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[Takashi Kuroda](https://orcid.org/0000-0001-6445-7673), Yusuke Hoshi, Satoru Masubuchi, Mitsuhiro Okada, [Ryo Kitaura](https://orcid.org/0000-0001-8108-109X), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Tomoki Machida

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[Dark-state impact on the exciton recombination of WS2 monolayers as revealed by multi-timescale pump-probe spectroscopy](https://mdr.nims.go.jp/datasets/48350a77-db86-4095-961a-4ca206242985)

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Dark-state impact on the exciton recombination of WS$_2$ monolayers as revealed by multi-timescale pump-probe spectroscopyPHYSICAL REVIEW B 102, 195407 (2020)Dark-state impact on the exciton recombination of WS2 monolayers as revealedby multi-timescale pump-probe spectroscopyTakashi Kuroda ,1,* Yusuke Hoshi ,2,3 Satoru Masubuchi ,3 Mitsuhiro Okada,4 Ryo Kitaura,4Kenji Watanabe ,1 Takashi Taniguchi,1,3 and Tomoki Machida31National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan2Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya-ku, Tokyo 158-0082, Japan3Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Maguro-ku, Tokyo 153-8505, Japan4Department of Chemistry, Nagoya University, Nagoya 464-8602, Japan(Received 4 September 2020; revised 17 October 2020; accepted 20 October 2020; published 5 November 2020)The luminescence yield of transition metal dichalcogenide monolayers frequently suffers from the formationof long-lived dark states, which include excitons with intervalley charge carriers, spin-forbidden transitions, anda large center-of-mass momentum located outside the light cone of dispersion relations. Efficient relaxation frombright exciton states to dark states suppresses the quantum yield of photon emission. In addition, the radiativerecombination of excitons is heavily influenced by Auger-type exciton-exciton scattering, which yields anothernonradiative relaxation channel at room temperature. Here, we show that Auger-type scattering is promoted notonly between (bright) excitons but also between excitons and long-lived dark states. We studied the luminescencedynamics of monolayer WS2 capped with hexagonal BN over broad time ranges of picoseconds to millisecondsusing carefully designed pump-and-probe techniques. We observed that luminescence quenching associated withAuger-type scattering occurs on 1–100-μs timescales, which thus correspond to the lifetimes of the relevant darkstates. The broad distribution of the measured lifetimes implies the impact of various types of long-lived stateson the exciton annihilation process.DOI: 10.1103/PhysRevB.102.195407I. INTRODUCTIONThe high-yield light emission associated with exciton re-combination makes transition metal dichalcogenide (TMD)monolayers unique platforms on which to demonstrate variousexciting physics phenomena [1–9]. Mechanisms behind thestrong light emission include (1) strong interband transitionssince both conduction and valence electron states consist ofstrongly localized metal d orbitals and the absorption co-efficients of TMD commonly exceed 10% per monolayerdepending on wavelength [10,11] and (2) large exciton bind-ing energies of the order of 0.5 eV [12–18], which ensures thestable formation of excitons even at room temperature. Theobservation of ultrafast spontaneous emissions with decaytimes of a few picoseconds confirms the enhanced excitonoscillator strengths [19–26]. However, it is also commonlyaccepted that standard monolayer TMD samples exhibit aquantum yield lower than 1%, possibly limited by the pres-ence of crystalline defects [27]; relaxation to various dark*Authors to whom correspondence should be addressed:kuroda.takashi@nims.go.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.states, which include intervalley excitons, spin-forbiddentriplet excitons, and excitons with nonzero center-of-massmomentum; and Auger-type scattering that leads to nonradia-tive exciton annihilation [28–31]. Of these phenomena, Augerscattering, i.e., nonradiative energy transfer between excitons,is regarded as a dominant reason for the room-temperaturequantum yield being limited, as the effect appears even formoderate densities lower than 1010 cm−2 [32,33]. The originof the efficient Auger process is not fully understood, butit constitutes a key issue in regard to developing practicallight-emitting devices working at room