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Xin Cong, Parisa Ali Mohammadi, Mingyang Zheng, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Daniel Rhodes, Xiao-Xiao Zhang

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[Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe2](https://mdr.nims.go.jp/datasets/cdba9004-c365-4215-8a2e-93c89941cd58)

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Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe2Article https://doi.org/10.1038/s41467-023-41475-4Interplay of valley polarized dark trion anddark exciton-polaron in monolayer WSe2Xin Cong1, Parisa Ali Mohammadi 1, Mingyang Zheng1, Kenji Watanabe 2,Takashi Taniguchi 3, Daniel Rhodes 4 & Xiao-Xiao Zhang 1The interactions between charges and excitons involve complex many-bodyinteractions at high densities. The exciton-polaronmodel has been adopted tounderstand the Fermi sea screening of charged excitons in monolayer transi-tion metal dichalcogenides. The results provide good agreement withabsorption measurements, which are dominated by dilute bright excitonresponses. Here we investigate the Fermi sea dressing of spin-forbidden darkexcitons in monolayer WSe2. With a Zeeman field, the valley-polarized darkexcitons show distinct p-doping dependence in photoluminescence when thecarriers reach a critical density. This density can be interpreted as the onset ofstrongly modified Fermi sea interactions and shifts with increasing excitondensity. Through valley-selective excitation and dynamics measurements, wealso infer an intervalley coupling between the dark trions and exciton-polaronsmediated by the many-body interactions. Our results reveal the evolution ofFermi sea screening with increasing exciton density and the impacts ofpolaron-polaron interactions, which lay the foundation for understandingelectronic correlations and many-body interactions in 2D systems.Excitonic physics in 2D semiconductors of monolayer transitionmetal dichalcogenides (TMD) has attracted great attention for overa decade1. This 2D system hosts exceptionally strong excitonicinteractions, different excitonic complexes, and rich valley and spindegrees of freedom1,2. In the presence of free charges, a new exci-tonic resonance appears below the neutral exciton energy. Thischarged excitonic resonance has been initially assigned to the three-body trion state, in which an additional charge binds with anexciton3. Recent experimental and theoretical studies reveal that theinteractions between the charge-neutral excitons and free carriersmimic the Fermi-polaron responses4–13, especially at a higher dopingdensity, where an exciton interacts not only with a single-particlefree charge but with Fermi sea fluctuations. At a low doping density,many-body interactions between charges and excitons are notstrong, and the initial neutral exciton and trion modeling are suffi-cient. As doping increases, neutral excitons and trions are expectedto go through a smooth transition into repulsive and attractiveexciton-polarons, accompanied by blueshifts and redshifts inenergy. These energy shifts, as well as the evolution of the excitonicoscillator strength measured from the bright excitons up to mod-erate doping, agree with the theoretical calculations using theexciton-polaron picture5,8,13.The Fermi-polaron model treats the quasiparticle responses of asingle mobile impurity in a surrounding Fermi sea14–16. In comparison,the exciton density in monolayer TMD can be tuned by laser fluenceand be comparable to or exceed the charge density, where the analogyto a single mobile impurity no longer applies. The modification toFermi sea screening at high exciton densities, however, is still not wellunderstood. Apart from the bright excitons previously studied inreflection contrast measurements4,6,7,11,12, different spin and momen-tum dark exciton species have been established, which are alsoexpected to have many-body interactions with charges. The couplingbetween these different species of exciton-polarons has not yet beenexperimentally investigated.Received: 14 May 2023Accepted: 6 September 2023Check for updates1Department of Physics, University of Florida, Gainesville, FL, USA. 2Research Center for Functional Materials, National Institute for Materials Science, 1-1Namiki, Tsukuba, Japan. 