gain, optimized for the best signal-to-noise into spatial separation, and a graphite rod mounted on ratio, with a 100-s integration time for each spectrum. 2 II. PL LINESHAPE FITTING The PL lineshapes of both neutral exciton (X0) and trion (X ) are found to be inhomogeneously broadened − in such a way that the broadening is on the same order of magnitude as the natural linewidth. Therefore, neither Lorentzian nor Gaussian lineshapes adequately fit the spectra, as shown in Fig. S1(a). The failure of these lineshapes is most evident in the “wings” of the resonances, where the best-fit Lorentzian curve overesti- matesthesignalwhiletheGaussiancurveunderestimates it. Asmentionedinthemaintext,wefitthespectrawith Voigtprofiles,orplasmadispersionfunctions. Explicitly, the Voigt profile, V(ω;ω ,σ,γ), is given by the convolu- 0 tionbetweenaGaussiancurve,G(ω;σ),andaLorentzian curve, L(ω;γ): ∞ V(ω;ω ,σ,γ )=A G(ω ω ;σ)L(ω ω ;γ )dω 0 0 0 0 0 0 0 − − Z−∞ 1 G(ω;σ)= exp( ω2/2σ2) σ√2π − γ 0 L(ω;γ )= 0 π(ω2+γ2) 0 Here, A is a proportionality constant, ω and σ the 0 average (center) and standard of deviation of the normally(Gaussian)distributedresonance,respectively,and γ the half width at half maximum (HWHM) of the 0 Lorentzian. For every PL spectrum, two separate sets offittingparameters,A,ω ,σ,andγ areneededforthe 0 0 X and X0 resonances. Fitting is accomplished by min- − FIG. S1. (a) Full spectrum of Fig. 2(b) in the main text imizing the squared error by performing multivariable showing lineshape fits with Voigt, Lorentzian and Gaussian nonlinear regression. Some spectra feature prominent profiles, for both X− and X0 resonances. (b) Same as Fig. narrow lines attributed to resonant Raman scattering. 4(a) in the main text, reproduced here for easier reference: These are fitted manually with Gaussian curves. Since best-fit γ of the X0 resonance. (c) The center of the X0 0 thelinewidthsofthesenarrowfeaturesaremuchlessthan resonance as a function of excitation energy. Shaded regions thatofX andX0,theirpresencehasminimalimpacton indicate phonon resonances obtained from Fig. 1(b). Error − theaccuracyoftheVoigtprofilefits. Asanexample, the bars represent 99% confidence intervals, defined as 2.58 ± × standard error of fitted parameter. full-spectrumfitofFig. 2(b)inthemaintextisshownin Fig. S1(a)below. TheexcellentfitsproducedwithVoigt profiles for both X and X0 resonances justify their use. − energypartiallyfollowsthelaserdetuninginthevicinity The fitting parameters are given in Table S1 below. of phonon resonance. This is likely due to the combined Interestingly, the best-fit γ and ω for X0 vary in an 0 0 effect of inhomogeneous broadening, energy redistribu- oscillatory manner with respect to the excitation en- tion via long-wavelength phonon scattering and energy ergy,whereasthoseofX remainrelativelyconstant. As − conservation during intervalley relaxation. Nevertheless, shown in Fig. S1(b), γ of X0 is reduced when the exci- 0 the physical mechanism behind the modulation of exci- tationlaserisonaphononresonance. Sinceγ isrelated 0 ton resonance seen here remains to be explored. tothedecayrateoftheneutralexciton,thisimpliesthat X0 hasaslowerdecayrateforexcitationonaphononres- onance, an effect reproduced by a direct measurement of theluminescencedecayintime-resolvedPLEasshownin III. EXCITONIC RISE TIME AND LIFETIME Fig. 4(e)inthemaintext. Inaddition,Fig. S1(c)reveals EXTRACTION thatω alsooscillateswithaperiodcorrespondingtothe 0 LA(M) phonon mode. However, the oscillations are not In time-resolved PLE measurements, due to the fi- inphasewiththatofγ becauseheretherisingedgesco- nite response time of the streak camera, the output is 0 incide with the phonon resonances. Seemingly, the peak the convolution of the time-dependent emission with the 3 instrument response function, IRF. Since the timescale of MoSe exciton dynamics is in the picosecond range, 2 on the same order of magnitude as the