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F. Cadiz, S. Gerl, [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), [K. Watanabe](https://orcid.org/0000-0003-3701-8119)

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[Imaging the effect of high photoexcited densities on valley polarization and coherence in MoS2 monolayers](https://mdr.nims.go.jp/datasets/b7b1f9ba-f85d-4e23-931c-a8335e1c9fca)

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Imaging the effect of high photoexcited densities on valley polarization and coherence in MoS2 monolayersARTICLE OPENImaging the effect of high photoexcited densities on valleypolarization and coherence in MoS2 monolayersF. Cadiz 1✉, S. Gerl 1, T. Taniguchi 2 and K. Watanabe 3We have investigated the laser-induced valley polarization and coherence of encapsulated MoS2 monolayer as a function oftemperature, power density, and spatial position. Besides a non-monotonic dependence on temperature, recently attributed to adependence of the valley relaxation time on the momentum scattering rate, we observe a two-fold increase of the valleypolarization when increasing the laser excitation power. We attribute this effect to a local heating induced by the energy relaxationof photoexcited excitons and to an increase of the exciton-exciton scattering rate. In contrast, only a moderate enhancement ofvalley coherence is observed, which exhibits a dramatic drop after further increasing the excitation power. We attribute thisbehaviour to the detrimental role of exciton-exciton interactions on the pure dephasing rate responsible for the loss of coherencebetween the valleys. This manifests itself by a strong dip in the spatial profile of the valley coherence at high photoexciteddensities.npj 2D Materials and Applications            (2022) 6:27 ; https://doi.org/10.1038/s41699-022-00303-xINTRODUCTIONAtomically thin layers of transition metal dichalcogenides (TMD)such as MX2 (M = Mo, W; X = S, Se, Te) have emerged aspromising 2D semiconductors for applications in valley/spintro-nics1–3. In monolayers, the interplay between inversion symmetrybreaking and the strong spin-orbit interaction inherent to theheavy transition metal atoms yields a spin/valley texture at the K+/K− points of the Brillouin zone, which is expected to provideadditional functionalities in future devices2,4–6. Due to enhancedCoulomb interaction in 2D, weak dielectric screening and largeeffective masses, the optical excitation couples mostly to excitonresonances7–9. Remarkably, light absorption due to these stronglybound excitons preserves the single-particle coupling betweenlight chirality and the valley degree of freedom10–14. Moreover, theshort exciton lifetime at cryogenic temperatures15 is comparableto the dephasing time16, so that coherent superpositions of K+and K− valley excitons can be detected in simple steady-statephotoluminescence (PL) experiments17–19. However, there is still alack of understanding of the different microscopic mechanismsthat govern valley polarization and coherence in TMD monolayers.In this work, we have fabricated encapsulated monolayer MoS2heterostructures; and we present an investigation of the spatiallyresolved, steady-state valley polarization and coherence of neutralexcitons as a function of sample temperature and excitationpower density. At low excitation power, we find that both valleypolarization and coherence attain a local maximum at atemperature of 40 ± 3 K, in agreement with very recent observa-tions20. We show that, at a fixed temperature of T= 6 K, a similarenhancement of the valley polarization can be achieved byincreasing the laser power density. The valley polarization attains amaximum at a photoexcited density of n* ~ 5 × 1010 cm−2, andslowly decreases for densities above n*. We attribute this to twolaser-related effects: local heating and increased rate of exciton-exciton scattering events. The latter is particularly detrimental tovalley coherence, for which we see only a small enhancement atn*, and a dramatic decrease upon further increase of the excitationpower. Spatially resolved PL shows that valley coherence developsa significant spatial gradient at high densities, reflecting theimportant role of the exciton density on the dynamics of valleycoherence.RESULTS AND DISCUSSIONSample characterizationFig. 