# Fileset [10.1515_nanoph-2023-0913.pdf](https://mdr.nims.go.jp/filesets/2fa89b55-7712-435f-b1f6-a4b00091bec4/download) ## Creator Aleksander Rodek, Kacper Oreszczuk, Tomasz Kazimierczuk, James Howarth, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Marek Potemski, Piotr Kossacki ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Interactions and ultrafast dynamics of exciton complexes in a monolayer semiconductor with electron gas](https://mdr.nims.go.jp/datasets/762ed750-f522-4547-ae90-0dd3ab333405) ## Fulltext Interactions and ultrafast dynamics of exciton complexes in a monolayer semiconductor with electron gasNanophotonics 2024; 13(4): 487–497Research ArticleAleksander Rodek*, Kacper Oreszczuk, Tomasz Kazimierczuk, James Howarth, Takashi Taniguchi,Kenji Watanabe, Marek Potemski and Piotr KossackiInteractions and ultrafast dynamics of excitoncomplexes in a monolayer semiconductorwith electron gashttps://doi.org/10.1515/nanoph-2023-0913Received December 12, 2023; accepted January 23, 2024;published online February 5, 2024Abstract: We present femtosecond pump-probe measure-ments of neutral and charged exciton optical response inmonolayer MoSe2 to resonant photoexcitation of a givenexciton state in the presence of 2D electron gas. We showthat creation of charged exciton (X−) population in a givenK+, K− valley requires the capture of available free carri-ers in the opposite valley and reduces the interaction ofneutral exciton (X) with the electron Fermi sea. We alsoobserve spectral broadening of the X transition line withthe increasing X− population caused by efficient scatteringand excitation induced dephasing. From the valley-resolvedanalysis of the observed effects we are able to extract the*Corresponding author: Aleksander Rodek, Faculty of Physics, Univer-sity of Warsaw, ul. Pasteura 5, 02-093 Warszawa, Poland,E-mail: aleksander.rodek@fuw.edu.pl.https://orcid.org/0000-0002-0263-3122Kacper Oreszczuk, Tomasz Kazimierczuk and Piotr Kossacki, Facultyof Physics, University of Warsaw, ul. Pasteura 5, 02-093Warszawa, Poland,E-mail: Piotr.Kossacki@fuw.edu.pl (P. Kossacki).https://orcid.org/0000-0001-8830-0005 (K. Oreszczuk).https://orcid.org/0000-0001-6545-4167 (T. Kazimierczuk).https://orcid.org/0000-0002-7558-1044 (P. Kossacki)James Howarth, National Graphene Institute, University of Manchester,M13 9PL, Manchester, UK. https://orcid.org/0000-0001-7434-9940Takashi Taniguchi, International Center for Materials Nanoarchitecton-ics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044,JapanKenji Watanabe, Research Center for Functional Materials, NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.https://orcid.org/0000-0003-3701-8119Marek Potemski, Faculty of Physics, University of Warsaw, ul. Pasteura 5,02-093Warszawa, Poland; Laboratoire National des ChampsMagnétiquesIntenses, CNRS-UGA-UPS-INSA-EMFL, 25 Av. des Martyrs, 38042 Grenoble,France; and CENTERA Labs, Institute of High Pressure Physics, PAS, 01-142Warszawa, Poland. https://orcid.org/0000-0001-8881-6618spin-valley relaxation times of free carriers as a function ofcarrier density. Moreover, we analyze the oscillator strengthand energy shift of X in the regime of interaction withelectron Fermi sea under resonant excitation. From thiswe can observe the process of X decay by radiative recom-bination paired with trion formation. We demonstrate anincrease of neutral exciton relaxation rate with the intro-duction of Fermi sea of electrons. We ascribe the observedeffect to the increased efficiency of the trion formation,as well as the radiative decay caused by the screening ofdisorder by the free carriers.Keywords: nonlinear spectroscopy; transition metal dichal-cogenide monolayer; Fermi sea; exciton; trion; ultrafastdynamics1 IntroductionSingle layers of semiconducting transition metal dichalco-genides (sTMDs) display a plethora of intriguing optical,electronic and valley properties which have driven largeinterest over the previous decade [1]–[5]. MoSe2 is uniqueamong sTMDs as the lowest available transition is also spinallowed [3], [6], [7]. The neutral exciton (X) resonance inthis material is accompanied by a ∼30 meV split trion orcharged exciton (X−) state with their relative amplitudesdepending on the carrier density, which may be influencedby a number of factors like the density of charged defects,hBN encapsulation or the properties of the optical excitation[8]–[10]. Large oscillator strengths (osc. str.) of these tran-sitions also facilitate studies of the dynamics of nonlineareffects; however, due to the short exciton lifetimes of a fewps, these attempts require ultrafast temporal resolutions[11]–[17]. Optically generated nonlinearities of neutral exci-ton transition, like bleaching, energy shifts and excitationinduced dephasing (EID) were observed, at least for thecase of naturally doped samples [17]–[22]. Recently, manystudies have turned towards probing the exciton-carrierinteractions. By means of electron beam litography oneOpen Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License.https://doi.org/10.1515/nanoph-2023-0913mailto:aleksander.rodek@fuw.edu.plhttps://orcid.org/0000-0002-0263-3122mailto:Piotr.Kossacki@fuw.edu.plhttps://orcid.org/0000-0001-8830-0005https://orcid.org/0000-0001-6545-4167https://orcid.org/0000-0002-7558-1044https://orcid.org/0000-0001-7434-9940https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-8881-6618488 — A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayercan manufacture electrodes in the vicinity of TMD flakesallowing for controlled tuning of the carrier density by theapplication of an external voltage [23]–[25]. This approachhas led tomilestone results in thefield of strongly-correlatedelectron systems: like Wigner crystallization [26], opticalsensing of the quantum Hall effect in graphene [27] andtunable quantum confinement of neutral excitons [28].Such carrier injection also directly influences the observ-able exciton transitions. Following the nomenclature coinedin atomic physics, the charged and neutral exciton statesare often described as attractive and repulsive polarons[29]. The experimental observations, as well as theoreticalmodeling of the interaction of excitons in TMDs with freecarriers point to pronounced changes of exciton energy,linewidth and oscillator strength [23], [24], [30]–[34] simi-larly to what has been observed for the traditional 2D sys-tems of II–VI [35]–[39] and III–V [40]–[42] quantum wells.Theoretical works also point to a significant