3International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan.4Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA. e-mail: xxzhang@ufl.eduNature Communications |         (2023) 14:5657 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2857-2778http://orcid.org/0000-0002-2857-2778http://orcid.org/0000-0002-2857-2778http://orcid.org/0000-0002-2857-2778http://orcid.org/0000-0002-2857-2778http://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/0000-0003-3701-8119http://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/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-5447-3394http://orcid.org/0000-0002-5447-3394http://orcid.org/0000-0002-5447-3394http://orcid.org/0000-0002-5447-3394http://orcid.org/0000-0002-5447-3394http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41475-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41475-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41475-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41475-4&domain=pdfmailto:xxzhang@ufl.eduHere we study the trion to exciton-polaron crossover for spin-forbidden dark excitons in a WSe2 monolayer and further reveal theinteractions between valley-polarized dark polarons. The spin-forbidden dark excitons correspond to the spin ±1 energy ground-state excitons in tungsten-based monolayer TMD due to the oppositespin alignment between the bottom conduction band and the topvalence band17–19. Optical detection of these dark states is possible byapplying an in-plane magnetic field19–21 or through a weak out-of-planedipole emission in photoluminescence (PL)18,22,23. Compared to theoptically-allowed bright excitons, these dark excitons hold muchlonger exciton and valley lifetimes due to the lack of a rapid radiativechannel and the absence of intervalley exchange interactions19,24. Inthis report, we extracted and analyzed the Zeeman-split dark excitonPL at the p-doping side with Fourier plane imaging spectroscopy. Adistinctively different doping dependence was observed for the K andK’ valley dark trions as the doping increased across a critical density,which corresponds to the onset of strong Fermi sea screening effects.We characterized the shifting of the critical density as the excitondensity increases with pulsed excitation and extracted the modifica-tion to polaron screening from the dilute to high exciton density. Theexciton dynamics for the different valley-polarized dark trions werefurther examined with time-resolved PL. Combined with valley-selective excitation measurements, we reveal the many-body interac-tions between the K and K’ valley dark trion and exciton-polaronmediated by the Fermi sea fluctuations.ResultsTwo-segment gate dependence of dark trion PLA low excitation density is first used to investigate the dark exciton PLin the dilute exciton limit. Figure 1a shows the gate-dependent PL froman hBN-encapsulatedmonolayerWSe2 device at 4 Kwith a pulsed laserof 1.88 eV and 0.6 µJ/cm2fluence (see “Methods”). The excitation laserwas linearly polarized unless otherwise specified. The different peakfeatures have been characterized in previous studies and are asso-ciated with bright exciton, dark exciton, phonon-assisted emissions,and multi-exciton complexes9,25,26. The spin-forbidden dark excitonshave a weak out-of-plane dipole and in-plane emission, while brightexcitons and dark phonon replicas have an in-plane dipole and out-of-plane emission. To explicitly examine the optically dark excitons, weused the Fourier plane imaging spectroscopy to obtain PL spectrawithboth photon energy and emission momentum resolutions27. The darkexciton contributions canbe extracted by comparing the PL’s differentmomentum distributions (see Supplementary Information for thesubtraction procedure). Figure 1b shows the extracted dark excitonswithin a zoomed-in gate voltage range. The peak at ~1.69 eV is theneutral dark excitonD,with the n-type andp-type dopeddark trionsD−and D+ observed at the positive and negative gate voltages,respectively.Under an out-of-plane magnetic field, the Zeeman-split p-typedark trions showdistinctly different doping dependencies, as shown inFig. 1d. The corresponding g-factors of the neutral dark exciton andp-type dark trions from their energy splitting are ~10, consistent withprevious reports28. The shifted electronic bands at the K and K’ valleysunder the magnetic field28 are sketched in Fig. 1c. Within the chargeneutral regime, the higher energy emission D1 excitons reside in the K’valley and the lower energyD2excitons are in theKvalley following theZeeman energy shifts, as labeled in Fig. 1c, d. The p-type dark trionshave the intervalley configuration as the lowest energy configuration,and excitonic structures of the corresponding D1+ (D1 dark exciton inK’ valley + K valley hole) and D2+ (D2 dark exciton in K valley + K’ valleyhole) are plotted in Fig. 1c. The PL signals of the D1+ (D2+) states comefrom the recombinationof theD1 (D2) excitonwhile leavingbehind theFig. 