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Denis Yagodkin, Abhijeet Kumar, Elias Ankerhold, Johanna Richter, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Cornelius Gahl, Kirill I. Bolotin

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[Probing the Formation of Dark Interlayer Excitons via Ultrafast Photocurrent](https://mdr.nims.go.jp/datasets/e27272a5-be99-4a72-be0e-e37ae480156a)

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Probing the Formation of Dark Interlayer Excitons via Ultrafast PhotocurrentProbing the Formation of Dark Interlayer Excitons via UltrafastPhotocurrentDenis Yagodkin, Abhijeet Kumar, Elias Ankerhold, Johanna Richter, Kenji Watanabe, Takashi Taniguchi,Cornelius Gahl, and Kirill I. Bolotin*Cite This: Nano Lett. 2023, 23, 9212−9218 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Optically dark excitons determine a wide range ofproperties of photoexcited semiconductors yet are hard to accessvia conventional time-resolved spectroscopies. Here, we develop atime-resolved ultrafast photocurrent technique (trPC) to probe theformation dynamics of optically dark excitons. The nonlinearnature of the trPC makes it particularly sensitive to the formationof excitons occurring at the femtosecond time scale after theexcitation. As a proof of principle, we extract the interlayer excitonformation time of 0.4 ps at 160 μJ/cm2 fluence in a MoS2/MoSe2heterostructure and show that this time decreases with fluence. Inaddition, our approach provides access to the dynamics of carriersand their interlayer transport. Overall, our work establishes trPC asa technique to study dark excitons in various systems that are hardto probe by other approaches.KEYWORDS: interlayer dark exciton, transition metal dichalcogenides (TMDs), 2D semiconductor heterostructures,time-resolved photocurrent, interlayer dark exciton dynamics, time-resolved differential reflectivityCoulomb-bound electron−hole pairs (excitons) dominatethe optical response of low-dimensional (0D, 1D, 2D)semiconductors.1 While early studies focused on opticallyallowed bright excitons, optically forbidden “dark” excitonshave been studied much less. The radiative recombination ofthese latter excitons is suppressed as they involve states withnonzero total momentum, noninteger total spin, or spatiallyseparated electron and hole wave functions.1,2 Due to the weakinteraction with light, these states exhibit a long lifetime. Thisbehavior of spin dark excitons is critical in understanding theefficiency limitations of charge collection in perovskite solarcells and photoluminescence (PL) in quantum dots.3,4Momentum dark excitons are the lowest energy excitation inmany transition-metal dichalcogenides (TMDs).5 Because ofthat, dark states likely dominate the long-range transport ofexcitons,6,7 determine temperature-dependent optical spectra,8and are responsible for long-lived spin signals.9,10 Furthermore,dark excitons are promising for realizing interacting bosonicmany-body states including the Bose−Einstein condensate andexcitonic Mott insulator in TMDs.11−13 Special approaches arerequired to investigate the properties of the dark states due totheir weak interaction with light. Spin dark excitons arebrightened in a strong magnetic field,;14 however, thedynamics of the state is changed upon brightening. Conversely,the brightening of momentum dark excitons is challenging,thereby limiting the range of available techniques. For example,time- and angle-resolved photoemission spectroscopy (trAR-PES) or spectroscopies in the terahertz and far-infraredfrequency ranges have been used to study dark excitons inTMDs and their heterostructures (HS).15−18 These ap-proaches typically require large (hundreds of μm2 area)homogeneous samples or are performed at room temperature.Another approach to probe dark excitons, time-resolvedphotoluminescence (trPL),12,19 has a submicrometer spatialresolution but features a lower time resolution and does notwork for states with vanishingly small oscillator strengths. As aresult, many questions related to dark exciton formation, e.g.,its time scale or the influence of phonon scattering andelectron screening, remain unresolved.Time-resolved photocurrent spectroscopy (trPC) hasrecently emerged as an approach to study optical processesin (2D) semiconductors.20−23 In trPC, a current across thesample is recorded vs the time delay between two light pulsesimpinging onto it. Critically, the technique is inherentlysensitive to nonlinear processes. The approach applies toReceived: May 8, 2023Revised: August 15, 2023Published: October 3, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society9212https://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−9218This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on October 27, 2023 at 01:25:08 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Denis+Yagodkin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Abhijeet+Kumar"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Elias+Ankerhold"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Johanna+Richter"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Cornelius+Gahl"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Cornelius+Gahl"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kirill+I.