influence ofcarriers on the specific relaxation dynamics of excitons [43].In particular, recent experimental studies on MoTe2 [44]show a significant prolongation of the valley polarizationfor larger densities of free carriers. This is also quite rel-evant in the context of the efficient exciton-trion forma-tion channel discovered in the naturally doped samples [9],whichmaybe partly responsible for the observable increaseof the exciton’s homogeneous linewidth with increasingcarrier density [45], [46]. Here, we consider these issues byfocusing on the exciton absorption,while capitalizing on thehigh temporal resolution of ultrafast pump-probe measure-ments on a charge-tunable monolayer (ML) MoSe2 sample.Incidence angle separation between the laser beams, whichfacilitates a high degree of filtering of the pump signal,allows us to perform measurements of the response of Xand X− transitions after selective excitation of a given state.Measurements performed for different configurations ofcircular polarizations probe the intra-/inter-valley excitondynamics and the influence of both valley occupations onthe excitonic absorption. In particular we show that theeffects observed under selective excitation of the K-valleycharged exciton can be explained by the capture of K′-valley electron leading to an effective change of the freecarrier density in one of the valleys and subsequent screen-ing of exciton interactions with the 2D carrier gas. Herewe are also able to pinpoint the effect of the neutral exci-ton dephasing induced by the population of photocreatedcharged excitons further elucidating the importance of cou-pling between these states. Time-resolved measurements inthe circular polarization basis allow us to probe the exci-ton valley and population dynamics in the first few ps andinvestigate their dependence on the increasing density ofelectron gas.2 Methods and samplecharacterizationIn Figure 1(a–b) we present an optical image of the sampleas well as the schematic of the heterostructure. It consistsof a single layer MoSe2 that was encapsulated between hBNflakes. Their thicknesses deduced from atomic force micro-scopemeasurements are hBNbottom = 34.5 nm and hBNtop ≈5 nm. In our case a graphite flake located below the thickhBN spacer acts as a bottom gate, while the top contacts aremade out of few-layer graphene flakes deposited directly onthe monolayer. The graphene/graphite flakes are connectedto golden contacts prepared by e-beam lithography.We opti-cally characterize the device by measuring reflectance of abroad fs laser (spectral full-width at half maximum FWHM≈ 40 meV) tuned between the neutral and charged excitontransitions (E ≈ 1642 meV, Figure 1(d)) in low temperature(T = 5 K). In the Figure 1(c) we show a differentialreflectance spectrum of the sample ((Rsample–Rref )/Rref ) withFigure 1: Sample characterization sample optical image (a) andheterostructure schematic (b). (c) Differential reflectance of the samplefor Vgate = 3 V with visible charged and neutral exciton resonances.(d) Normalized imaginary susceptibility obtained from Kramers–Kronigtransformation of the spectra in (c) with the reference fs laser spectrum.Dashed line indicates the cut-off energy for short-/long-pass filters usedfor resonant neutral/charged exciton excitation. (e) Electric scan of the Xand X− signal for Vgate=(−5:15)V Dashed line indicate the chargeneutrality point of the sample.A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer — 489the applied gate voltage of Vgate = 3 V in order to presentboth exciton resonances. By applying the Kramers–Kronigtransformation [20], [47], we obtain the imaginary partof sample’s susceptibility and disregard the interferencepatterns leading to the complex lorentzian shape of theexciton lines (Figure 1(c–d)). To characterize our sample asa function of free carrier density we tune the Vgate between−5 V and 15 V and present the obtained spectra in Figure1(e). The density of the free electrons induced by changingthe gate bias was calculated from a simple planar capacitormodel [23], [48] and equaled ne = 5.6 ∗ 1011 cm−2 per 1 V. Bychanging the gate voltagewe observe the expected responseof the neutral exciton peak to the increasing carrier density:(i) Transfer of the osc. str. from X to X−, (ii) Increase of the Xenergy, (iii) Broadening of the X peak.The pump-probemeasurements presented in this studywere performed in a back-reflection geometry [20]. Thebeams were focused onto the sample surface through ashort focal-length lens (f = 4 mm) with the spot diameter ofFigure 2: Polarization-resolved spectra of X and X− under X−-resonantexcitation. (a) Neutral and charged exciton spectra with/without X−excitation in the coincidence (Δt = 0) in a given circular polarizationconfiguration. Vgate = 1.6 V, ne = 11.8 ∗ 1011 cm−2, photocreated densityof nX− ≈ 2∗1011 cm−2. (b) Drawing of the influence of X− creation in a K+valley on the population of free carriers in K− valley. In the Fermi searegime of carrier density the photocreated population of X− binds withthe available free carriers effectively lowering electron densityin the opposite valley.the probing beam of d = 3.8 μm. This is particularly impor-tant for the case of measurements of TMD heterostructuresmanufactured through exfoliation-based methods as theynear-universally lead to significant spatial disorder. Thisaffects the exciton resonances, leading to large inhomoge-neous broadening. Microspectroscopy allows for the reduc-tion of such influence by probing a smaller sample area. Theoptical paths of the pump and probe laser beamswere sepa-rated by a small angle permitting us to distinguish betweenthe beams in the detection path. Both of the laser beamshad the same spectral shape centered between the excitonresonance. In the following experiments we used long- andshort-pass interference filters to select the pumping ener-gies to either above or below the energy of 1630 meV, whichallowed for the resonant excitation of either neutral orcharged exciton states. The temporal resolution of our setupwas limited by the time duration of the pulses 𝜎t ≈ 80 fs atthe sample surface.3 Selective excitation of X−We start our analysis with the simplest case of selectiveexcitation of X−. The charged exciton is the energetically-lowest state therefore the relaxation considered here is lessinvolved.Firstly, we discuss the results obtained at pulse overlapΔt = 0. We set the gate voltage to 1.6 V which correspondsto a relatively low-doping