1 | Gate-dependent dark exciton PL. a Gate-dependent photoluminescence(PL) of an hBN-encapsulatedmonolayerWSe2. The charge neutral point is near 0 V.bThe spin-forbidden dark exciton PL spectra extracted fromFourier-plane imagingare shown in a zoomed-in gate voltage range. D corresponds to neutral dark exci-ton. D+ and D− correspond to p-type and n-type dark trions. c The schematics ofelectronic bands near K and K’ valleys under an out-of-plane magnetic field in amonolayer WSe2. σ+ (σ−) polarized light creates direct optical excitation (brightexciton) in the K (K’) valley. The experimental assignment of the valley index andcircular polarizations are shown in Supplementary Information Section 3. In thep-doped regime, dark excitons bind with a hole in the other valley to form anintervalley dark trion. D1+ and D2+ indicated the dark trions in the K’ and K valley,respectively. d The dark exciton PL spectra under a 9 T out-of-planemagnetic field,with otherwise the same conditions as in (c). D1+ and D2+ and the Zeeman-split darktrions as denoted in (c). The dashed line at ~ −2V marks the crossover betweenregion (i) and region (ii).Article https://doi.org/10.1038/s41467-023-41475-4Nature Communications |         (2023) 14:5657 2hole in the K (K’) valley. When increasing hole doping, additional holecarriers will first populate the K valley valence band and, therefore,should favor the formation of D1 trions, D1+, if the two trions are inthermal equilibrium. In contrast, D1+ and D2+ show clear two-segmentgate dependencies as the gate voltage Vg reaches a crossover voltageVc (~ −2 V), labeled as region (i) and (ii) in Fig. 1d. In region (i), D1+ andD2+ have similar amplitudes, linewidths, and their peak energy red-shifts are both around 0.8meV/V. As the doping increases into theregion (ii), D2+ shows a decrease in amplitudes as its linewidthbroadens. On the other hand, the emission intensity increases for D1+,and its peak energy has a larger redshift as the doping densityincreases, with a slope of ~2.0meV/V. In addition, D1+ shows a slightlinewidth narrowing within this range. With further hole dopingbeyond region (ii),D1+ intensity also decreaseswhile the bright trion PLintensity increases. The fitted amplitudes and linewidths of D1+ andD2+, as well as the data with higher dopings are included in the Sup-plementary Information (SI) Sections 2 and 4, and Figs. S2, 3 and 6.The two-segment doping dependence of dark trions in Fig. 1d canbe first qualitatively understood by considering the trion and exciton-polaron responses. At very low doping density (near zero Vg), thecharge density in the K and K’ valleys are both small. As dark excitonshave a long exciton lifetime, dark excitons in both valleys can scatterand bind with an additional charge in the other valley to form the D1+and D2+ trions despite the low doping density. The thermal non-equilibrium between two dark trions is expected due to the lack ofintervalley exchange, which can lead to their similar amplitudesdespite the valley charge imbalance. At a higher doping density, the Kvalley valence band will be filled to high enough doping density suchthat themodified Fermi sea screening (Fermi-polaronor Suris tetron29)gives rise to a larger exciton energy redshift, corresponding to theincreased redshift of D1+ in region (ii). The slope increase in the exci-tonic energy redshift from the region (i) to (ii) also qualitatively agreeswith the expected slope changes during the trion to exciton-polaroncrossover8,13,30.Fluence and magnetic field dependence of the crossoverbehaviorThe crossover point, Vc, that defines region (i) and region (ii) can beshifted by the exciton density, which also confirms our assignment oftrion to exciton-polaron crossover. Figure 2a, b demonstrates thecontrasting behaviors with different exciton densities using an on-resonance pulsed excitation. The doping level at −2 V is estimated tobe around 1:4× 1012=cm2 with the device geometry and the hBN gatingdielectric thickness using the geometric capacitance. The low excitondensity (<1 × 1011=cm2) scenario in Fig. 2a has consistent dopingdependence as shown in Fig. 1d. Measurements done with alternativecontinuous wave laser (1.96 eV, 05–50 µW) yield the same results asFig. 2a, as the exciton densitieswere low to remain in the dilute excitonlimit. With a high exciton density of ~1 × 1013=cm2 (estimated frombright exciton absorption) shown in Fig. 2b, the gate-dependent PLsignals remain in the region (i) throughout the same gate voltagerange. We extract this crossover behavior as a function of excitondensity by tracing the D1+ peak energy and slope changes as a gatevoltage function. A pulsed 1.88 eV laser is used for fluence-dependentmeasurements below to avoid significant changes in absorptionamplitudes as a function of gate and fluence. As shown in Fig. 2c, theFig. 