+Bolotin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c01708&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://acsopenscience.org/open-access/licensing-options/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/devices down to the nanometer scale and is compatible withother probes such as magnetic or electric fields, temperature,or strain. Here, we use the nonlinear response of two-colorTrPC to probe the formation dynamics of dark excitonicspecies. To test our approach, we interrogate the formationdynamics of the commonly studied dark excitons in TMDs:interlayer excitons in MoS2/MoSe2 heterostructures.Toy Model of Time-Resolved Photocurrent. Our firstgoal of this work is to show that the dynamics of dark excitons,which are not accessible via conventional optical techniques,can be obtained from the time-dependent populations of freecarriers. To understand this, we consider a minimal model ofan optically excited semiconductor while analyzing thelimitations of this model later on. We track the time-dependentdensities of free electrons Ne(t) and free holes Nh(t). Weassume that electron and hole populations can be excitedtogether (direct excitation) or separately (indirect excitation),which we model by the generation functions Ge(t) and Gh(t).The relaxation processes of excited carriers can be broadlydivided into two groups: linear (∼Ne/h) and nonlinear (∼Ne/h2 ,∼NeNh with carrier density. We focus on the coupledrelaxation ∼NeNh, which describes the binding of an electronand a hole into an exciton24 (see Supplementary Note 1 fordiscussion on other parameters and detailed analysis of Auger-type and higher-order contributions). Overall, the carrierpopulations are described within our toy model by followingrate equations(1)Here τe/h is the linear relaxation times of electron and holepopulations, and γe−h is the nonlinear exciton formation rate.Since the decay of excitons is several orders of magnitudeslower compared to the relaxation/trapping of free electronsand holes,25,26 the density of the excitons is given byWhile the excitons described by Nex(t) can be dark (andhence hard to probe), their density can be reconstructed if wehave experimental access to Ne(t) and Nh(t). To accomplishthis, we numerically solve the above equations (see theSupporting Information for details). This simple modelbroadly characterizes systems with long-lived excitons.To gain insights into behaviors that eq 1 describes, weemploy a series of simplifying assumptions. We first assumethat holes and electrons can be excited separately (thenumerical solution is free of this assumption; dynamics inthis case is shown in Figure S1). When only holes are excited att1 = 0 ps and only electrons at, for example, t2 ≈ τh = 4 ps, thesolution yields the dynamics shown in Figure 1a−c. Initially,the excited population of holes decays exponentially. After thesecond pulse arrives, electrons are generated (Figure 1b). Therelaxation of holes speeds up due to the formation of excitonsif γe−h is nonzero. Interestingly, we see that the population ofexcitons (Figure 1c) qualitatively follows the differencebetween the hole populations with zero and nonzero γe−h(dashed and solid lines in Figure 1a). For the noninteractingcase (γe−h = 0), the hole density is not affected by the secondpulse exciting electrons (as in a single pulse excitation case),and therefore the population of excitons can also be equated tothe difference of hole densities between a single pulseexcitation (Gh ≠ 0; Ge = 0) vs two pulse excitation (Gh ≠ 0;Ge ≠ 0). We see that, in principle, the dynamics of darkexcitons can be obtained from the dynamics of free carriers.An obvious challenge arises when applying this toy model toa realistic physical system. Conventional optical techniques,such as transient reflectivity spectroscopy, detect combinedcontributions from photoexcited electron (Ne), hole (Nh), andexciton (Nex) populations. Therefore, an alternative techniquesensitive to charge carriers is needed. To address this problem,we use time-resolved photocurrent spectroscopy as ourmeasurement technique. Generally, photocurrent spectros-copies have the advantage of being directly sensitive tophotogenerated electrons/holes while being insensitive to(neutral) excitons.21,22 In trPC, the system is illuminated bytwo optical pulses separated by time interval Δt: Gh(t0) andGe(t0 + Δt), which generate populations of Nh0 and Ne0,respectively. The DC current across the material is recorded.The trPC signal is defined as the difference in current withboth pulses being present versus only a single pulse. In general,photocurrent is proportional to the total amount of freecarriers generated in a system over time. For the systems understudy, TMDs, the direct contribution of electrons to theFigure 1. Excitation dynamics and photocurrent. Dynamics of holes (a), electrons (b), and excitons (c) modeled by eq 1. Solid and dashed linescorrespond to nonzero and zero exciton formation rate (γe−h). After the excitation by a pulse resonant with the MoSe2 band gap (PMoSed2) at t = 0,the hole population (Nh) decays exponentially with the rate τh. This decay is accelerated after electrons are excited (PMoSd2) at Δt ≈ τh = 4 ps in thecase of γe−h ≠ 0. The quantitative measure of this acceleration, the shaded area in (a) is on the one hand determined by γe−h and, on the other hand,can be detected in a time-resolved photocurrent (trPC) experiment. (d) An optical pump pulse in resonance with MoSe2 bandgap (PMoSd2) excitespredominantly holes in the VBM of the heterostructure, while a MoS2 resonant pulse excites electrons in CBM (not shown). Binding of electronsand holes in individual layers yields dark interlayer excitons (inset in (c)).Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189213https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig1&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asphotocurrent can be neglected to simplify analytical derivation,as their lifetime is much lower and contact resistance is higherthan that of holes21,27 (see Supplementary Note 1). In thatcase, the photocurrent produced by only the first pulse is givenby the area under the dashed orange curve in Figure 1a. Therelaxation of the hole population, in this case, depends only onτh as Ge = 0 for a single pulse excitation. The same holds forγe−h = 0 since the nonlinear term in eq 1 vanishes for bothcases. The photocurrent produced by two pulses is given bythe area under the solid curve in Figure 1a and is smaller thanthat of a single pulse (dashed curve) because of holesrecombining with photoexcited electrons. It can be shownanalytically (Supplementary Note 4) that in the limit of smallγe−h and τh ≫ τe, the trPC scales linearly with the excitonformation rate(2)Here the relaxation time (denominator in the exponent) isτh if holes are excited first (positive delay time Δt > 0) and τe ifelectrons are excited first (negative delay time Δt < 0). Thisasymmetry stems from unequal generation terms Ge and Ghand allows the extraction of τe and τh as well as the rate ofexciton formation from the single measurement.We use the 2D heterostructure MoS2/MoSe2 as a system,where the generation rates for electrons and holes can becontrolled separately. Indeed, the conduction band minimum(CBM) and valence band maximum (VBM) of theheterostructure reside in different materials, MoS2 andMoSe2, respectively (Figure 1d). Because of that, an opticalpulse in resonance with, e.g., MoSe2 band gap (PMoSed2) excitesholes in the VBM of the structure (MoSe2), while the excitedelectrons can relax to the CBM (MoS2) through tunneling.Crucially, only around m ≈ 60% of these electrons reach theCBM of the structure in MoS228 (Figure 1d). The remainingelectrons are trapped and do not contribute to the photo-current.29,30 These electrons are not affected by the secondpulse.31 Similarly, a pulse resonant with the MoS2 band gap(PMoSd2) excites electrons to the CBM while m ≈ 60% ofphotoexcited holes reach the VBM of the structure (dynamicsof carriers for this case is shown in Figure S1). Overall, we seethat if m < 100%, the excitation of MoSe2 producespredominantly free holes in the VBM of the heterostructure,while the excitation of MoS2 produces predominantly freeelectrons in the CBM of the heterostructure.We now apply eq 1 to model the excitation dynamics of theMoS2/MoSe2 heterostructure. The parameter Ne(t) describesthe electron density in the CBM of the structure (MoS2) andNh(t) describes the hole density in the VBM (MoSe2). Thefree electron/hole relaxation time (the term linear with Ne/h)describes the combined contributions of defect capture,32intervalley scattering,33 and radiative decay processes.29,30 Therate γe−h describes the formation of (dark) interlayer excitons.Of course, intralayer exciton are formed by optical pulses,especially in resonant excitation. However, optically excitedintralayer excitons decay much faster (within <50 fs15) viacharge separation across the heterostructure, compared tointralayer exciton recombination and electron/hole populationcooling rate (>1 ps).34−36 Therefore, it is absorbed in thegeneration functions Ge and Gh. The latter containcontributions from both pulses (i.e., Ge(t) = PMoSd2(t,t0) + m·PMoSed2(t,t0+Δt); see the effect of m on the dynamics of chargecarriers in Figure S1). Finally, the excitonic ground state ofMoS2/MoSe2 is an interlayer exciton composed of an electronin MoS2 bound to a hole in MoSe2 (inset in Figure 1c). Whenthe twist angle between the heterostructure layers (θ) isnonzero, the interlayer exciton has large in-plane momentum:, where a is the averaged lattice constant of theheterostructure.37,38 In this case, the radiative recombinationmust involve a phonon and the state is dark.38 Thus, theinterlayer exciton decay (>100 ps) can be neglected on thetime scales of the population buildup.39 Our next goal is toobtain the dynamics of Nex(t) via trPC.Time-Resolved Photocurrent. For trPC measurements,we fabricate MoS2/MoSe2 on hBN samples (Figure 2a; seeSupplementary Note 2 for details). We observe the character-istic intralayer A and B excitons for both materials in staticphotocurrent spectroscopy in the heterostructure region(green dots in Figure 2b and Figure S9). In addition, weakphotoluminescence due to interlayer excitons (IX) is observedat 1.3 eV40 (blue line in Figure 2b). For time-resolvedmeasurements, the sample is illuminated with two time-delayed (with ∼10 fs precision) optical pulses, one inresonance with the MoS2 band gap and another with theMoSe2 band gap (PMoSed2= 50 μJ/cm2 unless otherwise stated).The photocurrent is measured with a lock-in amplifiersynchronized to an optical chopper in one of the beam pathswith no bias voltage applied. This measurement effectivelyallows us to evaluate the difference between single- and two-Figure 2. Sample structure and measurement techniques. (a) Schemeof two-color time-resolved photocurrent measurements (trPC). Aphotocurrent excited in the TMD heterostructure is measured vs timedelay between a pulse in resonance with MoSe2 (PMoSed2) and a pulsein resonance with MoS2 (PMoSd2). (b) Photocurrent responsivity (greendots, left axis) and PL (blue line, right axis) spectra of the MoS2/MoSe2 heterostructure. Intralayer A and B excitons of MoS2 andMoSe2 are seen (solid green fit) in PC at a bias voltage of 3.0 V. In PLan additional feature, an interlayer exciton (IX), is observed.