temperature.Recently, we observed that Auger-type exciton annihilationis greatly suppressed by the encapsulation of tungsten disul-fide (WS2) monolayers with hexagonal boron nitride (hBN),which is a useful substrate for two-dimensional (2D) materialsthanks to its reduced surface roughness and low background-carrier densities [34]. The improved surface homogeneity ofTMD/hBN leads to the formation of delocalized excitons,which are homogeneously dispersed over the 2D plane. Incontrast, TMDs supported on a common class of substrates(such as SiO2) tend to have dense localization centers, whichincrease the local exciton density and enhance the probabilityof contact-type exciton-exciton scattering.In this work we focus on the mechanism of efficient excitonannihilation in TMD monolayers at room temperature. Weextended the measurement timescale up to milliseconds byusing custom-designed luminescence-based pump-and-probetechniques, which made it possible to access hidden slowdynamics over broad timescales. Hence, we revealed efficient2469-9950/2020/102(19)/195407(7) 195407-1 Published by the American Physical Societyhttps://orcid.org/0000-0001-6445-7673https://orcid.org/0000-0001-6558-6581https://orcid.org/0000-0001-7039-6694https://orcid.org/0000-0003-3701-8119http://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.102.195407&domain=pdf&date_stamp=2020-11-05https://doi.org/10.1103/PhysRevB.102.195407https://creativecommons.org/licenses/by/4.0/TAKASHI KURODA et al. PHYSICAL REVIEW B 102, 195407 (2020)FIG. 1. Picosecond luminescence dynamics: (a) Time-resolvedluminescence signals of monolayer WS2 capped with hBN, excitedby 2-ps pulses with 76-MHz repetition rates for various excitationpowers. The measurements were performed at room temperature.(b) Decay time dependence on excitation power. (c) Microscopeimage of our sample. The white dashed line highlights the monolayerregion. (d) Luminescence spectra. The two signals measured at 20and 200 nW are normalized to their maxima. The arrow indicates thespectral integration window we used for our time-resolved analysis.Auger-type scattering between excitons and other long-lived“dark” states whose lifetimes are much longer than those ofbright excitons. The measured lifetimes were distributed in1–100-μs timescales, implying that various types of long-lived states contribute to exciton annihilations, which thuslead to the emergence of the previously reported low-injectionAuger scattering [32–34].This paper is organized as follows. Section II describessample preparation. In Sec. III, we measure the picosecondtimescale response after short-pulsed excitation and confirmthat long-lived dark states evidently cause Auger scattering. InSec. IV, we study the microsecond timescale response usinga fast modulated quasi-cw source. Then, we directly monitorthe accumulation and relaxation process of the long-livedstates and quantify their lifetimes. In Sec. V, we discuss theidentification of the measured long-lived states.II. SAMPLES AND SETUPSWe used a chemical vapor deposition grown WS2 mono-layer transferred onto a SiO2 substrate through a pickuptransfer process [35]. It revealed significant luminescencequenching at moderate excitation [34]. The WS2 monolayerwas capped with hBN film to avoid optical damage dur-ing the experiment. The sample preparation is detailed inRefs. [34,36]. [A microscope image of our sample can be seenin Fig. 1(c).] In the experiment, we used a home-built confocalsetup to collect luminescence signals within a diameter ofaround 1 μm on the monolayer flake region. The excitationand detection scheme will be described in later sections. Allthe experiments were performed at room temperature.III. STUDY WITH A HIGH-REPETITION,SHORT-PULSE EXCITATION SOURCEIn our first set of experiments, we excited the sample withpicosecond light pulses with a duration of 2 ps, a wave-length of 550 nm, and a repetition rate of 76 MHz, whichwere generated by an optical parametric oscillator. Then,the luminescence signals were analyzed temporally using asynchronously scanning streak camera with a maximum reso-lution of 2 ps.A. Picosecond luminescence decay dynamicsFigure 1(a) shows the decay curves of the neutral exci-ton line observed at 620 nm for different excitation powers.