regime with ne = 11.8 ∗ 1011 cm−2,however with already visible effects of carrier gas impact:oscillator strength transfer (significant X− absorption) andenergy shifts (neutral exciton blueshift of a few meV). InFigure 2(a) we present the optical response of neutral andcharged excitons for different polarization configurations(co-/cross-circular) with the pumping beam resonant withthe charged exciton. The pump pulse induces pronouncedreduction of the charged exciton oscillator strength in theco-polarized case with no visible change of this state in theopposite valley. This can be understood when consideringthe charged exciton as a bound three particle complex oftwo electrons from opposite K± valleys and a hole. As wecreate a population of K+ charged excitons, the free carriersfrom the K− valley become bound. This in turn reduces theavailable density of free electrons for the creation of a K+charged exciton. This process is illustrated in Figure 2(b).Conversely the population of free electrons inK+ valley doesnot change and as such the K− charged exciton remainsmostly unaffected.We now consider the response of the neutral exci-ton when pumping charged exciton. In the case where weexcite X− in the same K+ valley the X resonance exhibits a490 — A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayerredshift of ∼ 1 meV, an increase of its oscillator strengthand a linewidth narrowing. Again, an explanation of theseeffects can be provided by considering the density of freecarriers in the opposite K− valley. As the K+ charged andneutral excitons share a common ground state, upon theillumination of the sample a photon of a𝜎+ polarization canbe converted to either of these states with the probabilityratio depending on the availability of free carriers in theopposite K− valley. This results in the oscillator strengthstealing from the neutral to charged exciton in K+ valley ifthe number of K− free carriers increases.Reduction of K− free carrier density through the pho-tocreation of K+ charged excitons quenches the Fermi sea-induced effects upon the neutral exciton state and resultsin the increased oscillator strength, as well as an effectiveredshift and decreased linewidth. Interestingly, similar phe-nomenahave also been reported for standardQWs [49], [50].The neutral exciton in the opposite valley shows noenergy change. This is understandable as the free carrierdensity in the K+ valley is not influenced by the creationof a K+ charged exciton. The only observable effect is itslinewidth broadening, which cannot be explained by con-sidering solely the free electron population. Consequentlyany changes in the K− neutral exciton signalmust be relatedto the population of photocreated bound carriers formingthe charged excitons. Therefore we point out that the result-ing linewidth broadening can be considered as an excitationinduced dephasing (EID) of neutral exciton by the popula-tion of charged excitons. This effect has also been previouslyreported in works that revealed coherent coupling betweenthese states [51], [52], however, it has not been investigatedin greater detail.In order to provide a more quantitative description ofthis effect we performed power dependent measurementsof neutral exciton absorptionwith resonant charged excitonexcitation.In Figure 3(a, b) we present the difference in the neu-tral exciton signal induced by the charged exciton illumi-nation versus the power of the pump laser beam. In theco-circular excitation casewe observe the dominating effectof energy shift aswell as the additional linewidth narrowingand osc. str. increase. For the case of the cross-polarizedexcitation we see the pronounced broadening of excitonlinewidth without any changes in its energy.Quantitative determination of the behavior of the res-onance parameters was performed by fitting a Lorentzianfunction to the X absorption signal. We show the fitted val-ues in Figure 3(c–e). In all related cases we find a lineardependence of the extracted parameters on the excitationFigure 3: Power dependence of neutral X absorption while underresonant X− excitation (Δt = 0), Vgate = 1 V, ne = 8.4 ∗ 1011 cm−2 Xdifferential absorption in co-(a) and cross-(b) polarized configurationunder resonant X− excitation as a function of pump power.(c–e) X energy shift, linewidth and oscillator strength in the co- andcross-polarized detection under resonant X− excitation as a functionof excitation power. Solid lines indicate linear fits to the data.power and thus the density of photocreated charged exci-tons. This confirms that we operate far from the saturationregime.For the energy of the neutral exciton the only changeis observed in the co-circular excitation scheme. Its depen-dence on the free carrier density can be quantified throughan effective parameter 𝜂:ΔE±X= 𝜂∗n∓e(1)Since the photocreation of a charged exciton requires acapture of a free carrier the remaining free carrier densityis given by n±e= n±gate− n∓X− , where ngate is the initial densityof carriers induced by the gate bias. From the Figure 3(c) weextract 𝜂 = (0.8± 0.3) ∗ 10−11 meV cm2. The value of 𝜂 canbe also independently derived from the exciton blueshiftin the gate-dependent reflection measurement where nX−= 0. In this case we obtain 𝜂 = (1.3± 0.1) ∗ 10−11 meV cm2.While the similarity of these values gives further evidenceA. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer — 491to the proposed interpretation of the observed phenomena,where optical control of carrier density can be achieved byresonant photocreation of charged excitons, small discrep-ancies are expected. This is because in contrast to the situ-ation where the gas density is controlled only by the gate,reducing electron density by binding it in charged excitonsstill leaves such bound electrons in the band. Furthermore,the extracted trends persist for different gate biases (seeSupplementary Material) indicating a constant magnitudeof the many-body interaction strength in the investigateddoping range.Similarly, in the Figure 3(d) we present the valuesof neutral exciton linewidth Γ and its dependence onthe photocreated density of X−. For the co-polarizedcase, the linewidth narrowing scales as ΔΓX = (−0.4±0.1) ∗ 10−11 meV cm2∗nX− . For the exciton in the opposite val-ley, the linewidth increases asΔΓX = (1.4± 0.3) ∗ 10−11 meVcm2∗nX− , reflecting the EID by the population of chargedexcitons in the opposite valley.Accordingly to the proposed interpretation theseeffects of linewidth narrowing/broadening