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189214https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aspulse responses, which corresponds to the area between thedashed and solid curves in Figure 1a.Figure 3a shows experimental trPC data (green dots) of theMoS2/MoSe2 sample vs delay Δt between the excitationpulses. Positive delay corresponds to the pulses resonant withthe MoS2 band gap arriving first. The most prominent featuresof the data are a strong dip at zero time delay and apronounced asymmetry between positive and negative delays.We now show that these features can be understood within ourtoy model. First, a large drop in trPC suggests nonlinearinteraction between the carrier populations produced by bothpulses, described by γe−h in our model (eq 2). Second, theasymmetry can be understood from eq 2. It suggests that thelifetime of electrons photoexcited in MoS2 is much smallerthan the lifetime of holes excited in MoSe2 (see insets in Figure3a for the illustration of trPC at negative, zero, and positivetime delays). Third, we note a slower decaying component atΔt > 3 ps. This minor effect is missing in Figure 1a and occursfor m ≠ 0 (Supplementary Note 5). Its origin is the transfer ofholes excited by PMoS2 from MoS2 to the VBM of the structure(MoSe2). The ratio between fast and slow decayingcomponents is proportional to m2 (eq S12).To obtain the precise values of the model parameters, we fitthe numerical solution of eq 1 (the solid line in Figure 3a) tothe experimental data. We obtain relaxation times of τh = 6.0 ±0.5 ps, τe = 1.0 ± 0.2 ps, an interaction strength of γe−h = 0.13± 0.04 cm2/s, and a transfer efficiency of m = 55 ± 5%. Theeffect of the variation in every parameter is shown in Figure S2.Using the extracted values, we plot the generation dynamics ofinterlayer excitons vs excitation fluence (black dashed line inFigure 3b). Since the rate at which excitons are formed isproportional to NeNh within our model (eq 1), its accelerationis expected with a higher density of electrons/holes, as seen inthe simulations for several fluence values (solid lines in Figure3b). We observe the formation time (inset of Figure 3b)dropping by more than a factor of 2 in the range of fluencesbetween 100 and 500 μJ/cm2. Overall, the simulations suggesttwo key behaviors. First, we see a much faster relaxation of theelectron population compared to holes. Second, we obtain aformation time of the exciton, gex = 0.4 ps, at our experimentalincident fluence PMoSd2= 160 μJ/cm2.Next, we tested the predictions of these simulations. Tocheck the dependence of exciton formation on fluence given byour model (Figure 3b), we carried out fluence-dependent trPCmeasurements. We keep the incident fluence of PMoSed2fixed,while PMoSd2is varied in the range used in simulation: 75−450μJ/cm2 (dots in Figure 3c). We see that the magnitude of thedrop of the trPC at zero time delay increases with fluence fromaround 30% at 75 μJ/cm2 up to 50% at 450 μJ/cm2. Theexperimental data closely follow the independent predictionsof the model (lines in Figure 3c), where we used the sameparameters as in Figure 3a and only changed the fluence of thebeam (PMoSd2). We extract the formation time of interlayerexcitons gex (inset in Figure 3b) and find that it is more thanhalved in the given fluence range from 0.5 to 0.2 ps. Weobserve small deviations between simulated trPC and theexperiment around the delay Δt ≈ −5 ps and Δt ≈ 2 ps at highexcitation fluence (green in Figure 3c). The first deviationcould be the signature of the contribution of higher-orderterms in eq 1 (see Supplementary Note 1). The seconddeviation may be an effect of the electric field created by layer-separated carriers. This field reduces band offsets, resulting in adecrease of the interlayer transfer efficiency by Δm ≈ 10%(Figure S3).To independently check the dynamics of free carriers, wecarry out two-color time-resolved reflectivity (trRef) measure-ments26 (Figure 4). In this approach, one optical pulse, e.g., inresonance with the MoSe2 band gap, excites both holes andelectrons. Part of the electron population is transferred to theFigure 3. trPC measurements and extraction of exciton dynamics. (a) trPC response of a MoS2/MoSe2 heterostructure (points). The solid lineshows simulated dynamics from the eq 1 with the following model parameters: τe = 1.0 ps, τh = 6.0 ps, interaction strength γe−h = 0.13 cm2/s, andelectron/hole tunneling m = 55%. The insets display dynamics of holes (orange) and electrons (blue) for selected delays between pulses for thesimplified case of m = 0. The difference between response to a single optical pulse (solid) and two pulses (dashed) is proportional to ΔtrPC (greenarea). (b) Simulated dynamics of interlayer exciton formation for data in (a) (black dashed line) and for other fluences PMoSd2= 75, 150, 225, 300,375, 450 μJ/cm2 (solid lines from purple to yellow). The exciton formation becomes faster for higher fluences, as quantified by fitting to ,where gex is the exciton formation time. Inset: extracted gex for the aforementioned fluence range (blue points). The green area corresponds to thecross-correlation of the pulses. The formation time drastically decreases for high laser fluences. (c) Normalized fluence dependence of trPCresponse (points, each data set is offset by 0.2) and independent from measurement simulations using eq 1 with parameters from (a) (lines). Athigher fluences (yellow), the trPC drop at zero time delay increases, suggesting a faster formation and higher number of excitons.