nominal reso- lution (1 ps) of the streak camera, the measured time evolution of the emission will be noticeably stretched by about 1 ps. To obtain more accurate timing parameters, we perform deconvolution on the streak camera output withlinearleast-squaresregression[3]. Byscatteringlight from a mode-locked Ti-Sapphire laser with about 100 fs pulse width into the streak camera, we measured a 1.5 ps full-width-at-half-maximum (FWHM) response. This is shown in Fig. S2(a) (dotted line) below and taken as the IRF for deconvolution. To avoid overfitting and to improve numerical stability of the deconvolution pro- tocol, Tikhonov regularization[3] is applied. With an appropriate choice of Tikhonov factor, the noise in the reconstructed temporal profile can be suppressed without affecting the overall response, as exemplified by the time traces of the trion emission, before (dashed line) and after (solid line) deconvolution, in Fig. S2(a). The same deconvolution procedure is applied for all streak camera images taken at different excitation frequencies. Expectedly, we find that the rise times of X0 and X − emission are reduced by roughly 1 ps following deconvolution, as compared with those extracted from the raw data. Nonetheless, their variations with respect to excitation frequency remain qualitatively similar. From the deconvolved data, we obtain the rise times and lifetimes of X0 and X with respect to excitation − energy as presented in Fig. 4 in the main text. The rise time is simply defined as the time interval for which the rising edge of the luminescence moves from 10% to 90% ofpeakemission. Toobtainthedecayrate,alinearfitto the logarithm of the falling edge is applied between the 90%and10%levels,wheretheslopegivesthedecaytime FIG. S2. (a) Vertical time traces of trion emission from Fig. constant, γ. The extracted excitation dependent decay 4(b). Red dashed curve is the raw streak camera measure- rates for the first sample is shown in Fig. S2(b). To ment while blue solid curve the deconvolved data, with the facilitate comparison with the rise time, the data in the IRFrepresentedbythedottedline. (b)Excitationfrequency- main text is presented as the lifetime, τ = 1/γ. For the dependentdecayrate,γ,ofX− (crosses)andX0 (circles). (c) conversion of the error bars from (cid:15)(γ) to (cid:15)(τ), the first Samedataasin(b),presentedasthelifetime,τ. Reproduced order approximation (cid:15)(τ)=(cid:15)(γ)/γ¯2 is adopted, where γ¯ from Fig. 4(f). denotesthemeanvalueofγ. Theresultoftheconversion TABLE S1. Best fit parameter values for both X− and X0 is reproduced here in Fig. S2(c). transitions. Withtheexceptionofγ andω fortheX0 tran- 0 0 sition,allotherparametersgivenherearefoundtovaryonly slightly with respect to the excitation energy, and without a IV. EXCITON AND TRION DECAY RATES IN clear oscillatory feature. TIME-RESOLVED LUMINESCENCE Resonance Parameter Best-fit value (meV) γ0 2.30 0.05 The exciton dispersion curve is shown in Fig. S3(a), ± X− σ 2.80 0.05 where only excitons inside the light cone (k ω /c) ± X0 ω 1622.4 0.1 ≤ 0 ± can radiatively recombine. To model the exciton decay γ Varies. See Fig. S1(b) 0 process, we consider a simplified three-level system as X0 σ 2.80 0.05 ± shown in Fig. S3(b). D represents the dark exciton ω Varies. See Fig. S1(c) 0 | i state outside the light cone (k > ω /c), with time de- X0 4 constants, x and x . Under a low temperature we can f s take[5] Γ 3ps 1 γ such that (Γ +γ γ )2 r − 1 r 2 1 ∼ (cid:29) − (cid:29) 4γ γ ,thefast(slow)decayconstantx (x )isthengiven 1 2 f s by Γ +γ +Γ +γ Γ +γ γ x = t 2 nr 1 + ( r 2− 1)2+γ γ f 1 2 2 2 r Γ +γ t 2 ≈ FIG. S3. (a) Dispersion relation of neutral exciton, where Γ +γ +Γ +γ Γ +γ γ the horizontal axis represents center-of-mass momentum. x = t 2 nr 1 ( r 2− 1)2+γ γ s 1 2 2 − 2 The light cone (yellow region) corresponds to center-of-mass r wavevector, k ≤ ωX0/c, in which excitons are bright and ≈Γnr+γ1 