in theco/cross-polarized excitation scheme also persist for theentire range of investigated bias values (see SupplementaryMaterial). Here, a more in-depth analysis is, however,obstructed by the presence of inhomogeneous additionto the exciton linewidth. Previous four-wave-mixingstudies [45], [46], which are able to independentlyextract the homogeneous and inhomogeneous linewidth,show, that increasing density of free carriers leads toincreasing homogenenous broadening, related to theshortening of exciton coherence time, as well as thescreening of disorder and decreasing inhomogeneousbroadening. In our case this leads to an effectivebroadening of exciton resonance as we increase thegate bias ΔΓX = (0.8± 0.1) ∗ 10−11 meV cm2∗ ne. Similarmagnitudes of exciton linewidth changes induced by thegate injection of free electrons and by their capture throughcharged excitons creation again point to the same originof these effects, as was the case for the considerations ofexciton energy shifts.As previously mentioned, the neutral exciton totalabsorption also changes, particularly for the case of co-polarized excitation as it displays a pronounced increase.Its dependence on the density of photocreated X− is pre-sented in the Figure 3(e). This behavior can be quantita-tively described as:ΔA±X= −AX (0)[𝛼∗n∓e+ 𝛽(n+X− + n−X−)](2)where AX (0) – neutral exciton osc. str. in the neutralityregime used here as a normalization parameter, 𝛼, 𝛽 –effective parameters quantifying the change in theX absorp-tion due to the population of free carriers and photocre-ated charged excitons. From linear fitting shown in theFigure 3(e)we determine𝛼 = (6.3± 1.4) ∗ 10−13 cm2 and𝛽 =(2.8± 0.6) ∗ 10−13 cm2Again the gate-dependent measurement give a consis-tent value of 𝛼 = (5± 0.2) ∗ 10−13 cm2. In the Supplemen-tary Figure S1 we also present the behavior of charged- andneutral exciton total absorption, illustrating the effect ofoscillator strength transfer.3.1 Time-resolved pump-probewith selective excitation of X−In order to investigate the ultrafast dynamics we haveperformed the pump-probe measurements with a variabledelay Δt between the laser pulses. In the Figure 4(a) wepresent the time evolution of neutral and charged excitonoscillator strengths and neutral exciton energy in the pump-probe measurement.For Δt = 0 we observe the previously mentionedchanges in the integrated osc. str. of the resonances, as wellas the neutral exciton energy redshift. The most strikingeffect occurs in the first few ps where we see a rapidlydecreasing difference in the polarization dependence of theobserved effects with a single characteristic time of tnr =(2.7± 0.2) ps.In order to gain further understanding of the mea-sured dynamics we develop a rate equations approach thatconsiders a change in population of free carriers n±ebyphotocreation of charged excitons n∓X− in the opposite K-valley. The dependence of neutral exciton energy and osc.str. on the simulated carrier populations is described bythe equations (1) and (2). Additionally, we introduce anotherparameter 𝛾 governing the change of the charged excitonoscillator strength:ΔA±X− = AX (0)[𝛾∗n∓e](3)In ourmodel we include two decaymechanisms impor-tant for the dynamics of X−:– the charged exciton decay with characteristic time tX−= 40 ps, which was independently extracted from thetime-resolved photoluminescence measurement on astreak camera (see Supplementary Material)– the intervalley scattering of free carriers tnr.The following set of rate equations was used for producingthe simulations of pump-probe experiments presented inthe Figure 4(a).492 — A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayerFigure 4: X, X− dynamics under X−-resonant excitation(a) valley-resolved X, X− amplitude and X energy shift dynamics underX−-resonant excitation in the first few ps. Solid lines denote valuesobtained from the simulations. Simulated population of photocreatedcharged excitons and related change in the free carrier density.Vgate = 1.6 V (b) valley-resolved dependence of the X redshift timeevolution for different gate voltages. (c) Extracted spin-valley relaxationtimes of free carriers as a function of gate voltage.dn±X−dt= Θ±Laser(t)− n±X−tX−(4)dn±edt= −Θ∓Laser(t)− n+e− n−etnr∕2+ n∓X−tX−(5)whereΘ∓Laser– excitation laser intensity given by aGaussianpulse, n±X− – population density of charged excitons, n±e– change of the free carrier population with respect to thenet density at the particular gate bias (at Vgate = 1.6 V n0e=11.8∗1011 cm−2), tX− , tnr – relaxation time of charged excitonand intervalley scattering time of free carriers. Equation (1)governs the evolution of charged excitons after their res-onant creation by the pump pulse. Equation (2) describesthe changes in the free carrier density induced by the cre-ation of charged excitons. The simulated populations arepresented in Figure 4(a).The outcome of the simulation is plotted as solid linesin the Figure 4(a) illustrating an excellent agreement withthe data and confirming a dominant role of free carriersin the exciton dynamics after resonant creation of chargedexcitons.In particular, within the proposed model the differ-ences in the co-/cross-polarized signals directly reflect thechange in the valley populations of unbound carriers. As thetrion consists of two electrons from both K-valleys and onehole, its intervalley scattering does not affect the electronpopulations and in principle could be taking place at a dif-ferent timescales.We also investigate the intervalley scattering processas a function of the gate voltage. In the Figure 4(b) we plotthe neutral exciton energy shifts in co-/cross-polarizationconfigurations for selected gate voltages. It shows a pro-nounced shortening of the scattering time for higher elec-tron densities, which can be easily extracted by fitting thedecay of the difference in exciton energy redshifts with anexponential function. The obtained decay times are shownin the Figure 4(c). We observe an order of magnitude reduc-tion of this scattering time starting from around 6 ps forlow electron density of 1012 cm−2 to 0.7 ps measured at 2.5 ∗1012 cm−2 carrier density. This is particularly interesting inthe context of previous studies on this process for variousTMD systems [53]–[59]. While most of these works focusedon other TMDmaterials, which differ fromMoSe2 with theirparticular band configuration and the optical activity ofthe ground exciton state, the ones that explored the depen-dence of the spin-flip