2 | Fluence-dependent trion to exciton-polaron crossover. a Dark excitongate dependencewith low fluence excitation condition taken at 4 K, 9 T. The pulsedexcitation is chosen to be resonant with the bright neutral exciton at ~1.72 eV. PLspectrawere takenwith a long pass filter at ~1.69 eV to filter out the excitation laser.b Same measurements as in (a) taken with a high excitation fluence. Throughoutthe same gate voltage range, D1+ andD2+ remain in region (i). cTheD1+ peak energy(with pulsed 1.88 eV excitation) at low and high fluences are plotted to show theextractionand the shift of Vc. The2.5μJ=cm2 data aredisplayed vertically for clarity.TheD1+ energy shift canbefittedwith a two-segment linear dependenceon the gatevoltage. The crossing of the two linear functions, denoted by the inverted triangle,is taken as the Vc. d The percentage linewidth broadenings of the D2+ state arecompared for different fluences, with pulsed 1.88 eV excitation. The fitted resultsfor 50 and 100 µJ/cm2 have higher uncertainty because of the overall broadening ofthe PL signals at high fluences. The shaded areas are guides to eyes. c, d are bothtaken at 4 K, 9 T. e The fluence dependenceofVc as extracted fromD1+ peak energyshifts, which can befittedwith a linear function, indicated by the dashed line. fWiththe low fluence condition (2.5 μJ=cm2, pulsed 1.88 eV), the extracted Vc at differentout-of-plane magnetic fields at 4 K, and at 30K, 9 T.Article https://doi.org/10.1038/s41467-023-41475-4Nature Communications |         (2023) 14:5657 3D1+ peak energy canbe fittedwith two-segment linear functions for thelow and high doping regimes with a crossover point at Vc. The data for2.5 and 100 µJ/cm2 are plotted and vertically displayed for clarity,showing a shift of Vc from −1.92 to −2.65 V. The fitted region (ii) slopefor the high fluence data is smaller than that of lower fluence, which isalso consistent with expected charge screening effects at an elevatedexciton density. Figure 2e plots the extracted Vc as a function of themeasured fluences. As the exciton density increases with increasinglaserfluence, there is an increase inVc amplitude,whichcanbefitted toa linear functionof the gate voltagewith a slopeof−8meVper (µJ/cm2).The dark exciton density can be evaluated using 1% absorption of thefluence, which gives 3:3 × 1012=cm2 for 100 µJ/cm2fluence, and 1 V ofgate voltage change is estimated to provide ~0:7 × 1012=cm2 change indoping density. The fitted slope thus indicates the crossover requires~0.2 hole per extra exciton.The crossover onset can be alternatively extracted from thebroadening of the D2+ peak, which shows a consistent gate depen-dence as the D1+ energy slope changes. The percentage broadening ofthe D2+ compared to the narrowest linewidth for different fluency isplotted in Fig. 2d. The onset voltages extracted from the linewidth (seeSI) provide a similar slope of the Vc as a function of exciton density asthepreviousmethod (Fig. 2e).Here,we emphasize that theonset ofD1+slope change and D2+ broadening is similar only for linearly polarizedexcitation and, therefore, with equal K and K’ valley excitations. Wecompare the distinctions with valley excitations and further discussthe D2+ dynamics in the latter part of the report and in SI Section 3.Notably, the crossover Vc is not sensitive to the magnetic fieldstrength, as shown in Fig. 2f, if the Zeeman splitting is sufficient to liftthe energy degeneracy of the two dark trions with minimal spectraloverlaps. This reveals that the observed crossover does not originatefrom the shifting of the Fermi level when it touches both Zeeman-splitvalence bands, in contrast with the magnetic field dependence in thebright exciton energy kinks in absorption31 shown in Fig. 3. At theobserved Vc ~−2 V in the dilute exciton limit, the Fermi level is also wellbelow both valance bands and corresponds to a doping density of1 × 1012=cm2 in the K valley and 4× 1011=cm2 in the K’ valley (takinggv = 1228 as the Zeeman splitting between the two valence bands). Onthe other hand, the crossover point Vc shows a significant increasewhen the temperature is higher (see Fig. 2f). This can be qualitativelyunderstoodby considering the thermal excitations of carriers athighertemperatures, which then require a higher doping to reach the samecritical doping density. The Γ5 phonon replicas of D1+ and D2+ alsoexhibit consistent gate dependence (see SI Section 4 and Fig. S6), inwhich we can observe the D2+ phonon replicas eventually show anincrease in energy redshift at even higher gate voltage when there aresufficient carriers in both valleys.Combing the above fluence dependence measurements, ourresults infer that, at the dilute exciton limit, a crossover to a stronglymodified Fermi sea screening occurs at a critical density ofnc = ð1 ±0:1Þ× 1012/cm2. This critical density corresponds to the carrierdensity in the K valley, and give rise stronger screening of D1+, fol-lowing the band schematics in Fig. 1c. Once reaching the nc, an