1 a shows a schematic drawing of the MoS2-based Van derWaals heterostructure deposited onto a SiO2/Si substrate. A thingraphite flake is used to screen possible charge puddles locatedon the SiO2 substrate21 and also to minimize reflections of the PLcoming from the substrate, which could affect PL imaging. Amicroscope image of the sample under white light illumination isshown in Fig. 1b. The high-optical quality of our sample isconfirmed by a ~2 meV neutral exciton linewith in PL at lowtemperatures and low excitation power, close to the homoge-neous limit16,19,22.Figure 1 c shows the spatially averaged PL spectrum,decomposed into its co-polarized (Ico) and cross-polarized (Icross)components with respect to the laser polarization for a lowexcitation power of 20 μW. Also shown is the degree ofpolarization at each emitted photon energy, defined asP ¼ ðIco � IcrossÞ=ðIco þ IcrossÞ. Under circular excitation, exci-tons are selectively generated in either the K+ or the K− valleydepending on the laser’s helicity. The steady-state degree ofcircular polarization of the PL, given by PC ¼ τv=τ, reflects theratio between the valley lifetime τv and the exciton lifetime τ.Under linear excitation, a coherent superposition of excitons in theK+ and K− valleys is generated17. The phase coherence betweenthe valleys in the superposition is lost after the valley coherencetime τvc given by 1=τvc ¼ 1=ð2τvÞ þ γ�v , where γ�v is the pure(valley) dephasing rate. Due to the very short exciton lifetime τ inthe picosecond (ps) range15,23–26, comparable to the valley1Laboratoire de Physique de la Matière Condensée, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. 2International Center for MaterialsNanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 3Research Center for Functional Materials, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba 305-0044, Japan. ✉email: fabian.cadiz@polytechnique.eduwww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00303-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00303-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00303-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00303-x&domain=pdfhttp://orcid.org/0000-0002-4773-8147http://orcid.org/0000-0002-4773-8147http://orcid.org/0000-0002-4773-8147http://orcid.org/0000-0002-4773-8147http://orcid.org/0000-0002-4773-8147http://orcid.org/0000-0002-3067-8352http://orcid.org/0000-0002-3067-8352http://orcid.org/0000-0002-3067-8352http://orcid.org/0000-0002-3067-8352http://orcid.org/0000-0002-3067-8352http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119https://doi.org/10.1038/s41699-022-00303-xmailto:fabian.cadiz@polytechnique.eduwww.nature.com/npj2dmaterialscoherence time τvc, this valley superposition is partially preservedbefore radiative recombination yielding a degree of linearpolarization PL ¼ τvc=τ of the PL. The observation PL >PC allowsone to conclude that, at these low photoexcitation densities, thevalley coherence time is mostly limited by τv.Temperature dependence of valley polarization andcoherenceRemarkably, increasing the sample temperature leads to anincrease of both the valley polarization PC and the valleycoherence PL, both peaking at T ~ 40 K, before decreasing againupon further increase of the temperature. This is in agreementwith very recent findings20. At T ~ 40 K the degree of valleypolarization can reach PC � 50%, whereas valley coherence canbe as high as PL � 60% although this maximum value was foundto be sample and position-dependent, probably due to inhomo-geneities of the dielectric environment and strain.These findings can be ascribed to a non-monotonic tempera-ture dependence of the valley lifetime τv that can be explained bythe competition of two mechanisms, as discussed by Wu et al.20.At low temperatures the valley lifetime is limited by the long-range electron-hole exchange interaction, in the so-calledMaialle–Silva–Sham (MSS) mechanism23,27. This interaction isequivalent to an effective magnetic field around which the valleypseudospin precesses with a Larmor frequency Ωð k!Þ, where k!isthe exciton’s center-of-mass momentum. This is similar to theDyakonov-Perel spin-relaxation mechanism in non-centrosymmetric semiconductors28. When the momentum relaxa-tion time τc is much shorter than the pseudospin precession timeΩ−1, the valley relaxation time varies as 1=ðΩ2ð k!