process on electrostatic doping consis-tently show that its characteristic timescale decreases withthe increasing free carrier density. Only difference are thereported intervalley scattering times of resident carriers,which were in the order of hundreds of ns. Furthermore, arecent report, which directly probed the carrier relaxationdynamics in MoSe2 occupying the Landau quantized statesin high magnetic field, also shows a similarly slow pro-cess [60]. Interestingly, this work provides strong evidencefor the increased efficiency of the resident electron spin-flip process induced by the presence of neutral excitons.While this could partially explain such rapid scattering ratesobtained in our study (if we assume that the pumping beamoverlaps some part of the low-energy tail of neutral excitonabsorption) it also implies that the measured values wouldcorrespond to neutral exciton intervalley scattering times.However such an assumption directly contradicts previousworks that showed instead timescales of hundreds of fs [20],A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer — 493[61]. Alternatively, we may consider that a similar processof valley-depolarization of carriers can be mediated by thecharged exciton complexes. In this scenario, the observedtimescales would be related to the intervalley scattering ofbound carriers i.e. X−. This interpretation is further fortifiedby the fact that previous works reported similarly short psvalley depolarization times of trions in the naturally dopedsamples [61].4 Selective excitation of XIn this section we present the investigation of excitondynamics after resonant driving of the neutral exciton. InFigure 5(a) we show the change in excitons spectra at zerodelay for Vgate = 1.6 V. The neutral exciton shows a slightblueshift, aswell as the apparent bleaching of its total ampli-tude. These effects are similar, although present in a smallerscale, to what is observed in the non-doped regime withoutfree carriers and is resultant of the exciton-exciton interac-tions (Figure S2, [20]). For the charged excitons we see anapparent decrease in its signal for both K-valleys. This canbe again attributed to the influence of neutral exciton popu-lation by means of the excitation induced dephasing on thecharged exciton. It is also a demonstration of the previouslyreported efficient coupling between these quantum states[45], [51], [52], [61], [62].In principle, the cross-circularly polarized configura-tion of the pump-probe experimentmay facilitate the obser-vation of biexciton states, even for the case in which theyare not visible in direct reflection measurements. Whilesome works [62] indicate the presence of the biexciton tran-sition line in MoSe2 monolayers with the binding energyof ∼20 meV, we do not observe any presence of such addi-tional resonances in our case, even while changing thegate bias. We therefore omit the biexciton states in furtherconsiderations.In Figure 5(b) we show the time evolution of excitonoscillator strengths and the neutral exciton energy in thepump-probe measurement. In the co-polarized configura-tion we observe that after the initial decrease of the neutralexciton oscillator strength it exhibits a slight increase in thefirst ps. This is accompanied by the transition of its energyfrom the initial blue-shift to a red-shift (ΔE ≈ 1 meV), anda large decrease of the charged exciton oscillator strength.Such dynamics is a fingerprint of the charged exciton for-mation process, where the neutral exciton captures an elec-tron from the opposite valley thus lowering the free carrierdensity, while affecting the absorption spectra in a similarway as for the already discussed case of direct photocreationof charged excitons. The non-equilibrium population of freeFigure 5: X, X− dynamics under X-resonant excitation (a) neutral andcharged exciton spectra with/without X excitation in the coincidence(Δt= 0) depending on the circular polarization configuration.Vgate = 1.6 V (b) Valley-resolved X, X− amplitude and X energy shiftdynamics under X-resonant excitation in the first few ps. Solid linesdenote values obtained from the simulations. Simulated population ofphotocreated excitons and related change in the free carrier density.Vgate = 1.6 V (c) normalized X redshift dynamics under X-resonantexcitation for different gate voltages with fitted exponential decay.(d) Extracted relaxation times of neutral X as a function of gate voltage.electrons relaxes then to the opposite valley with the sametimescale of tnr = (2.7± 0.2) ps as in the Figure 4(a), whichresults in the diminishing difference in themeasured valuesfor the co-/cross-polarization configurations. Importantly,the neutral excitons also efficiently scatter to the oppositevalley, which, in particular, induces the initial blueshift ofthe resonance energy even for the cross-polarized configu-ration. This process is an order of magnitude faster than the494 — A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayerfree carrier scattering and occurs at the timescale of≈240 fsconsistently with other literature reports [20].In Figure 5(b) we plot as solid lines the results of rateequations simulation. Nowwe also include in ourmodel thepopulation of neutral excitons n±Xand consider the follow-ing mechanisms of its relaxation: (i) intervalley scatteringwith tXnr= 240 fs, (ii) trion formation process with tTF , (iii)radiative recombination with tX .Below we present the used rate equations.dn±Xdt= Θ±Laser(t)− n+X− n−XtXnr∕2 − n±XtX− n±XtTF(6)dn±X−dt= n±XtTF− n±X−tX−(7)dn±edt= −n+e− n−etnr∕2− n∓XtTF+ n∓X−tX−(8)Where n±X– population density of neutral excitons.Equation (6) governs the evolution of neutral excitons aftertheir resonant creation by the pump pulse. We considerhere intervalley scattering, radiative decay and chargedexciton formation. In principle the formation of X− is athree-particle process with its rate depending on the prod-uct of the total populations of neutral excitons and availablefree carriers. Here however we can simplify our modelwhen we consider that the change of the free carrier den-sity during the experiment is much lower than its initialvalue. In such a case the influence of ne on this relaxationprocess is included through the value of the tTF parameter.Equations (7) and (8), which describe temporal evolutionof charged excitons and free carriers differ from the pre-viously introduced equations (4) and (5) by the additionalcomponent of this charged exciton formation process. Mea-sured