furtherincrease of excitons density will require adding more charges torecover a similar screening effects. The extracted shift of 0.2 hole/exciton from Fig. 2e serves as a lower bound estimation. Consideringthe longer dark exciton propagation distance and the potential over-estimation of dark exciton density, the estimated shift can be 1–2 hole/exciton. The crossover at such a critical density is not expected withinthe current exciton-polaron picture, which predicts a smooth transi-tion between the trion and polaron at a much lower density5,8,13. Othercrossover mechanisms including the transition between trion-holecomplexes and exciton-polarons, and the development of rotons havebeen discussed in quantum wells32 and TMDs33,34, which predicts acomparably high crossover doping density. However, those discus-sionswere focusedonbright excitons and absorption signals. The darkexcitonic states do not show observable absorption signals and wecannot make a direct comparison. A microscopic understanding of ncis beyond the scope of this report and will require further theoreticalconsiderations.Dark excitons are generated through bright exciton absorptionand subsequent phonon-assisted relaxations, but this crossoverbehavior does not originate from the bright excitons’ gate depen-dence. Figure 3a shows the corresponding white-light reflection con-trast measurement of the sample. With a 9 T out-of-plane field, we canobserve Landau levels at high n- and p-type dopings, consistent withprevious reports10,31,35. At the p-doped side, the kink in the bright trionenergy has been assigned to the relative position of the Fermi levelcompared to the two valence bands31. The doping dependence of thebright trion absorption signal therefore has a strong magnetic fielddependence, which is distinctly different from that of the dark excitonFig. 3 | Gate-dependent reflection contrast spectroscopy. a Gate-dependentwhite light reflection contrast spectroscopy of the monolayer WSe2 device at 4 K,9 T. Landau level can be observed at high n-doped and p-doped regimes. b Thepeakenergy of the p-typebright trion as a function of gate voltages at different out-of-planemagnetic fields. cThe crossover voltages when the p-trion energy changesfrom redshift to blueshift with increasing doping density are plotted as function ofthe magnetic field. The 0T field data are omitted due to the relatively largeerror bar.Article https://doi.org/10.1038/s41467-023-41475-4Nature Communications |         (2023) 14:5657 4crossover behavior (Fig. 2f). We extracted the magnetic field depen-dence of the bright trion absorption “kink” by taking the gate voltagefor the p-type trion energy shifts from a redshift to blueshift (seeFig. 3c). Indeed, the “kink” transition voltage plotted in Fig. 3b shows alinear dependenceof 0.2 V/T. Taking the estimateddopingdensity andthe hole effective mass as ~0.4 me36, the extracted Fermi level shiftyields a g-factor of ~12 for the K andK’ valencebands, agreeingwith thereported value28. We also note that the onset of the “kink” does notoccur as the Fermi level is shifted down and touches the K’ valley(following the schematics in Fig. 1c), but instead occurs after thedoping of the K’ valley reaches ~1:2 × 1012=cm2, a doping density con-sistentwith the above extracted critical density from thedark excitons.Many-body interactions between valley polarized dark trionsFinally, we focus on analyzing the gate dependence of the D2+, whichshows a quenching at higher hole dopings, opposite to the con-ventionally expected behavior of charged excitons. We measured theD1+ and D2+ exciton lifetimes with time-resolved PL (TR-PL), in whichwe selectively probed the emission dynamics with large momentumnear the edge of the Fourier imaging plane to exclude the contributionfrom different bright states near the dark exciton energies. These darktrion lifetimes within this gate voltage range were measured to have adecay time of ~1 ns and therefore reach quasi-thermal equilibriumwithin each excitonic species. Figure 4a shows the TR-PL measure-ments of the D2+ peak (12.5 uJ/cm2 excitation) as a function of the gatevoltages. The exciton rise time of D2+ showed significant changesacross Vc (~ −2 V), while negligible changes were observed in the cor-responding dynamics of D1+ (see SI). The rise dynamics can be fittedwith two exponential rise functions, with a fast (<10 ps) and a slowcomponent (hundreds of ps). As summarized in Fig. 4d, the slow risetimes are around 200ps in the region (i), similar to the fitted results ofD1+. The rise time shows a significant slowdown with the further dop-ing increase in region (ii) and becomes comparable to the decay life-time. The flattened rising edge for the −3 V and −3.5 V traces in Fig. 4aresults from a rise and decay of similar