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189215https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asCBM in MoS2. The relaxation time of that electron populationis probed by the second (probe) pulse in resonance with theMoS2 band gap, PMoSd2= 150 μJ/cm2 (blue points in Figure 4).Conversely, the pump in resonance with MoSe2 band gap andthe probe in resonance with MoS2 band gap detect thedynamics of holes in MoS2 (green points in Figure 4). Timeconstants for electron and hole populations obtained by fittingthe data of Figure 4 to our model (Supplementary Note 3), τe= 1.4 ps and τh = 6.3 ps, are close to what is obtained fromtrPC, further validating that approach. In addition, the detailedanalysis of this model suggests that the biexponential decayseen for holes (green in Figure 4) across a range of fluences(Figure S4), as well as observed in other works,26,27 originatesfrom the formation of dark excitons.Conclusion and Outlook. To summarize the discussionabove, we proposed a unique method to probe the electron−hole dynamics as well as the dynamics of dark excitons viatime-resolved photocurrent spectroscopy. We extract thefollowing parameters of the system: e−h coupling (γe−h =0.13 ± 0.04 cm2/s), relaxation times of electrons and holes (τe= 1.0 ± 0.2 ps and τh = 6.0 ± 0.5 ps), and efficiency ofinterlayer transport (m = 55 ± 5%), for all fluence regimes.The interlayer exciton formation time varies from 0.2 to 0.5 psin the range of fluences 450−75 μJ/cm2. It is useful to comparethese values with those obtained by other approaches.Electron/hole lifetimes are consistent with those broadlyreported from optical measurements.9,29,36,41,42 The discrep-ancy in the lifetimes of electrons and holes, with electronsexhibiting shorter lifetimes, likely arises from trapping at defectstates located closer to the conduction band.43−45 Theobserved exciton formation time gex = 0.4 ps at 160 μJ/cm2fluence matches the time scales reported in trARPES (∼230fs),15 trTHz reflectivity (∼350 fs),46 and trFIR (∼800 fs)47experiments. The interlayer transfer efficiency m has beenestimated from THz measurements to be 50−70%,28 also closeto the values here. Overall, our approach provides simpleaccess to the dynamics of the dark excitons. Moreover, theproposed model describes trRef dynamics of heterostructuresand explains the biexponential decay reported before.26,27While our model of trPC based on eq 1 is transparent andmatches the main observed behavior, its simplified naturenecessitates several key approximations that may affect itsvalidity. First, the model assumes that the entire photocurrentis produced by free electrons and holes quasi-instantaneouslycreated by the excitation pulses. In reality, the photocurrent isalso produced by nonradiative Auger processes21,29 and field-induced dissociation of both inter- and intralayer excitons.21We believe that these effects are only relevant at high excitationfluences and large applied bias voltages (Vb > 5 V) as wasshown before.12,22 Second, the model neglects the decay of theinterlayer excitons. This is a well-controlled approximationgiven that their decay is 4 orders of magnitude slowercompared to the rate of their formation.25,26,39 The dynamicsof the intralayer exciton is absorbed within the model into thegeneration functions of the carriers. That is justified as long asthe charge separation across the interface is much fastercompared to other decay channels.15,24 Third, the separation ofelectron and hole dynamics in the data such as Figure 3 isfacilitated by the difference of electron/hole generationfunctions (Gh ≠ Ge in eq 1) giving rise to a pronouncedasymmetry between positive and negative time delays.Nevertheless, the same time-resolved photocurrent techniquecan also be applied to systems without such an asymmetry, forexample, single-layer TMDs or perovskites. In that case,relaxation constants for electrons and holes should be obtainedvia an independent measurement, such as optical reflectivity.Finally, the model makes a simplifying assumption of a 1 − mfraction of carriers staying in the layer where they were excitedand the fraction m tunnels across the layers. While thisassumption matches our data as well as previously reportedexperiments by others,28 it can only be confirmed via futuredetailed studies of localized and free carrier dynamics.To conclude, we demonstrate an approach for studying thedark exciton formation dynamics. In the future, this approachcan be used to study other systems where the excitonic groundstate is optically dark, e.g., monolayer TMDs, organic films,and perovskites. Unlike other approaches, trPC is fullycompatible with other optical techniques (trRef and PLshown here, Kerr and ellipticity spectroscopies, second-harmonic generation), has a spatial resolution of hundreds ofnanometers, and works at cryogenic temperatures. It will beparticularly interesting to use trPC to uncover the effects ofmany-body interactions (exciton Mott transition, localizationat low temperature), electric field, and twist angle on theexciton formation time.■ ASSOCIATED CONTENTData Availability StatementThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708.Dynamics of the holes, electrons, and interlayer excitonsfor nonzero interlayer transfer, effect of the parametervariation of the simulated trPC and carrier dynamics,high fluence effects in trPC, fluence dependence of trRef,and discussion of the model, methods, two-color time-resolved reflectivity, analytical solution of the chargeFigure 4. Testing the model: reflectivity dynamics. Semilog plot oftime-resolved reflectivity signal from the MoSe2/MoS2 heterostruc-ture. Green points correspond to the probe pulse in resonance withMoSe2 band gap (pump MoS2) and blue in resonance with MoS2band gap (pump MoSe2). The inset shows a longer time scale. Linesare fits (eq S1) derived from the model in eq 1.