ÞτcÞ. Hence,thermally activated momentum scattering (which shortens τc)suppresses the valley pseudospin relaxation. Increasing thetemperature will thus be accompanied by an increase of thevalley relaxation time τv. However, at sufficiently high tempera-tures the valley lifetime will no longer be limited by the MMSmechanism. Instead, it will be governed by an ultrafast intervalleyrelaxation driven by phonon mediated processes, which becomefaster than 1 ps above 100 K29. This is likely the reason why thevalley lifetime and coherence drop when increasing the tempera-ture above T ~ 40 K in our experiments. Under a tightly focusedlaser excitation, we can therefore expect the valley dynamics to bestrongly power and spatially dependent, which is why we will nowfocus on PL imaging at different photoexcited exciton densities.Figure 2 a shows the resulting image of the excitonluminescence at T= 6 K and 5 μW excitation power. The PLspatial distribution exhibits a clear rotational symmetry, so thatthe PL intensity depends only on the distance r with respect to thelaser spot. A radial profile of the PL is obtained by averaging cutsalong different directions, the result for Fig. 2a is shown in Fig. 2bfor both circular and linear excitation (blue squares and opencircles, respectively).Also shown is the normalized radial profile of the laser (blackopen circles), and its Gaussian fit (dashed line). Since the PL clearlyextends beyond the laser spot, we can obtain an effectivediffusion length L by fitting the PL intensity I with the convolutedsolution of the steady-state diffusion equation in 2D:IðrÞ /Z þ1�1K0 jrj=Lð Þe�ðr�r0 Þ2=σ2dr0 (1)where K0 is the modified Bessel function of the second kind andσ= 0.3 μm. This fit is shown by a red line in Fig. 2b and yields adiffusion length of L= 0.55 ± 0.025 μm at T= 6 K. Such a largediffusion length is unlikely to reflect the diffusion of brightexcitons. Indeed, considering a population decay time of τ ~ 5ps15, an exciton mass of mX ~m0, where m0 is the electron mass, atemperature of T= 10 K and a momentum relaxation time of τc=0.05− 1 ps20, we expect an exciton diffusion length in the rangeLX ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffikBTτcmXτs� 6� 28 nm (2)where kB is Boltzmann’s constant (here we have assumed thatEinstein’s relation is valid even for such a short-lived species). Thisis at least 18 times smaller than the observed effective diffusionlength of L ≈ 0.5 μm at T= 6 K. Moreover, it has been predictedthat exciton transport should be anisotropic under linearexcitation30, but as shown in Fig. 2b, no difference is observedin the spatial profiles between circular and linear excitation.Recently, it has been shown in encapsulated MoSe2 monolayersthat the PL intensity at cryogenic temperatures displays a spatialprofile that extends over 1.5 μm, for both neutral excitons andtrions despite their very different (and short) lifetimes. It has beenproposed that the observed PL spatial distribution at lowFig. 1 Temperature dependence of valley polarization and coherence of monolayer MoS2. a Schematic side-view of the sample. The MoS2monolayer is encapsulated between two thin h-BN flakes to provide high-optical quality and to prevent photodoping effects. A thin graphiteflake is used to screen charge disorder from the substrate and to avoid back reflections for PL imaging. The whole heterostructure is depositedonto a silicon substrate with a 90 nm-thick silicon dioxide layer. b Microscope image of the sample. The length of the scale bar is 10 μm.c Polarization-resolved PL spectra under linear (top) and circular (bottom) excitation at 1.96 eV for different sample temperatures. Theexcitation power was kept at 20 μW. Also shown is the degree of polarization as a function of photon emission energy. The dashed lines are aguide to the eye indicating the polarization at the energy at which the PL intensity is maximum.F. Cadiz et al.2npj 2D Materials and Applications (2022)    27 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;temperatures is likely to be the result of fast hot-excitonpropagation which occurs before relaxing into the light-cone31.Indeed, the diffusion length of hot excitons can be orders ofmagnitude larger than that of bright excitons due to their muchlarger effective temperature32 and because the relaxation timeinto the light-cone can be larger than the exciton radiative lifetimeat cryogenic temperatures33. Varying the sample temperatureproduces a slight change in the measured effective diffusionlength L, as shown in Fig. 2c together with the degree of valleypolarization and valley coherence. It is found that L decreases from0.55 μm at T= 6 K down to 0.45 μm at T= 30 K. An increase of thescattering rate with temperature is indeed consistent with areduced distance over which hot excitons can travel beforeenergy relaxation. This simple picture explains why, when thetemperature is increased, L decreases while the valley polarizationand coherence increase. The non-monotonic behavior of L withtemperature could be due to the competition between ashortening of the momentum relaxation time and the increaseof diffusivity with temperature.Another key result which is consistent with our interpretation ofthe PL profiles is the spatial dependence of the degree of