[The luminescence spectra are shown in Fig. 1(d).] For thelowest excitation at 100 nW, the decay signal showed a single-exponent decay with a time constant of 590 ps (blue line).When the excitation power was increased to 1 μW, the signaldecayed faster with a time constant of 85 ps (green line). Afurther increase in the excitation power to 10 μW resulted ina short time constant of 18 ps (red line). (The decay curve at10 μW deviates from a single-exponent curve. Thus, we fit-ted the data using a double-exponent function and evaluatedthe decay time as the weighted average of extracted timeconstants.) The decay time dependence on excitation poweris shown in Fig. 1(b). Such a reduction in lifetime with ex-citation power is a signature feature of Auger-type excitonannihilation, where excitons are recombined nonradiativelyvia contact scattering with other excitons [28–33]. It is note-worthy that the phenomenon appears at excitation power aslow as 100 nW, from which we estimate a photoinjection den-sity of the order of 109 cm−2, much smaller than commonlyencountered 2D exciton densities that induce nonlinear scat-tering events in II-VI and III-V quantum well systems [37].Note that the luminescence intensity at the time origin(0 ps in this Fig. 1) is nearly proportional to the excita-tion power, while the decay constant changes monotonically.Hence, higher excitation curves fall below the lower excita-tion curves at particular delay times depicted by the verticalarrows. The observed “signal crossing” behavior suggests thatthe luminescence intensity does not simply follow the tran-sient population of excitons generated by each pulse. Instead,the luminescence decay is influenced by previous pulses thataccumulate the population of long-lived states whose lifetimesare longer than the exciton lifetime.B. Pump-and-probe measurement while monitoringluminescence decay curvesTo confirm the above hypothesis, we carry out a pump-and-probe-type measurement, where we divide excitation pulsesinto two pulses and study the impact of preceding “pump”pulses on the luminescence induced by delayed “probe”pulses. [See the measurement scheme in Fig. 2(c).] Figure 2(a)shows a time trace of luminescence signals excited by pulsepairs. The pulse separation is set at 1.44 ns, which is suf-ficiently longer than the measured luminescence decay time(�600 ps). Nevertheless, the luminescence signals gener-ated by both the pump and probe pulses are simultaneouslyanalyzed in the same streak camera curve that covers the195407-2DARK-STATE IMPACT ON THE EXCITON … PHYSICAL REVIEW B 102, 195407 (2020)FIG. 2. Luminescence-based pump-and-probe measurement:(a) The top panel shows a luminescence trace excited with strongpump pulses (1 μW) followed by weak probe pulses (200 nW).The pulse separation is set at 1.44 ns, so that the pump-inducedluminescence has entirely finished before the probe pulses areinjected. The bottom panel shows a luminescence trace excited withprobe pulses alone. (b) Pump-power dependence of probe-inducedsignals. The dashed line shows an instrumental response curve,which we measured with picosecond excitation pulses. The fullwidth at half maximum is estimated to be 11 ps, which gives thetime resolution of this setup. (c) Measurement scheme.measurement window of ∼2.1 ns. Figure 2(b) is a summaryof the pump power dependence of the decay curves of probegenerated signals. The decay time decreases monotonicallywith increasing pump power, while the peak intensity at thetime origin remains unchanged, in contrast to the previousobservations using single-excitation pulses shown in Fig. 1.Hence, the luminescence decay is crucially influenced by thepresence of long-lived “dark” states, which were injected bymuch earlier pump pulses.Tuning the time separation between the pump and probepulses could allow us to detect dark-state relaxation. However,the probe luminescence was not significantly dependent onthe pulse separation up to 11 ns, which was limited by therepetition rate of our light source. The measurement resultis briefly described in the Appendix. Thus, we conclude thatthe relevant dark states have lifetimes longer than the 10-nstimescales.IV. STUDY WITH A FAST MODULATED QUASI-CWLIGHT SOURCETo examine such slow dark-state dynamics, we introducean alternative scheme that utilizes quasi-cw light as an ex-citation source. Output from a cw laser with a wavelengthof 532 nm was temporally modulated using a high-speedTeO2 acousto-optic modulator (AOM, center frequency ofFIG. 