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189216https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?goto=supporting-infohttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ascarrier and exciton dynamics, and resulting the photo-current and dynamics in case of nonzero transferefficiency (m ≠ 0) (PDF)■ AUTHOR INFORMATIONCorresponding AuthorKirill I. Bolotin − Department of Physics, Freie UniversitätBerlin, Berlin 14195, Germany; Email: kirill.bolotin@fu-berlin.deAuthorsDenis Yagodkin − Department of Physics, Freie UniversitätBerlin, Berlin 14195, Germany; orcid.org/0000-0002-9135-8918Abhijeet Kumar − Department of Physics, Freie UniversitätBerlin, Berlin 14195, GermanyElias Ankerhold − Department of Physics, Freie UniversitätBerlin, Berlin 14195, Germany; orcid.org/0000-0003-3879-5673Johanna Richter − Department of Physics, Freie UniversitätBerlin, Berlin 14195, GermanyKenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Cornelius Gahl − Department of Physics, Freie UniversitätBerlin, Berlin 14195, Germany; orcid.org/0000-0002-9833-8581Complete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c01708Author ContributionsD.Y., K.I.B., and C.G. conceived and designed the experiments.D.Y., E.A., A.K., and J.R. prepared the samples. D.Y., A.K., andE.A. performed the optical measurements. D.Y. analyzed thedata. E.A. wrote software for simulations. D.Y. and E.A.performed the calculations and helped to rationalize theexperimental data. D.Y. and K.I.B. wrote the manuscript withinput from all coauthors.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThe authors thank Nele Stetzuhn for her comments on thepaper. The authors acknowledge the German ResearchFoundation (DFG) for financial support through theCollaborative Research Center TRR 227 Ultrafast SpinDynamics (project B08) and the Federal Ministry of Educationand Research (BMBF, Projekt 05K22KE3).■ REFERENCES(1) Wang, G.; Chernikov, A.; Glazov, M. M.; Heinz, T. F.; Marie, X.;Amand, T.; Urbaszek, B. Colloquium: Excitons in atomically thintransition metal dichalcogenides. Rev. Mod. Phys. 2018, 90, 021001.(2) Mueller, T.; Malic, E. Exciton physics and device application oftwo-dimensional transition metal dichalcogenide semiconductors. npj2D Materials and Applications 2018, 2, 29.(3) Canneson, D.; Shornikova, E. V.; Yakovlev, D. R.; Rogge, T.;Mitioglu, A. A.; Ballottin, M. V.; Christianen, P. C. M.; Lhuillier, E.;Bayer, M.; Biadala, L. Negatively charged and dark excitons inCsPbBr3 perovskite nanocrystals revealed by high magnetic fields.Nano Lett. 2017, 17, 6177.(4) Mullenbach, T. K.; Curtin, I. J.; Zhang, T.; Holmes, R. J. Probingdark exciton diffusion using photovoltage. Nat. Commun. 2017, 8,14215.(5) Malic, E.; Selig, M.; Feierabend, M.; Brem, S.; Christiansen, D.;Wendler, F.; Knorr, A.; Berghäuser, G. Dark excitons in transitionmetal dichalcogenides. Physical Review Materials 2018, 2, 014002.(6) Rosati, R.; Schmidt, R.; Brem, S.; Perea-Causín, R.; Niehues, I.;Kern, J.; Preuß, J. A.; Schneider, R.; Michaelis de Vasconcellos, S.;Bratschitsch, R.; Malic, E. Dark exciton anti-funneling in atomicallythin semiconductors. Nat. Commun. 2021, 12, 7221.(7) Rosati, R.; Brem, S.; Perea-Causín, R.; Schmidt, R.; Niehues, I.;Michaelis de Vasconcellos, S.; Bratschitsch, R.; Malic, E. Strain-dependent exciton diffusion in transition metal dichalcogenides. 2DMaterials 2021, 8, 015030.(8) Zhang, X. X.; You, Y.; Zhao, S. Y. F.; Heinz, T. F. Experimentalevidence for dark excitons in monolayer WSe2. Phys. Rev. Lett. 2015,115, 257403.(9) Jin, C.; Ma, E. Y.; Karni, O.; Regan, E. C.; Wang, F.; Heinz, T. F.Ultrafast dynamics in van der waals heterostructures. Nat. Nano-technol. 2018, 13, 994.(10) Tang, Y.; Mak, K. F.; Shan, J. Long valley lifetime of darkexcitons in single-layer WSe2. Nat. Commun. 2019, 10, 4047.(11) Steinhoff, A.; Florian, M.; Rösner, M.; Schönhoff, G.; Wehling,T. O.; Jahnke, F. Exciton fission in monolayer transition metaldichalcogenide semiconductors. Nat. Commun. 2017, 8, 1166.(12) Wang, J.; Ardelean, J.; Bai, Y.; Steinhoff, A.; Florian, M.; Jahnke,F.; Xu, X.; Kira, M.; Hone, J.; Zhu, X. Y. Optical generation of highcarrier densities in 2d semiconductor heterobilayers. Science Advances2019, 5, 1.(13) Wang, Z.; Rhodes, D. A.; Watanabe, K.; Taniguchi, T.; Hone, J.C.; Shan, J.; Mak, K. F. Evidence of high-temperature excitoncondensation in two-dimensional atomic double layers. Nature 2019,574, 76.(14) Zhang, X.-X.; Cao, T.; Lu, Z.; Lin, Y.-C.; Zhang, F.; Wang, Y.;Li, Z.; Hone, J. C.; Robinson, J. A.; Smirnov, D.; Louie, S. G.; Heinz,T. F. Magnetic brightening and control of dark excitons in monolayerWSe2. Nat. Nanotechnol. 2017, 12, 883.(15) Schmitt, D.; Bange, J. P.; Bennecke, W.; AlMutairi, A.;Meneghini, G.; Watanabe, K.; Taniguchi, T.; Steil, D.; Luke, D. R.;Weitz, R. T.; Steil, S.; Jansen, G. S. M.; Brem, S.; Malic, E.; Hofmann,S.; Reutzel, M.; Mathias, S. Formation of moire ́ interlayer excitons inspace and time. Nature 2022, 608, 499.(16) Madéo, J.; Man, M. K.; Sahoo, C.; Campbell, M.; Pareek, V.;Wong, E. L.; Al-Mahboob, A.; Chan, N. S.; Karmakar, A.; Mariserla,B. M. K.; Li, X.; Heinz, T. F.; Cao, T.; Dani, K. M. Directly visualizingthe momentum-forbidden dark excitons and their dynamics inatomically thin semiconductors. Science 2020, 370, 1199.(17) Wallauer, R.; Perea-Causin, R.; Münster, L.; Zajusch, S.; Brem,S.; Güdde, J.; Tanimura, K.; Lin, K.-Q.; Huber, R.; Malic, E.; Höfer,U. Momentum-resolved observation of exciton formation dynamics inmonolayer WS2. Nano Lett. 2021, 21, 5867.(18) Yagodkin, D.; Nádvorník, L.; Gueckstock, O.; Gahl, C.;Kampfrath, T.; Bolotin, K. I. Ultrafast photocurrents in MoSe2 probedby terahertz spectroscopy. 2D Materials 2021, 8, 025012.(19) Paik, E. Y.; Zhang, L.; Burg, G. W.; Gogna, R.; Tutuc, E.; Deng,H. Interlayer exciton laser of extended spatial coherence in atomicallythin heterostructures. Nature 2019, 576, 80.(20) Massicotte, M.; Schmidt, P.; Vialla, F.; Schädler, K. G.;Reserbat-Plantey, A.; Watanabe, K.; Taniguchi, T.; Tielrooij, K. J.;Koppens, F. H. L. Picosecond photoresponse in van der waalsheterostructures. Nat. Nanotechnol. 2016, 11, 42.(21) Massicotte, M.; Vialla, F.; Schmidt, P.; Lundeberg, M. B.;Latini, S.; Haastrup, S.; Danovich, M.; Davydovskaya, D.; Watanabe,K.; Taniguchi, T.; Fal’ko, V. I.; Thygesen, K. S.; Pedersen, T. G.;Koppens, F. H. Dissociation of two-dimensional excitons inmonolayer WSe2. Nat. Commun. 2018, 9, 1.