circular(or linear) polarization of the PL. As shown in Fig. 2d, e, thepolarization is approximately constant in space at low excitationpower at T= 6 K. In our scenario, a spatially constant polarizationis consistent with the fact that the PL spot reflects the initial brightexciton distribution and not bright exciton diffusion. Onealternative explanation would be that both the valley polarizationand the valley coherence lifetimes are much longer than theexciton lifetime τ, so that no loss of polarization occurs duringexciton propagation. If this was the case, however, we shouldobserve a close to 100 %-polarized emission at low temperaturesand one should be able to observe a spatial decay of thepolarization at sufficiently high temperature. Figure 2f shows thatchanging the sample temperature up to T= 100 K only changesthe overall degree of polarization, but it remains spatiallyindependent at all temperatures.The role of exciton-exciton interactionsWu and co-workers20 have shown that the enhancement of valleypolarization can also be achieved by keeping a fixed temperatureand adding carriers to the system with the application of a gatebias. This was shown to be detrimental for valley coherence,however, due to an intervalley polaron dressing which results in ahigher scattering rate for the in-plane pseudospin. We studyanother mechanism of valley polarization enhancement: increas-ing the excitation laser power and, therefore, exciton-excitoninteractions. Figure 3a shows the total PL intensity as a function ofthe excitation power, in a large range going from 1 μW up to 10mW. Importantly, no change in the PL spectrum is observed afterlaser exposure at such high power densities, which permits us toexclude the presence of laser-induced photodoping effects34thanks to h-BN encapsulation. The linear regime, represented bythe red line in Fig. 3a, is valid below 100 μW. Increasing the powerleads to a sub-linear behaviour of the exciton luminescence. At100 μW, we can roughly estimate the photogenerated excitondensity to be n0 ~ 2 × 109 cm−2 by taking an absorption coefficientof α= 1 %, a lifetime τ= 5 ps and a uniform distribution inside acircle of radius L= 0.5 μm. We conclude that attributing this non-linearity to the onset of Auger-like exciton-exciton recombinationwould imply an extremely large Auger coefficient of γ ~ 1/(n0τ)=100 cm2 s−1. In addition, the behaviour observed in Fig. 3a cannotFig. 2 Imaging the spatial distribution of excitons and their valley index. a Spatially resolved PL intensity under cw laser excitation at 5 μWat T=6 K. The radial distance with respect to the excitation spot is denoted by r. The length of the scale bar is 1 μm. b Radial profile of the PLintensity shown in (a) obtained after averaging over different directions, for a circular (squares) and linear (open circles) laser excitation. Alsoshown is the laser profile (black circles) together with a Gaussian profile (dashed black line) with a radius of 0.3 μm. The red line is a fit with asolution of the 2D diffusion equation (Eq. (1)) giving an effective diffusion length of L= 0.55 ± 0.025 μm. c Degree of polarization under circularand linear excitation for an excitation power of 20 μW as a function of sample temperature. Also shown is the effective diffusion length Lextracted from the spatially resolved PL images. Continuous lines are a guide to the eye. d Spatially resolved linear polarization under linearexcitation for the same conditions as (a). Same scale as in (a). e Spatially resolved circular polarization under circular excitation for the sameconditions as (a). Same scale as in (a). f Radial profile of the photoluminescence’s circular and linear polarization for selected values of thesample temperature. The laser excitation is kept at 20 μW.F. Cadiz et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    27 be described by a simple model based solely on exciton-excitonannihilation since the latter predicts, at high densities, a variationof the intensity I of the form I / ffiffiffiffiffiffiPexpwhere Pex is the excitationpower, which does not fit the data. Instead, we attribute the sub-linear behaviour of the PL intensity to a local heating of the latticecreated by the relaxation of hot excitons31. At 10 mW, thelinewidth increases up to 10 meV (Fig. 3a) and the exciton peakredshifts by 5 meV, both consistent with a significant increase ofthe local temperature up to TL ≈ 100 K according to thetemperature dependence of the PL spectrum at low excitationpower (see Supplementary Notes 1 and 2). This indicates thatsources of line broadening other than exciton-phonon interac-tions do not seem to play a