canradiativelyrecombine(wavyarrow). Excitonsoutsidethe light cone are optically dark. Interconversion between bright Now x corresponds to the total decay rate of the bright f and dark excitons (dashed arrows) can occur via scattering. excitons inside the light cone, and x that of the dark s (b) Three level model for neutral excitons, with relaxation excitons outside the light cone. rates indicated. D : dark exciton, B : bright exciton, 0 : | i | i | i Theory has shown that bright excitons in monolayer vacuumstate. (c)Dispersionrelationofthetrion(solidblack curve) and its radiative decay (red wavy arrows). Unlike the TMDs have a very short radiative lifetime[5], as evi- exciton, the radiative decay rate of the trion varies slowly denced by the measured decay rate[4, 6] of xf 3ps−1. ∼ with k, such that the scattering induced by long-wavelength This value is significantly larger than the inverse of PL phonons(greencurvedarrows)barelychangestheoverallde- risetime(0.2–1ps 1)anddecayrate(0.2–1ps 1)given − − cayrate. Thethicknessofthewavyarrowsillustratesvarying in Fig. 4(e) and 4(f) in the main text. Possibly, in our decay rate with respect to wavevector. time-resolved measurements, by the time the recorded luminescence intensity reaches its maximum, the bright pendent density N (t), which nonradiatively decays to exciton density inside the light cone is depleted. The lu- D the vacuum state 0 with a rate Γ . B is the bright minescencedetectedatalatertimepredominantlycomes nr | i | i exciton state inside the light cone (with k ω /c), from scattering-induced dark-to-bright exciton conver- X0 ≤ bwoitthhtrimadei-adteivpeelnydeanntddnenonsirtaydNiaBti(vte)l,yw, hwicithhdaecatoytsatlor|a0tie, s0i.o2n,– w1hposs−e1d.ecTahyeravateriaistiogniveonf PbLy xdseca≈y Γtinmre+(xγs1−1∼) Γ = Γ + Γ . The nonradiative decay rate includes mainlycomesfromthemodulationofthescatteringrate, t nr r relaxation from excitons to trions. Scattering with other γ1, which increases with the density of long-wavelength excitons, free carriers, impurities, and long-wavelength phonons. A related behavior due to the weak scattering (small k) phonons can induce interconversion from D rate at low temperature, termed “exciton-phonon relax- | i to B andviceversa,withthecorrespondingratesgiven ation bottleneck”, has also been discussed in a recent | i by γ and γ , respectively. Given the meV linewidth paper[7]. 1 2 ∼ of excitons inside the light cone[4], interconversion from In contrast to the exciton, trion has rather different D to B can be induced by both phonon emission and radiative properties[5]. In particular, a trion with large | i | i absorption,whosecouplingstrengthsareproportionalto momentumcanradiativelydecay,asthemomentumcon- √N +1and√N ,respectively,whereN isthenumber servationcanbesatisfiedwiththeleft-behindelectronin- k k k of k-vector phonon. Consequentially, γ and γ increase herits the trion wavevector (the electron recoil effect[8]). 1 2 with N . The radiative decay rate varies slowly with the trion k N (t) and N (t) are governed by the coupled rate wavevector[5], suchthatscatteringwithlong-wavelength B D equations: phononsbarelychangestheoveralldecayrateofthetrion (seeFig. S3(c)). Therefore,unliketheexciton,triondoes d N = (Γ +γ )N +γ N not show lifetime oscillation with the excitation energy. B t 2 B 1 D dt − d N =γ N (Γ +γ )N D 2 B nr 1 D dt − V. EXCITON AND TRION STEADY-STATE Solving the above rate equations, we find DYNAMICS NB(t)=Ae−xft+Be−xst The contrasting behaviors of exciton and trion lumi- ND(t)=A0e−xft+B0e−xst nescenceinPLEwithexcitationenergycanbeexplained where A, B, A and B are time-independent constants by their distinct radiative properties. For the excitons, 0 0 determined by the initial values N (0). The PL emis- momentumconservationallowsonlythoseinsidethenar- B,D sion rate is given by Γ N (t), which has two decay time row light cone (k ω /c 10 3 ˚A 1) to radiatively r B X0 − − ≤ ∼