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189217https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01708/suppl_file/nl3c01708_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kirill+I.+Bolotin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:kirill.bolotin@fu-berlin.demailto:kirill.bolotin@fu-berlin.dehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Denis+Yagodkin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-9135-8918https://orcid.org/0000-0002-9135-8918https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Abhijeet+Kumar"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Elias+Ankerhold"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3879-5673https://orcid.org/0000-0003-3879-5673https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Johanna+Richter"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3701-8119https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Cornelius+Gahl"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-9833-8581https://orcid.org/0000-0002-9833-8581https://pubs.acs.org/doi/10.1021/acs.nanolett.3c01708?ref=pdfhttps://doi.org/10.1103/RevModPhys.90.021001https://doi.org/10.1103/RevModPhys.90.021001https://doi.org/10.1038/s41699-018-0074-2https://doi.org/10.1038/s41699-018-0074-2https://doi.org/10.1021/acs.nanolett.7b02827?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.7b02827?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/ncomms14215https://doi.org/10.1038/ncomms14215https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1103/PhysRevMaterials.2.014002https://doi.org/10.1038/s41467-021-27425-yhttps://doi.org/10.1038/s41467-021-27425-yhttps://doi.org/10.1088/2053-1583/abbd51https://doi.org/10.1088/2053-1583/abbd51https://doi.org/10.1103/PhysRevLett.115.257403https://doi.org/10.1103/PhysRevLett.115.257403https://doi.org/10.1038/s41565-018-0298-5https://doi.org/10.1038/s41467-019-12129-1https://doi.org/10.1038/s41467-019-12129-1https://doi.org/10.1038/s41467-017-01298-6https://doi.org/10.1038/s41467-017-01298-6https://doi.org/10.1126/sciadv.aax0145https://doi.org/10.1126/sciadv.aax0145https://doi.org/10.1038/s41586-019-1591-7https://doi.org/10.1038/s41586-019-1591-7https://doi.org/10.1038/nnano.2017.105https://doi.org/10.1038/nnano.2017.105https://doi.org/10.1038/s41586-022-04977-7https://doi.org/10.1038/s41586-022-04977-7https://doi.org/10.1126/science.aba1029https://doi.org/10.1126/science.aba1029https://doi.org/10.1126/science.aba1029https://doi.org/10.1021/acs.nanolett.1c01839?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.1c01839?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1088/2053-1583/abd527https://doi.org/10.1088/2053-1583/abd527https://doi.org/10.1038/s41586-019-1779-xhttps://doi.org/10.1038/s41586-019-1779-xhttps://doi.org/10.1038/nnano.2015.227https://doi.org/10.1038/nnano.2015.227https://doi.org/10.1038/s41467-018-03864-yhttps://doi.org/10.1038/s41467-018-03864-ypubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(22) Klots, A. R.; Newaz, A. K.; Wang, B.; Prasai, D.; Krzyzanowska,H.; Lin, J.; Caudel, D.; Ghimire, N. J.; Yan, J.; Ivanov, B. L.;Velizhanin, K. A.; Burger, A.; Mandrus, D. G.; Tolk, N. H.; Pantelides,S. T.; Bolotin, K. I. Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy. Sci. Rep.2014, 4, 1.(23) Wang, H.; Zhang, C.; Chan, W.; Tiwari, S.; Rana, F. Ultrafastresponse of monolayer molybdenum disulfide photodetectors. Nat.Commun. 2015, 6, 6.(24) Ovesen, S.; Brem, S.; Linderälv, C.; Kuisma, M.; Korn, T.;Erhart, P.; Selig, M.; Malic, E. Interlayer exciton dynamics in van derwaals heterostructures. Communications Physics 2019, 2, 23.(25) Rivera, P.; Seyler, K. L.; Yu, H.; Schaibley, J. R.; Yan, J.;Mandrus, D. G.; Yao, W.; Xu, X. Valley-polarized exciton dynamics ina 2d semiconductor heterostructure. Science 2016, 351, 688.(26) Kumar, A.; Yagodkin, D.; Stetzuhn, N.; Kovalchuk, S.;Melnikov, A.; Elliott, P.; Sharma, S.; Gahl, C.; Bolotin, K. I. Spin/valley coupled dynamics of electrons and holes at the MoS2 − MoSe2interface. Nano Lett. 2021, 21, 7123.(27) Ceballos, F.; Bellus, M. Z.; Chiu, H.-Y.; Zhao, H. Ultrafastcharge separation and indirect exciton formation in a MoS2 − MoSe2van der waals heterostructure. ACS Nano 2014, 8, 12717.(28) Ma, E. Y.; Guzelturk, B.; Li, G.; Cao, L.; Shen, Z. X.;Lindenberg, A. M.; Heinz, T. F. Recording interfacial currents on thesubnanometer length and femtosecond time scale by terahertzemission. Science Advances 2019, 5, 1.(29) Wang, H.; Zhang, C.; Rana, F. Ultrafast dynamics of defect-assisted electron−hole recombination in monolayer MoS2. Nano Lett.2015, 15, 339.(30) Qiu, H.; Xu, T.; Wang, Z.; Ren, W.; Nan, H.; Ni, Z.; Chen, Q.;Yuan, S.; Miao, F.; Song, F.; Long, G.; Shi, Y.; Sun, L.; Wang, J.;Wang, X. Hopping transport through defect-induced localized statesin molybdenum disulphide. Nat. Commun. 2013, 4, 2642.(31) Jadczak, J.; Bryja, L.; Kutrowska-Girzycka, J.; Kapusćinśki, P.;Bieniek, M.; Huang, Y.-S.; Hawrylak, P. Room temperature multi-phonon upconversion photoluminescence in monolayer semiconduc-tor WS2. Nat. Commun. 2019, 10, 107.(32) Alkauskas, A.; Yan, Q.; Van de Walle, C. G. First-principlestheory of nonradiative carrier capture via multiphonon emission. Phys.Rev. B 2014, 90, 075202.(33) Ferry, D. K. First-order optical and intervalley scattering insemiconductors. PHYSICAL REVIEW B 1976, 14, 1605.(34) Robert, C.; Lagarde, D.; Cadiz, F.; Wang, G.; Lassagne, B.;Amand, T.; Balocchi, A.; Renucci, P.; Tongay, S.; Urbaszek, B.; Marie,X. Exciton radiative lifetime in transition metal dichalcogenidemonolayers. Phys. Rev. B 2016, 93, 205423.(35) Zhang, J.; Hong, H.; Zhang, J.; Fu, H.; You, P.; Lischner, J.; Liu,K.; Kaxiras, E.; Meng, S. New pathway for hot electron relaxation intwo-dimensional heterostructures. Nano Lett. 2018, 18, 6057.