3. Microsecond luminescence dynamics: Time evolution ofluminescence signals under square-wave excitation with a durationof 50 μs and a duty ratio of 10%. The square pulses are formed ofcw light with a (peak) power of 500 nW and a wavelength of 532 nm.The luminescence evolution is analyzed with a time bin of 10 ns. Themeasurement scheme is shown in the inset.200 MHz, Panasonic, EFLM200) to form square-wave pulseswith sharp rising/falling edges (rise time shorter than 10 ns).Then, we measured the time evolution of the “steady-state” luminescence intensity using a single-photon detector(PerkinElmer, SPCM-AQR) and a fast multichannel scalerwith a minimum time bin of 5 ns (Becker & Hickl, MSA-300).A. Microsecond luminescence quenchingunder square-wave excitationFigure 3 shows the time evolution of luminescence signalsunder square-wave excitation with a gate width of 50 μs anda duty ratio of 10% (excitation period of 0.5 ms). It revealssignificant luminescence quenching with time, along with anaccumulation of the dark-state population; that is, the numberof excited dark states increases with time after the start ofphotoinjection, the probability of Auger scattering increases,and the luminescence intensity decreases.The signal trace in Fig. 3 consists of two distinct com-ponents with different characteristic times. The fast decayingcomponent appears as a spike signal just after the photoinjec-tion began. The slower decaying component, which decreasedgradually with time, had not reached its saturation value evenat the time the photoinjection was stopped. These findingsimply contributions by different long-lived states, which havelifetimes of the orders of 1 and � 50 μs, to exciton lumines-cence quenching.B. Pump-and-probe measurement while monitoringthe luminescence recoveryDark-state relaxation can be directly explored by mon-itoring the recovery of the luminescence yield, which isaccompanied by a progressive decrease in the dark-state den-sity. To accomplish this task we operated the AOM to formbroad pump gates followed by much narrower probe gatesand measured the probe-induced luminescence intensity asa function of delay time. The relative timing of the pump195407-3TAKASHI KURODA et al. PHYSICAL REVIEW B 102, 195407 (2020)Pump Probe1 µs 40 ns0-10 µs50 µsPump Probe50 µs 2 µs0-0.4 ms0.5 ms(a)(b)FIG. 4. Timing diagram of pump and probe gate operations formeasuring (a) the microsecond timescale response and (b) the sub-microsecond timescale response.and probe gates was systematically controlled using a digitalpulse generator (Quantum Composers, 9200 Plus). The tim-ing diagram of the gate sequence is shown in Fig. 4. In thefollowing we observe the time trace of luminescence signalsexcited with a controlled gate sequence and analyze the probe-induced luminescence intensity, which becomes higher as theprobe pulses are further delayed.1. Microsecond timescale responseFirst, we focus on the rapid dynamics that led to the spikesignal in the 50-μs gate curve (Fig. 3), which suggested thepresence of dark states with a lifetime of the order of 1 μs.Thus, we set relatively narrow pump and probe gates withdurations of 1 μs and 40 ns, respectively (repetition periodof 50 μs). See the gate timing in Fig. 4(a). Figure 5(a) showsthe intensity trace of luminescence signals excited with thecontrolled gate sequence. The intensity trace clearly revealsthe light emission at the pump gate (gray curve) and that atthe probe gate (blue curve). The pump-induced signal exhibitsa significant temporal decay, which reproduces the spike sig-nature seen at the time origin in Fig. 3. The probe-inducedsignal increases with delay time towards the initial equilib-rium intensity observed at the moment the pump gates wereopened, as expected.Figure 5(b) is a summary of probe signal intensities as afunction of delay time (blue circles). The time trace of thepump-induced signals is also plotted by the gray line. Thedownward and upward arrows seen above the data curvesindicate the progressive change in the luminescence yield,accompanied by the accumulation and relaxation of long-liveddark states, respectively. The probe luminescence intensity isrecovered with a time constant of 4 (±1) μs, which thus givesthe lifetime of the relevant dark states that yielded the fastdecaying component in the intensity curve in Fig. 3.FIG. 5. Microsecond pump and probe measurement. (a) Timetrace of luminescence signals excited by 1-μs square pump pulsesfollowed by 40-ns probe pulses for different delay times. SeeFig. 