significant role. The PL yield of MoS2monolayer is reduced by almost one order of magnitude between6 K and 100 K (see Supplementary Note 1) and this cansignificantly contribute to the sub-linear behaviour of thephotoluminescence.Since in this temperature range the linewidth is much moresensitive to the temperature than the PL emission energy, wehave extracted the effective local temperature induced by thelaser excitation by comparing the power-induced broadening ofthe exciton linewidth with the temperature-induced broadening(shown in the Supplementary Note 1). The result is shown in Fig.3b, together with the degree of valley polarization PC and valleycoherence PL as a function of excitation power. We note that 100μW also corresponds to the onset of a rapid increase of the valleypolarization, with a two-fold increase from 20 % at low excitationpower up to 40% achieved at 1.5 mW. In this power range, theeffective local temperature starts to increase and reaches TL= 40K. This behaviour is remarkably consistent with the temperaturedependence of the valley polarization, confirming that local laser-induced heating is probably at the origin of the observedenhancement. Above TL= 40 K, valley polarization stops toincrease and eventually decreases again, but slightly and slowly.This is different, however, to what is expected based solely ontemperature effects, which should lead to a sharp polarizationdrop above TL= 40 K. This can be explained as follows: in additionto the increase of the local temperature, increasing the laserpower also modifies the rate of exciton-exciton collisions, whichshortens even further the momentum relaxation time τc, similar towhat has been observed in GaAs35 where the scattering rateincreases linearly with the photoexcited electron density andresults in an increase of the spin lifetime. This compensates for thethermal activation of valley relaxation mechanisms other than theMMS mechanism. As a result of the competition between thesemechanisms, the valley lifetime τv varies weakly above 1 mW.Eventually, exciton-exciton interactions will negatively impact thevalley lifetime and so τv starts to decrease36.Note that, in contrast, valley coherence shows a significantlyreduced enhancement effect between 100 μW and 1.5 mW, andrapidly decreases upon further increase of the excitation power.The reduced enhancement is probably due to the competitionbetween an increase of the valley relaxation time τv and anincrease of the valley dephasing rate γ�v induced by exciton--exciton interactions, which are expected to be significant atphotoexcitation densities comparable to n* ~ 1010 cm−236. Indeed,the typical distance between excitons in the n= 1010−1011 cm−2density range is of the order of ℓ � 1=ffiffiffiffiffiffiπnp ¼ 18� 56 nm, whichseems to compare well with the estimated bright exciton diffusionlength. This exciton-exciton interaction is expected to causesimilar detrimental effects on valley coherence as, for example,additional charge carriers as recently observed20. Since weobserve that the valley lifetime τv varies weakly at high excitationdensities above 1 mW, the rapid decrease in valley coherence canbe explained by a significantly increase of the pure dephasing rateγ�v that becomes the limiting mechanism that breaks phasecoherence between the K+ and K− valleys. For a more quantitativeanalysis of the effect of the photoexcited exciton density n on thevalley dephasing rate γ�v , we plot in Fig. 3c the quantityPC=PL � 1=2ð Þ=PC ¼ τγ�v as a function of the estimated photo-excited exciton concentration n. We observe a linear relationshipbetween τγ�v and n, the red line is a fit given byτγ�v ¼ 1:0þ 1:5 nð1011cm�22Þ. Taking an exciton lifetime oftypically τ= 5 ps yields thereforeγ�vðnÞ ¼ 0:2þ 0:3 nð1011cm�22Þps�1: (3)Spatial profiles at high exciton densitiesWe finally focus on the spatial evolution of the valley polarizationand coherence when increasing the laser power. The normalizedradial profiles of the exciton luminescence for selected excitationpowers are shown in Fig. 4a. They reveal a moderate broadeningof the exciton distribution, probably due to a spatially dependentmomentum relaxation time and PL yield which flattens the radialprofiles near r= 0. It can also be the beginning of the formation ofa halo-like profile due to Seebeck drift under the presence of atemperature gradient31,37,38. Remarkably, the radial profiles for thevalley polarization and valley coherence exhibit very differentbehaviour. The valley polarization, shown in Supplementary Note3, is found to be spatially independent for excitation powersbelow 2 mW. This indicates that the mechanism responsible forthe valley polarization enhancement in this power range isspatially homogeneous. In our scenario, this implies that the localtemperature TL varies slowly accross the PL spot size. This isconsistent with the absence of a clear halo-like profile for the PLintensity31. At higher powers, exciton-exciton interactions begin toshorten the valley lifetime36 and, therefore, generate a spatialdependence of the emitted circular polarization which exhibits asmall dip at the center above a few mW. Valley coherence, incontrast, develops a significant dip at r= 0 above 1 mW as shownin Fig. 4b, consistent with the strong variation of the valleyFig. 