parameters depend on the respective populationsof excitons and carriers as described in the Supplemen-tary Material (Section 4, eq. (2)–(4)), where we extend thealready introduced equations (1)–(3) in order to include theeffects induced by the presence of neutral excitons.Again in the Figure 5(b) we see excellent agreementbetween the obtained data and simulated exciton-carrierdynamics. Interestingly, we can already note that the char-acteristic times of exciton decay extracted from the simula-tion tTF , tX ≈ 1.2, 0.8 ps are much lower than the tX = 6 psmeasured in the streak camera and pump-probe experi-ments in the neutrality regime.To further investigate the neutral exciton dynamics wepresent in the Figure 5(c) its redshift evolution for selectedgate biases. As we increase the carrier density it exhibitsrapid increase of its effective decay rate teff from which weisolate the charged exciton formation process via:1teff= 1tX+ 1tTF(9)In the entire range of investigated electron densitiesthe neutral exciton decay can be estimated by fitting anexponential decay function to its redshift time evolution.These values are presented by the black curve in Figure 5(d).Moreover, in a simplified case where X− decay would occuron a much longer timescale than the experimental window,one can also independently extract the ratio of tTF andtX times by considering the final charged exciton density(estimated e.g. from the maximum X redshift) and the ini-tial population of photocreated neutral excitons. Here, therelaxation rates are found by simultaneous fitting of thepresented model to the exciton dynamics in X/X− resonantexcitation (Figure 5(d)). While more general, we note that inour case this method yields values similar to the approachbased on simple comparison of the estimated initial/finalexciton density (see Supplementary Material). This is donefor gate biases Vgate=(0–3)V, where there is appropriatelystrong signal of both resonances.For the neutrality regime at negative gate voltage wefind teff = tX = 6 ps. With the increasing density of freecarriers we observe a significant shortening of the X− for-mation time and faster X recombination which lead to theaforementioned decrease of teff down to ≈130 fs for carrierdensity of ne = 2.5 ∗ 1012 cm−2.These findings are consistent with the recent literaturereports of the influence of free carriers on the neutral exci-ton relaxation rate [45], [46] and directly show the role of theX− formation process on the overall exciton dynamics. Thepresence of the Fermi sea also leads to the screening of theelectronic disorder, thus reducing the exciton’s inhomoge-neous broadening, which is in turn related to the radiativedecay rates [15], [45].5 Conclusions and outlookTo conclude we presented an investigation of the ultrafastdynamics of the optical response of charged and neutralexciton complexes in monolayer MoSe2 and their depen-dence on the density of free carriers introduced by elec-trostatic gating. The involved temporal evolution of theoptical transition lines was reliably reproduced by a sim-ple rate equations-based model, in which we consideredinteractions between exciton complexes and free carriers.We showed that selective excitation of a charged excitoncomplex in a given valley is related to an immediate captureof a free carrier in the opposite K valley. It allows for directoptical control of the density of free carriers and providesadditional path for achieving the polarization of electronA. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer — 495gas in zero magnetic field. As such we introduce a simpleand handy method for direct studies of valley-scatteringmechanisms which can be easily expanded to other TMDsystems. This is particularly interesting in the context ofmaterials with different configuration of electronic bandsthat also exhibit a plethora of charged exciton complexes[47], [59], [63]–[65]. The information about their particu-lar dynamics can be easily explored by selective excitationschemes. Additionally we directly showed how the increas-ing density of free carriers leads to a rapid decrease ofthe neutral exciton lifetime and increased rate of the trionformation channel. In the future we also aim to utilize ourapproach for directly probing the interaction of 2D carriergaswith an externalmagnetic field,wheremany-body inter-actions strongly enhance the magnetic susceptibility of thissystem [66].Acknowledgments: We thank Jacek Kasprzak, PawełMachnikowski and Daniel Wigger for their constructivecomments on themanuscript andmany fruitful discussions.Research funding: This work was supported by NationalScience Centre, Poland under projects 2021/41/N/ST3/04240and 2020/39/B/ST3/03251. We also acknowledge partial sup-port from the EU Graphene Flagship and from FNP Poland(IRA-MAB/2018/9 Grant, SG 0P Program of the EU).Author contributions: All authors have accepted responsi-bility for the entire content of thismanuscript and approvedits submission.Conflict of interest: Authors state no conflicts of interest.Informed consent: Informed consent was obtained from allindividuals included in this study.Ethical approval: The conducted research is not related toeither human or animals use.Data availability: The datasets generated and/or analysedduring the current study are available from the correspond-ing author upon reasonable request.References[1] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thinMoS2: a new direct-gap semiconductor,” Phys. Rev. Lett., vol. 105,no. 4, p. 136805, 2010..[2] A. Splendiani, et al., “Emerging photoluminescence in monolayerMoS2,” Nano Lett., vol. 10, no. 4, pp. 1271−1275, 2010..[3] G. Wang, et al., “Colloquium: excitons in atomically thin transitionmetal dichalcogenides,” Rev. Mod. Phys., vol. 90, no. 2, p. 021001,2018..[4] K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valleypolarization in monolayer MoS2 by optical helicity,” Nat.Nanotechnol., vol. 7, no. 8, pp. 494−498, 2012..[5] X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins inlayered transition metal dichalcogenides,” Nat. Phys., vol. 10, no. 5,pp. 343−350, 2014..[6] C. Robert, et al., “Measurement of the spin-forbidden dark excitonsin MoS2 and MoSe2 monolayers,” Nat. Commun., vol. 11, no. 1,p. 4037, 2020..[7] Z. Lu, et al., “Magnetic field mixing and splitting of bright and darkexcitons in monolayer MoSe2,” 2D Materials, vol. 7, no. 1, p. 015017,2019..[8] F. Cadiz, et al., “Excitonic linewidth approaching the homogeneouslimit in MoS2-based van der waals heterostructures,” Phys. Rev. X ,vol. 7, no. 2, p. 021026, 2017..