4(a) for the gate sequence. (b) Probe-induced luminescence asa function of delay time revealing an intensity recovery with a timeconstant of 4 (±1) μs (blue circles). A pump-induced signal trace isalso shown by a gray line.2. Submillisecond timescale responseNext, we focus on the slower dynamics that led to a gradualdecrease in the intensity curve in Fig. 3. The pump and probegates are extended and given durations of 50 and 2 μs, respec-tively (repetition period of 0.5 ms). In this case, the dark statewith a 4-μs lifetime is entirely saturated when the pump gatesare opened. See the gate timing in Fig. 4(b). Figure 6 showsthe measurement results we obtained when we adopted theseexcitation sequences, and they reveal the clear recovery of theprobe luminescence intensity on a submillisecond scale. Thetime constant is roughly estimated to be 250 (±50) μs, whichis thus the lifetime of the relevant states that caused the slowluminescence quenching.It should be mentioned that of the two distinct long-livedstates with lifetimes of 4 and 250 μs, the longer-lifetime statelikely dominates the source of the luminescence quenchingunder stationary (and moderate) injections. This is becausethe steady-state (saturated) population of a long-lived state195407-4DARK-STATE IMPACT ON THE EXCITON … PHYSICAL REVIEW B 102, 195407 (2020)FIG. 6. Submillisecond dynamics. The result of pump and probemeasurements adopting excitation sequences with 50-μs pumpgates followed by 2-μs probe gates (0.5-ms repetition period). SeeFig. 4(b) for the excitation scheme. The trace of the pump-inducedluminescence is indicated by a gray line, and the intensity of theprobe-induced luminescence is plotted with red open circles.is proportional to its lifetime, and the longer-lifetime state ismore populated than the other. Hence, exciton annihilationsat room temperature are predominantly driven by scatteringwith long-lived states that have lifetimes on a submillisecondtimescale.V. DISCUSSION: IDENTIFICATION OF MEASUREDLONG-LIVED STATESIn the following we discuss three issues with respect toidentifying the observed long-lived states. First, we addressthe role of exciton center-of-mass motions. Our study fo-cuses on room-temperature dynamics. Hence, excitons arethermally distributed along different momentum states, andonly the small portions located inside the light cone of dis-persion relations are allowed to emit light [26]. The otherstates with finite in-plane momenta propagate along the 2Dlayer, and they cannot emit light into free space. Since mo-mentum scattering occurs on timescales shorter than a fewpicoseconds, as the relevant process does not require spinflip [38], we can assume that both bright and dark excitonsare fully thermalized regarding center-of-mass motions dur-ing our observations. In this case, thermalized excitons areexpected to decay with an average lifetime, which is muchlonger than the intrinsic lifetime determined by the oscilla-tor strength. Our observation of relatively long luminescencelifetimes (590 ps for a weak-excitation limit) compared withreported low-temperature values (a few picoseconds) arisesdue to the thermal equilibrium condition.Second, we consider spin-forbidden states. The lowest-energy excitons in tungsten dichalcogenide monolayers areknown to be optically inactive as they comprise spin tripletconfigurations [39]. A study of high-field magnetophotolumi-nescence in WS2 monolayers confirmed a dark-bright splittingof 47 meV [40], which exceeds the room-temperature thermalenergy. Hence, the majority of excitons stay in spin-forbiddendark states even at room temperature. In view of this fact,we attribute the observed long-lived state that has a lifetimeof 4 μs (Fig. 5) to spin-forbidden dark excitons. Note thatrecent observations of intervalley biexcitons, which consist ofbright and dark excitons and thus appear for very low (cw)excitations [41–44], are consistent with our findings aboutefficient bright-dark exciton scattering.Third, we discuss environment charge effects. StandardTMD samples tend to contain residual charge carriers, whichare mostly electrons resulting from chalcogenide vacancies.Some of them are trapped at localization centers and arelikely activated via photoinjection. The moving charge car-riers would serve as efficient scattering centers for excitons,which suffer from Auger-type annihilation. We attribute theobserved slow dynamics with a time constant of ∼250 