time scales. Figure 4b, c showsthe zoomed-in TR-PL of the −2 V and −3 V measurements, and thefittings with different rise times are plotted for comparison.The lack of significant decay lifetime changes over this rangeindicates that no specific doping-activated relaxation channels con-tribute to the spectral changes in D2+. When considering the origin ofthe long rise time component, we first note that the photoexcitedelectrons into the optically-allowed upper conduction bands shouldrelax to the bottom conduction bands within a few ps from brightexciton PL lifetime. Thesedark trions are also the energy ground stateswith no known lower-energy exciton reservoir. The exciton rise time ofsimilar time scales has been associated with themomentum relaxationof excitons in previous studies in GaAs-based quantum wells37. Ourresults, therefore, suggest that there is a slowing down and blockage inD2+ momentum relaxation or exciton formation across the criticaldensity nc. The linewidth broadening can arise from increased phononscattering during the slow relaxation/formation process and theblockage above nc leads to the decrease in D2+ amplitude.To further verify the origin of D2+ spectral changes at higherdoping, circularly-polarized excitations were used to compare the D2+doping dependence with and without the presence of D1+. The valley-selective dark trion excitation pathway is explained in detail in the SI.With σ+ excitation, K valley bright excitons are excited and create ahigher electron population in the K’ valley through intervalley scat-tering, which leads to a higher D1+, K’ valley dark trion population(Fig. 4f). With σ− excitation, it directly excites K’ valley brightexciton and favors the formation of D2+ despite the lower hole popu-lation in the K’ valley (Fig. 4g). When comparing results with σ−polarization (D2+ excitation) and linearpolarization excitation (D1+ andD2+ excitation), the D2+ linewidth broadening showed a delayed onsetof 0.2 V (see SI for the fitted linewidths) and amore gradual amplitudedecrease. With the further doping increase, the energy separationbetween the D1+ and D2+ continues to decrease due to their differentenergy redshifts, which can lead to the broadening of D2+. Combinedwith the TR-PL discussed above, we can infer that the Fermi sea fluc-tuations in the K valley valence band due to D1+ contribute to thebroadening of D2+. These two dark states have no direct couplingwithin the single-particle picture. However, the formation andrecombination of D2+ will require a hole carrier within the same Fermisea that dresses the D1+ polaron and, therefore, can be affected aboveFig. 4 | D2+ dynamics and intervalley interactions. a Time-resolved PL of the D2+peak different gate voltages. b, c are the zoomed-in view of the D2+ rising edge at−2V and −3V. The solid red and green lines are the fitted dynamics with a 1 ns and0.2 ns rise time, respectively, and they are plotted to contrast the different risetimes. The black dashed line in (c) is the dynamics with zero rise time, which doesnot agree with the data. d The fitted rise time of D2+ as a function of the gatevoltage. The shaded area denotes the error bar of the time scales. At Vg < −3V, therise time is comparable to the decay time, making the upper bound estimationinaccurate. eAbove nc, Fermi sea in K valley interacts with the K’ valley dark excitonthrough Fermi seafluctuations. The same Fermi sea contributes to the K valley darktrion recombination, which correspondingly shows a possible blockage in emis-sion/formation. The K’ valley hole that binds with the K valley dark exciton isomitted for schematics clarity. f Gate-dependent PL spectra of dark trions (at thelow fluence limit, 4 K and 9 T) are shown with different circularly-polarized andvalley excitations. σ+ excitation favors the formation of D1+ trion and σ− favors theformation of D2+.Article https://doi.org/10.1038/s41467-023-41475-4Nature Communications |         (2023) 14:5657 5nc when correlations start to dominate. Our results suggest a strongcoupling between the different trion and exciton-polaron statesmediated by the Fermi sea fluctuations.DiscussionIn summary, we reveal complex interactions between the dark trionand dark exciton-polaron states in monolayer WSe2. By tracing theevolution of exciton screening as a function of charge and excitondensityieswe identified a critical densitync of ~1 × 1012=cm2 as an onsetof enhanced many-body interactions of the Fermi sea carriers for thedilute exciton limit. This crossover behavior at suchahighdensity ofncis beyond the current exciton-polaronmodel andmay imply additionalelectronic correlation effects suchasWigner crystals38,39. The Fermi seascreening of excitons is investigated with varying exciton density,which provides insights into