[9] A. Singh, et al., “Trion formation dynamics in monolayer transitionmetal dichalcogenides,” Phys. Rev. B, vol. 93, no. 4, p. 041401, 2016..[10] A. A. Mitioglu, et al., “Optical manipulation of the exciton chargestate in single-layer tungsten disulfide,” Phys. Rev. B, vol. 88,no. 24, p. 245403, 2013..[11] C. Poellmann, et al., “Resonant internal quantum transitions andfemtosecond radiative decay of excitons in monolayer WSe2,” Nat.Mater., vol. 14, no. 9, pp. 889−893, 2015..[12] G. Moody, et al., “Intrinsic homogeneous linewidth andbroadening mechanisms of excitons in monolayer transition metaldichalcogenides,” Nat. Commun., vol. 6, no. 1, p. 8315, 2015..[13] T. Jakubczyk, et al., “Radiatively limited dephasing and excitondynamics in MoSe2 monolayers revealed with four-wave mixingmicroscopy,” Nano Lett., vol. 16, no. 9, pp. 5333−5339, 2016..[14] T. Jakubczyk, et al., “Impact of environment on dynamics of excitoncomplexes in a WS2 monolayer,” 2D Mater., vol. 5, no. 3, p. 031007,2018..[15] T. Jakubczyk, et al., “Coherence and density dynamics of excitons ina single-layer MoS2 reaching the homogeneous limit,” ACS Nano,vol. 13, no. 3, pp. 3500−3511, 2019..[16] A. Steinhoff, et al., “Biexciton fine structure in monolayer transitionmetal dichalcogenides,” Nat. Phys., vol. 14, no. 12, pp. 1199−1204,2018..[17] F. Katsch, M. Selig, and A. Knorr, “Theory of coherentpump−probe spectroscopy in monolayer transition metaldichalcogenides,” 2D Materials, vol. 7, no. 1, p. 015021, 2019..[18] C. Boule, et al., “Coherent dynamics and mapping of excitons insingle-layer MoSe2 and WSe2 at the homogeneous limit,” Phys.Rev. Mater., vol. 4, no. 3, p. 034001, 2020..[19] F. Katsch, M. Selig, and A. Knorr, “Exciton-scattering-induceddephasing in two-dimensional semiconductors,” Phys. Rev. Lett.,vol. 124, no. 25, p. 257402, 2020..[20] A. Rodek, et al., “Local field effects in ultrafast light−matterinteraction measured by pump-probe spectroscopy of monolayerMoSe2,” Nanophotonics, vol. 10, no. 10, pp. 2717−2728, 2021..[21] P. Back, S. Zeytinoglu, A. Ijaz, M. Kroner, and A. Imamoğlu,“Realization of an electrically tunable narrow-bandwidthatomically thin mirror using monolayer MoSe2,” Phys. Rev. Lett.,vol. 120, no. 3, p. 037401, 2018..[22] G. Scuri, et al., “Large excitonic reflectivity of monolayer MoSe2encapsulated in hexagonal boron nitride,” Phys. Rev. Lett., vol. 120,p. 037402, 2018..[23] K. F. Mak, et al., “Tightly bound trions in monolayer MoS2,” Nat.Mater., vol. 12, no. 3, pp. 207−211, 2013..[24] J. S. Ross, et al., “Electrical control of neutral and charged excitonsin a monolayer semiconductor,” Nat. Commun., vol. 4, no. 1,p. 1474, 2013..[25] A. M. Jones, et al., “Optical generation of excitonic valley coherencein monolayer WSe2,” Nat. Nanotechnol., vol. 8, no. 9, pp. 634−638,2013..496 — A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer[26] T. Smoleński, et al., “Signatures of wigner crystal of electrons in amonolayer semiconductor,” Nature, vol. 595, no. 7865, pp. 53−57,2021..[27] A. Popert, et al., “Optical sensing of fractional quantum hall effectin graphene,” Nano Lett., vol. 22, no. 18, pp. 7363−7369, 2022..[28] D. Thureja, et al., “Electrically tunable quantum confinement ofneutral excitons,” Nature, vol. 606, no. 7913, pp. 298−304,2022..[29] M. Koschorreck, D. Pertot, E. Vogt, B. Fröhlich, M. Feld, andM. Köhl, “Attractive and repulsive fermi polarons in twodimensions,” Nature, vol. 485, no. 7400, pp. 619−622, 2012..[30] A. Chernikov, et al., “Electrical tuning of exciton binding energiesin monolayer WS2,” Phys. Rev. Lett., vol. 115, no. 12, p. 126802, 2015..[31] D. K. Efimkin and A. H. MacDonald, “Many-body theory of trionabsorption features in two-dimensional semiconductors,” Phys.Rev. B, vol. 95, no. 3, p. 035417, 2017..[32] M. M. Glazov, “Optical properties of charged excitons intwo-dimensional semiconductors,” J. Chem. Phys., vol. 153, no. 3,p. 034703, 2020..[33] M. Sidler, et al., “Fermi polaron-polaritons in charge-tunableatomically thin semiconductors,” Nat. Phys., vol. 13, no. 3,pp. 255−261, 2017..[34] Y.-W. Chang and D. R. Reichman, “Many-body theory of opticalabsorption in doped two-dimensional semiconductors,” Phys. Rev.B, vol. 99, no. 12, p. 125421, 2019..[35] K. Kheng, R. T. Cox, M. Y. d’ Aubigné, F. Bassani, K. Saminadayar,and S. Tatarenko, “Observation of negatively charged excitons x−in semiconductor quantum wells,” Phys. Rev. Lett., vol. 71, no. 11,pp. 1752−1755, 1993..[36] P. Kossacki, et al., “Neutral and positively charged excitons: amagneto-optical study of a p-doped Cd1−xMnxTe quantum well,”Phys. Rev. B, vol. 60, no. 23, pp. 16018−16026, 1999..[37] V. Ciulin, et al., “Radiative behavior of negatively charged excitonsin CdTe-based quantum wells: a spectral and temporal analysis,”Phys. Rev. B, vol. 62, no. 24, pp. R16310−R16313, 2000..[38] V. Huard, R. T. Cox, K. Saminadayar, A. Arnoult, and S. Tatarenko,“Bound states in optical absorption of semiconductor quantumwells containing a two-dimensional electron gas,” Phys. Rev. Lett.,vol. 84, no. 1, pp. 187−190, 2000..[39] G. V. Astakhov, et al., “Oscillator strength of trion states inznse-based quantum wells,” Phys. Rev. B, vol. 62, no. 15,pp. 10345−10352, 2000..[40] P. Hawrylak, “Optical properties of a two-dimensional electrongas: evolution of spectra from excitons to fermi-edgesingularities,” Phys. Rev. B, vol. 44, no. 8, pp. 3821−3828,1991..[41] S. A. Brown, J. F. Young, J. A. Brum, P. Hawrylak, and Z. Wasilewski,“Evolution of the interband absorption threshold with the densityof a two-dimensional electron gas,” Phys. Rev. B, vol. 54,pp. R11082−R11085, 1996..[42] G. Yusa, H. Shtrikman, and I. Bar-Joseph, “Onset of excitonabsorption in modulation-doped GaAs quantum wells,” Phys. Rev.B, vol. 62, no. 23, pp. 15390−15393, 2000..[43] F. Rana, O. Koksal, M. Jung, G. Shvets, and C. Manolatou,“Many-body theory of radiative lifetimes of exciton-trionsuperposition states in doped two-dimensional materials,” Phys.Rev. B, vol. 103, no. 3, p. 035424, 2021..[44] Q. Zhang, H. Sun, J. Tang, X. Dai, Z. Wang, and C. Z. Ning,“Prolonging valley polarization lifetime through gate-controlledexciton-to-trion conversion in monolayer molybdenumditelluride,” Nat. Commun., vol. 13, no. 1, p. 4101,2022..[45] A. Rodek, et al., “Controlled coherent-coupling and dynamics ofexciton complexes in a MoSe2 monolayer,” 2D Materials, vol. 10,no. 2, p. 025027, 2023..