3 Spatially averaged valley polarization and coherence at high excitation densities. T = 6 K. a Integrated PL intensity (blue dots) as afunction of the laser excitation power. The red line represents a linear relationship between intensity and excitation power. The excitonlinewidth is shown in black squares. b Degree of polarization as a function of the laser excitation power. Also shown is the effectivetemperature extracted from the linewidth of the neutral exciton peak. The continuous lines are a guide to the eye. c Extracted γ�vτ product as afunction of the exciton density, where τ is the exciton lifetime and γ�v the pure dephasing rate of valley coherence.F. Cadiz et al.4npj 2D Materials and Applications (2022)    27 Published in partnership with FCT NOVA with the support of E-MRSdephasing time γ�v with exciton concentration deduced from Fig.3c. Since γ�v varies much more than τv with the exciton density inthis regime, the spatial dependence of the valley coherencereflects directly the influence of the local exciton density n(r) onthe pure valley dephasing time γ�vðrÞ. To test the validity of ourinterpretation, we have fitted the spatial dependence of the valleycoherence PLðrÞ ¼ τvcðrÞ=τ with a simple model that considersτ= 5 ps and the valley lifetime τv as constants and takes intoaccount the spatial variation of the exciton density n on the valley-coherence time through Eq. (3), so thatτvcðrÞ ¼ 12τvþ γ�vðnðrÞÞ� ��1(4)Here, n(r)= αPexn0(r) where α is a free parameter of the model, Pexis the excitation power and n0 is the normalized convolutedsolution of the diffusion equation which reproduces the PL profileat low power. The resulting curves (together with n0(r) forcomparison) are shown as solid lines in Fig. 4b, reproducing quitewell the experimental data with α= 0.42 × 1011 cm−2mW−1. Thevalley lifetime τv is treated as a free parameter for each excitationpower, and the result as a function of the (spatially averaged)exciton density is shown in Fig. 4c, together with the valleycoherence time τvc. Of course, these extracted lifetimes depend onthe particular choice of τ that we have used, and should not beconsidered as precise since they are the result of a rather simplemodel that captures nevertheless the essential physics behind thespatial variation of the valley coherence. Below 1010 cm−2, bothlifetimes are enhanced due to the increase of τv with the localtemperature, whereas above n*= 1010 cm−2 the exciton-excitoninteractions reduce τv but also γ�v , the result being a dramatic dropof the valley coherence time τvc. Although the identification of theexact mechanism by which exciton-exciton interactions shortensthe pure dephasing time γ�v goes beyond the scope of this work,one can consider for example a polarization-dependent exciton-exciton interaction. This leads to a precession of the valleypseudospin around the z-axis, similar to the mechanism predictedfor exciton polaritons in microcavities39,40.CONCLUSIONSIn summary, this work brings additional elements for theunderstanding of the different mechanisms that may influencethe dynamics of valley polarization and valley coherence in TMDmonolayers. We have shown that, in addition to increasing thesample temperature or the resident carrier density, valleypolarization can be enhanced by increasing the photogeneratedexciton density up to ~1010 cm−2. Further increase of theexcitation density, together with the significant increase of thelocal temperature, compensate (and eventually counteracts) thisenhancement of valley polarization. Valley coherence is shown tobe only moderately enhanced, before dropping quickly as afunction of the exciton density due to a significant increase on thepure dephasing rate, demonstrating the detrimental effect ofexciton-exciton interactions for the preservation of coherentsuperposition of valley excitons.METHODSEncapsulated MoS2 monolayers such as the one shown in Fig. 1a, b werefabricated by mechanical exfoliation of bulk molybdenite crystals from themanufacturer’s 2D