the exciton-polaron modeling withexciton-exciton interaction.We also showa strong intervalley couplingbetween the dark trions and exciton-polarons that is mediated by themany-body interactions of the Fermi sea fluctuations. Our results laythe foundation for understanding the exciton-polaron effects afterincorporating the exciton-exciton interactions, which will be impor-tant for probing excitonic phase transitions, e.g., Bose-Einsteincondensation40, in 2D systems.MethodsSynthesis of WSe2 crystalsWSe2 single crystals were synthesized by a self-fluxmethod using Se asthe flux.Wpowder (99.999%, Alfa Aesar 12973) and Se shot (99.9999%,Alfa Aesar 10603) were sealed in a quartz ampoule under vacuum(~10−6 Torr). Subsequently, the ampoules were heated to 1080 °C over12 h, held there for 2 weeks, and cooled to 500 °C over 2 weeks. From500 °C, the samples were cooled to room temperature °C over 2 days.Subsequently, the resulting boule of Se flux and WSe2 single crystalswere reloaded into anewquartz ampoulewith aluminawool acting as afilter for the Se flux. The ampoules were heated to 300 °C and cen-trifuged. The then isolated single crystals were removed and sealed athird time in quartz and annealed in a temperature gradient(Thot = 275 °C, Tcold = 100 °C) with crystals on the hot end for 2 days toremove any remaining excess Se.Sample and device fabricationThe measured monolayer WSe2 was encapsulated with hBN, and topand bottom graphite layers were used as electrodes. An additionalstripe of graphite was attached to the WSe2 for grounding. All layeredmaterials were first mechanically exfoliated from their bulk crystalsonto SiO2/Si substrates and identified by their color contrast under awhite light opticalmicroscope. The 2Dmaterial stackwasbuiltwith thedry transfer technique using a PC stamp and released onto a substratewith pre-patterned gold electrodes.MeasurementsFourier plane imaging is achieved by placing an additional Fourier lens(~1m focal length) in the collection path to project the back focal planeonto the spectrometer CCD. Details of the setup and typical results areshown in the Supplementary Information. The laser excitation was thesecond harmonic of an optical parametric oscillator output fromCompact OPO pumped by Coherent Chameleon, with a repetition rateof 78MHz and pulse duration of 200 fs. Time-resolved PL was mea-sured with an avalanche photodiode (PicoQuant, PDM) coupled to atime-correlated single photon counter (HydraHarp 400). The col-lected PL signal was first sent into the spectrometer (Teledyne Prin-ceton Instruments, SpectraPro HRS 300) and was filtered in bothphoton energy and emission momentum before the time-resolved PLmeasurements. The decay and rise lifetimes are fitted with the con-volution of the instrument response function (~40ps FWHM). Allmeasurements were carried out in a closed-cycle optical cryostat(attoDRY 1000) with a base temperature of 4 K and a superconductingmagnet up to 9 T.Data availabilityThe data that support the findings of this study are available within thepaper and its Supplementary Information. Additional data are availablefrom the corresponding authors upon request.References1. Wang, G. et al. Colloquium: excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).2. Regan, E. C. et al. Emerging exciton physics in transition metaldichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778–795 (2022).3. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater.12, 207–211 (2012).4. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atom-ically thin semiconductors. Nat. Phys. 13, 255–261 (2017).5. Efimkin, D. K. & MacDonald, A. H. Many-body theory of trionabsorption features in two-dimensional semiconductors. Phys. Rev.B 95, 035417 (2017).6. 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All authors discussed theresults and commented on the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-41475-4.Correspondence and requests for materials should be addressed toXiao-Xiao Zhang.Peer review information Nature Communications thanks Yia-ChungChang, Erfu Liu and the other, anonymous, reviewer(s) for theircontribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-41475-4Nature Communications |         (2023) 14:5657 7https://doi.org/10.48550/arXiv.2006.04895https://doi.org/10.48550/arXiv.2006.04895https://doi.org/10.1038/s41467-023-41475-4http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe2 Results Two-segment gate dependence of dark trion PL Fluence and magnetic field dependence of the crossover behavior Many-body interactions between valley polarized dark trions Discussion Methods Synthesis of WSe2 crystals Sample and device fabrication Measurements Data availability References Acknowledgements Author contributions Competing interests Additional information