μsto the charge fluctuation process. Note that recent observa-tions of near-unity quantum yields in field-effect devices alsosuggest the strong impact of background charge densities onexciton recombination [45]. Nevertheless, we cannot excludeother environment mechanisms as possible origins of the ob-served slow dynamics. Further studies using a charge-tunableand hBN-encapsulated device would help to determine theinfluence of the environment on radiative dynamics.Here, we considered three representative long-lived states,i.e., large-momentum excitons, spin triplets, and photoacti-vated free carriers, as a source of the measured slow relaxationprocesses. These states are nonemissive and dark. Thus, theirlifetimes are much longer than those of emissive bright ex-citons. Hence, under stationary excitation, these long-livedstates are populated more densely than bright excitons, andthey can serve as efficient scattering centers for (bright)excitons, which are then annihilated nonradiatively throughAuger-type energy transfer. We successfully quantified thelifetimes of the long-lived states by analyzing the process ofluminescence recovery after stopping photoexcitation. Notethat these long-lived states have independent origins. Thus,the experimentally measured curves simply follow the linearsuperposition of different curves, each of which is describedby a single decay process. In our experiment, we observedluminescence signals that decay (or rise) with very dif-ferent timescales (see, e.g., two decaying components inFig. 3); thus, we can safely and precisely quantify 4 and250 μs as their lifetimes.VI. CONCLUSIONIn conclusion, we studied exciton recombination dynamicsin WS2 monolayers capped with hBN over broad timescalesfrom picoseconds to milliseconds and confirmed that lu-minescence efficiency was governed by Auger scatteringbetween excitons and long-lived dark states. Custom-designedpump-and-probe techniques enabled us to determine thatthe lifetimes of the optically inaccessible states were 4 and250 μs. We attributed the state with the 4-μs lifetime tospin-forbidden dark excitons and the state with the 250-μslifetime to photoactivated environment charge carriers. Hence,we found that Auger annihilation occurs even for modestinjections, which could easily be achieved in standard light-emitting devices. A potential way of suppressing nonradiative195407-5TAKASHI KURODA et al. PHYSICAL REVIEW B 102, 195407 (2020)FIG. 7. Pump-and-probe response of luminescence decay sig-nals. The gray line is a signal induced by probe pulses (50 nW) alone.The blue and red lines indicate signals with pump pulses (200 nW)that arrived 2 and 11 ns prior to the probe pulses, respectively.exciton recombination is to realize a clean environment that isfree from residual charge carriers and localization centers byadopting hBN-encapsulated charge-tunable structures.ACKNOWLEDGMENTSWe acknowledge the support of CREST, Japan Science andTechnology Agency (JST), under Grants No. JPMJCR15F3and No. JPMJCR16F3 and the Japan Society for the Pro-motion of Science, JSPS KAKENHI under Grants No.JP19H01820, No. JP20H00127, No. JP20H00354, and No.JP20H05664.APPENDIX: EFFECT OF PUMP-AND-PROBE DELAYTIME ON LUMINESCENCE DECAY SIGNALSIn Sec. III B, we analyzed the luminescence decay signalsexcited with pump and probe pulses, which were separatedby 1.44 ns (Fig. 2). Here, we vary the pulse separation andobserve its effect on the probe luminescence decay curve. Fig-ure 7 shows the luminescence decay signals induced by probepulses. The gray line is a signal excited with probe pulsesalone (without pump pulses). The blue curve is a signal wherepump pulses are injected 2 ns prior to probe pulses. It revealsthe acceleration in the luminescence decay, as also describedin Sec. III B. The red line is a signal with pump pulses injected11 ns prior to the probe pulses. The red and blue lines overlapperfectly, and there is no significant difference between them.Hence, we can conclude that the long-lived states, whichcause Auger scattering, have lifetimes much longer than 11 ns.Thus, the observed long-lived states are in a stationary regimeunder 76-MHz excitation. To study such slow dynamics, weneed to introduce an alternative excitation scheme that uses afast modulated quasi-cw source, as described in Sec. IV.[1] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman,and M. S. 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