semiconductors. The layers were deterministically andsequentially transferred onto an SiO2 (90 nm)/Si substrate by using atransparent viscoelastic stamp41. A hyperspectral confocal micro-PL set-upis used to excite and detect the polarized exciton emission at cryogenictemperatures42,43. The samples are excited with a continuous wave (cw)solid-state laser at 633 nm (~1.96 eV), tightly focused onto a diffraction-limited spot in the sample plane. At T= 6 K, this laser is detuned by 23meV from the neutral exciton transition. The Airy-disk of the laser’sintensity on the sample plane can be approximated by a gaussian profile ofthe form e�r2=σ2 , with r the radial distance from the center of the laser spotand σ ≈ 0.3 μm. The polarization of both the laser and the detected PL iscontrolled with liquid crystal retarders and linear polarizers. The resultingPL spot is imaged onto the entrance slit of a 320 mm focal lengthspectrometer equipped with a 600 grooves/mm diffraction grating. For PLimaging, tunable filters were used to select the neutral exciton emission,whose spatial distribution was then imaged onto a cooled Si-CCD camera.Reporting summaryFurther information on research design is available in the Nature ResearchReporting Summary linked to this article.DATA AVAILABILITYThe datasets generated and/or analyzed during the current study are available fromthe corresponding author on reasonable request.Received: 29 October 2021; Accepted: 14 March 2022;REFERENCES1. Behnia, K. Condensed-matter physics: polarized light boosts valleytronics. Nat.Nanotechnol. 7, 488 (2012).Fig. 4 Spatial dependence of valley coherence at high excitation densities T=6 K. a Normalized PL profiles for selected excitation powers.b Spatially resolved valley coherence for selected excitation powers. The continuous lines are obtained by fitting with Eq. (4). Also shown is thenormalized concentration profile n0(r). (c) Extracted valley lifetime τv and valley coherence time τvc from the fitting of the curves shown in (b).The continuous liens are a guide to the eye.F. Cadiz et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    27 2. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics inmonolayers of MoS2 and other group-vi dichalcogenides. Phys. Rev. Lett. 108,196802 (2012).3. Butler, S. Z. et al. Progress, challenges, and opportunities in two-dimensionalmaterials beyond graphene. ACS Nano 7, 2898 (2013).4. Li, L. et al. Room-temperature valleytronic transistor. Nat. Nanotechnol. 15, 743(2020).5. Li, L. et al. Electrical switching of valley polarization in monolayer semiconductors.Phys. Rev. Mater. 4, 104005 (2020).6. Huang, Z. et al. Robust room temperature valley hall effect of interlayer excitons.Nano Lett. 20, 1345 (2020).7. Ramasubramaniam, A. 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Deterministic transfer of two-dimensional materialsby all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).42. Favorskiy, I. et al. Circularly polarized luminescence microscopy for the imaging ofcharge and spin diffusion in semiconductors. Rev. Sci. Instrum. 81, 103902 (2010).43. Cadiz, F. et al. Exciton diffusion in WSe2 monolayers embedded in a van derWaals heterostructure. Appl. Phys. Lett. 112, 152106 (2018).ACKNOWLEDGEMENTSF.C. acknowledges the Grant “SpinCAT” No. ANR-18-CE24-0011-01. F.C. would like tothank X. Marie and C. Robert for fruitful discussions. K.W. and T.T. acknowledgesupport from the Elemental Strategy Initiative conducted by the MEXT, Japan (GrantNumber JPMXP0112101001) and JSPS KAKENHI (Grant Numbers 19H05790,20H00354, and 21H05233).AUTHOR CONTRIBUTIONSF.C. conceived and planned the experiments, and supervised the findings of thiswork. F.C. and S.G. carried out the experiments and data treatment. F.C. wrote themanuscript. T.T. and K.W. have provided the hBN crystals.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-022-00303-x.Correspondence and requests for materials should be addressed to F. Cadiz.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022F. Cadiz et al.6npj 2D Materials and Applications (2022)    27 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-022-00303-xhttp://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Imaging the effect of high photoexcited densities on valley polarization and coherence in MoS2 monolayers Introduction Results and discussion Sample characterization Temperature dependence of valley polarization and coherence The role of exciton-exciton interactions Spatial profiles at high exciton densities Conclusions Methods Reporting summary DATA AVAILABILITY References Acknowledgements Author contributions Competing interests ADDITIONAL INFORMATION