(36) Nie, Z.; Long, R.; Sun, L.; Huang, C.-C.; Zhang, J.; Xiong, Q.;Hewak, D. W.; Shen, Z.; Prezhdo, O. V.; Loh, Z.-H. Ultrafast carrierthermalization and cooling dynamics in few-layer MoS2. ACS Nano2014, 8, 10931.(37) Wu, F.; Lovorn, T.; MacDonald, A. H. Theory of opticalabsorption by interlayer excitons in transition metal dichalcogenideheterobilayers. Phys. Rev. B 2018, 97, 035306.(38) Yu, H.; Wang, Y.; Tong, Q.; Xu, X.; Yao, W. Anomalous lightcones and valley optical selection rules of interlayer excitons in twistedheterobilayers. Phys. Rev. Lett. 2015, 115, 187002.(39) Jiang, Y.; Chen, S.; Zheng, W.; Zheng, B.; Pan, A. Interlayerexciton formation, relaxation, and transport in TMD van der waalsheterostructures. Light: Science and Applications 2021, 10, 72.(40) Hanbicki, A. T.; Chuang, H.-J.; Rosenberger, M. R.; Hellberg,C. S.; Sivaram, S. V.; McCreary, K. M.; Mazin, I. I.; Jonker, B. T.Double indirect interlayer exciton in a MoSe2/WSe2 van der waalsheterostructure. ACS Nano 2018, 12, 4719.(41) Wang, H.; Zhang, C.; Rana, F. Surface recombination limitedlifetimes of photoexcited carriers in few-layer transition metaldichalcogenide MoS 2. Nano Lett. 2015, 15, 8204.(42) Chi, Z.; Chen, H.; Chen, Z.; Zhao, Q.; Chen, H.; Weng, Y.-X.Ultrafast energy dissipation via coupling with internal and externalphonons in two-dimensional MoS 2. ACS Nano 2018, 12, 8961.(43) Kar, S.; Su, Y.; Nair, R. R.; Sood, A. K. Probing photoexcitedcarriers in a few-layer MoS 2 laminate by time-resolved optical pump−terahertz probe spectroscopy. ACS Nano 2015, 9, 12004.(44) Pandey, M.; Rasmussen, F. A.; Kuhar, K.; Olsen, T.; Jacobsen,K. W.; Thygesen, K. S. Defect-tolerant monolayer transition metaldichalcogenides. Nano Lett. 2016, 16, 2234.(45) Yagodkin, D.; Greben, K.; Eljarrat, A.; Kovalchuk, S.; Ghorbani-Asl, M.; Jain, M.; Kretschmer, S.; Severin, N.; Rabe, J. P.;Krasheninnikov, A. V.; Koch, C. T.; Bolotin, K. I. Extrinsic localizedexcitons in patterned 2d semiconductors. Adv. Funct. Mater. 2022, 32,2203060.(46) Merkl, P.; Mooshammer, F.; Steinleitner, P.; Girnghuber, A.;Lin, K. Q.; Nagler, P.; Holler, J.; Schüller, C.; Lupton, J. M.; Korn, T.;Ovesen, S.; Brem, S.; Malic, E.; Huber, R. Ultrafast transition betweenexciton phases in van der waals heterostructures. Nat. Mater. 2019, 18,691.(47) Chen, H.; Wen, X.; Zhang, J.; Wu, T.; Gong, Y.; Zhang, X.;Yuan, J.; Yi, C.; Lou, J.; Ajayan, P. M.; Zhuang, W.; Zhang, G.; Zheng,J. Ultrafast formation of interlayer hot excitons in atomically thinMoS2/WS2 heterostructures. Nat. Commun. 2016, 7, 1.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01708Nano Lett. 2023, 23, 9212−92189218https://doi.org/10.1038/srep06608https://doi.org/10.1038/srep06608https://doi.org/10.1038/ncomms9831https://doi.org/10.1038/ncomms9831https://doi.org/10.1038/s42005-019-0122-zhttps://doi.org/10.1038/s42005-019-0122-zhttps://doi.org/10.1126/science.aac7820https://doi.org/10.1126/science.aac7820https://doi.org/10.1021/acs.nanolett.1c01538?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.1c01538?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.1c01538?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn505736z?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn505736z?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn505736z?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1126/sciadv.aau0073https://doi.org/10.1126/sciadv.aau0073https://doi.org/10.1126/sciadv.aau0073https://doi.org/10.1021/nl503636c?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nl503636c?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/ncomms3642https://doi.org/10.1038/ncomms3642https://doi.org/10.1038/s41467-018-07994-1https://doi.org/10.1038/s41467-018-07994-1https://doi.org/10.1038/s41467-018-07994-1https://doi.org/10.1103/PhysRevB.90.075202https://doi.org/10.1103/PhysRevB.90.075202https://doi.org/10.1103/PhysRevB.14.1605https://doi.org/10.1103/PhysRevB.14.1605https://doi.org/10.1103/PhysRevB.93.205423https://doi.org/10.1103/PhysRevB.93.205423https://doi.org/10.1021/acs.nanolett.8b03005?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.8b03005?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn504760x?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn504760x?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1103/PhysRevB.97.035306https://doi.org/10.1103/PhysRevB.97.035306https://doi.org/10.1103/PhysRevB.97.035306https://doi.org/10.1103/PhysRevLett.115.187002https://doi.org/10.1103/PhysRevLett.115.187002https://doi.org/10.1103/PhysRevLett.115.187002https://doi.org/10.1038/s41377-021-00500-1https://doi.org/10.1038/s41377-021-00500-1https://doi.org/10.1038/s41377-021-00500-1https://doi.org/10.1021/acsnano.8b01369?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.8b01369?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b03708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b03708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b03708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.8b02354?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.8b02354?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.5b04804?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.5b04804?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.5b04804?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b04513?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b04513?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1002/adfm.202203060https://doi.org/10.1002/adfm.202203060https://doi.org/10.1038/s41563-019-0337-0https://doi.org/10.1038/s41563-019-0337-0https://doi.org/10.1038/ncomms12512https://doi.org/10.1038/ncomms12512pubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01708?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as