[46] D. Huang, et al., “Quantum dynamics of attractive and repulsivepolarons in a doped MoSe2 monolayer,” Phys. Rev. X , vol. 13, no. 1,p. 011029, 2023..[47] J. G. Roch, et al., “Spin-polarized electrons in monolayer MoS2,”Nat. Nanotechnol., vol. 14, no. 5, pp. 432−436, 2019..[48] T. Smoleński, et al., “Interaction-induced shubnikov−de haasoscillations in optical conductivity of monolayer MoSe2,” Phys. Rev.Lett., vol. 123, no. 9, p. 097403, 2019..[49] P. Płochocka, et al., “Femtosecond study of the interplay betweenexcitons, trions, and carriers in (Cd,Mn)Te quantum wells,” Phys.Rev. Lett., vol. 92, no. 17, p. 177402, 2004..[50] P. Kossacki, et al., “Femtosecond study of interplay betweenexcitons, trions, and carriers in (Cd,Mn)Te quantum wells,” Proc.SPIE 5725, Ultrafast Phenomena in Semiconductors and NanostructureMaterials IX , vol. 5725, pp. 275−284, 2005..[51] A. Singh, et al., “Coherent electronic coupling in atomically thinMoSe2,” Phys. Rev. Lett., vol. 112, no. 21, p. 216804, 2014..[52] K. Hao, et al., “Coherent and incoherent coupling dynamicsbetween neutral and charged excitons in monolayer MoSe2,” NanoLett., vol. 16, pp. 5109−5113, 2016..[53] L. Yang, et al., “Long-lived nanosecond spin relaxation and spincoherence of electrons in monolayer MoS2 and WS2,” Nat. Phys.,vol. 11, no. 10, pp. 830−834, 2015..[54] W.-T. Hsu, et al., “Optically initialized robust valley-polarized holesin monolayer WSe2,” Nat. Commun., vol. 6, no. 1, p. 8963,2015..[55] X. Song, S. Xie, K. Kang, J. Park, and V. Sih, “Long-lived holespin/valley polarization probed by kerr rotation in monolayerWSe2,” Nano Lett., vol. 16, no. 8, pp. 5010−5014, 2016..[56] E. J. McCormick, et al., “Imaging spin dynamics in monolayer WS2by time-resolved kerr rotation microscopy,” 2D Materials, vol. 5,p. 011010, 2017..[57] P. Dey, et al., “Gate-controlled spin-valley locking of residentcarriers in WSe2 monolayers,” Phys. Rev. Lett., vol. 119, no. 13,p. 137401, 2017..[58] J. Kim, et al., “Observation of ultralong valley lifetime in wse2/mos2heterostructures,” Sci. Adv., vol. 3, no. 7, 2017, Art. no. e1700518.[59] J. Li, M. Goryca, K. Yumigeta, H. Li, S. Tongay, and S. A. Crooker,“Valley relaxation of resident electrons and holes in a monolayersemiconductor: dependence on carrier density and the role ofsubstrate-induced disorder,” Phys. Rev. Mater., vol. 5, no. 4,p. 044001, 2021..[60] T. Smoleński, K. Watanabe, T. Taniguchi, M. Kroner, andA. Imamoğlu, “Spin-valley relaxation and exciton-induceddepolarization dynamics of landau-quantized electrons in MoSe2monolayer,” Phys. Rev. Lett., vol. 128, no. 12, p. 127402,2022..[61] K. Hao, et al., “Trion valley coherence in monolayersemiconductors,” 2D Mater., vol. 4, no. 2, p. 025105, 2017..[62] K. Hao, et al., “Neutral and charged inter-valley biexcitons inmonolayer MoSe2,” Nat. Commun., vol. 8, no. 1, p. 15552,2017..A. Rodek et al.: Interactions and ultrafast dynamics of exciton complexes in a monolayer — 497[63] Z. Li, et al., “Revealing the biexciton and trion-exciton complexes inbn encapsulated WSe2,” Nat. Commun., vol. 9, no. 1, p. 3719,2018..[64] M. He, et al., “Valley phonons and exciton complexes in amonolayer semiconductor,” Nat. Commun., vol. 11, no. 1, p. 618,2020..[65] M. Zinkiewicz, et al., “Excitonic complexes in n-doped WS2monolayer,” Nano Lett., vol. 21, no. 6, pp. 2519−2525, 2021..[66] K. Oreszczuk, et al., “Enhancement of electron magneticsusceptibility due to many-body interactions in monolayerMoSe2,” 2D Materials, vol. 10, p. 045019, 2023..Supplementary Material: This article contains supplementary material(https://doi.org/10.1515/nanoph-2023-0913).https://doi.org/10.1515/nanoph-2023-0913 1 Introduction 2 Methods and sample characterization 3 Selective excitation of Xtnqx2212; 3.1 Time-resolved pump-probe with selective excitation of Xtnqx2212; 4 Selective excitation of X 5 Conclusions and outlook<< /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (Euroscale Coated v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.7 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.1000 /ColorConversionStrategy /sRGB /DoThumbnails true /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 35 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness false /PreserveHalftoneInfo false /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Remove /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages false /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 10 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages false /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages false /MonoImageMinResolution 600 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1000 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.10000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError false /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /DEU /ENU () /ENN () >> /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ << /AsReaderSpreads false /CropImagesToFrames true /ErrorControl /WarnAndContinue /FlattenerIgnoreSpreadOverrides false /IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint /Legacy >> << /AllowImageBreaks true /AllowTableBreaks true /ExpandPage false /HonorBaseURL true /HonorRolloverEffect false /IgnoreHTMLPageBreaks false /IncludeHeaderFooter false /MarginOffset [ 0 0 0 0 ] /MetadataAuthor () /MetadataKeywords () /MetadataSubject () /MetadataTitle () /MetricPageSize [ 0 0 ] /MetricUnit /inch /MobileCompatible 0 /Namespace [ (Adobe) (GoLive) (8.0) ] /OpenZoomToHTMLFontSize false /PageOrientation /Portrait /RemoveBackground false /ShrinkContent true /TreatColorsAs /MainMonitorColors /UseEmbeddedProfiles false /UseHTMLTitleAsMetadata true >> << /AddBleedMarks false /AddColorBars false /AddCropMarks false /AddPageInfo false /AddRegMarks false /BleedOffset [ 0 0 0 0 ] /ConvertColors /ConvertToCMYK /DestinationProfileName (ISO Coated v2 \(ECI\)) /DestinationProfileSelector /UseName /Downsample16BitImages true /FlattenerPreset << /ClipComplexRegions true /ConvertStrokesToOutlines false /ConvertTextToOutlines false /GradientResolution 300 /LineArtTextResolution 1200 /PresetName /PresetSelector /HighResolution /RasterVectorBalance 1 >> /FormElements true /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MarksOffset 8.503940 /MarksWeight 0.250000 /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /UseName /PageMarksFile /RomanDefault /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams<< /HWResolution [600 600] /PageSize [595.276 841.890]>> setpagedevice