1s-intraexcitonic dynamics in monolayer MoS2 probed by ultrafast mid-infrared spectroscopy

The 1s exciton—the ground state of a bound electron-hole pair—is central to understanding the photoresponse of monolayer transition metal dichalcogenides. Above the 1s exciton, recent visible and near-infrared investigations have revealed that the excited excitons are much richer, exhibiting a series of Rydberg-like states. A natural question is then how the internal excitonic transitions are interrelated on photoexcitation. Accessing these intraexcitonic transitions, however, demands a fundamentally different experimental tool capable of probing optical transitions from 1s ‘bright' to np ‘dark' states. Here we employ ultrafast mid-infrared spectroscopy to explore the 1s intraexcitonic transitions in monolayer MoS2. We observed twofold 1s→3p intraexcitonic transitions within the A and B excitons and 1s→2p transition between the A and B excitons. Our results revealed that it takes about 0.7 ps for the 1s A exciton to reach quasi-equilibrium; a characteristic time that is associated with a rapid population transfer from the 1s B exciton, providing rich characteristics of many-body exciton dynamics in two-dimensional materials.

Above the fundamental 1s exciton, theories predicted the presence of densely spaced exciton states in monolayer MoS 2 with 1s exciton E bind of 0.4-0.54 eV (refs [18][19][20][21][28][29][30][31], whose (s-like) bright and (p-like) dark exciton characters were later confirmed by a series of seminal experiments via linear one-photon absorption 21,22 , two-photon photoluminescence excitation (PLE) [22][23][24]32 and nonlinear wave-mixing spectroscopy 25,32 , whereby E bind was experimentally measured to be between 0. 22 (ref. 26) and 0.44 eV (refs 23,26); the reported E bind , however, shows somewhat discrepancy depending on the measurement methods and is varied from samples to samples 23,26,27 . These experimental techniques, although they are appropriate to clarify the optical state of the excitons, may address indirectly the dynamic transient information between the 1s 'bright' and the excited np 'dark' exciton (n is the principle quantum number); we denoted the exciton states in analogy to the hydrogen series 21 . By contrast, if one measures the 1s-np transitions, then the data should describe the internal excitonic transients, directly providing the transient optical nature of the fundamental 1s exciton dynamics. This, so called intraexcitonic spectroscopy 33 , fundamentally differs from band-to-band and other time-resolved spectroscopies 8,[34][35][36] , and the technique can not only explain the transient response of the 1s exciton, but more importantly, may provide experimental manoeuvre in exploiting the photoinduced excitonic responses to the TMDC-based optoelectronic devices. For example, knowledge of the 1s and np exciton energies and their associated dynamics afford the first-order quantitative information on the exciton dissociation energy, where in an ideal case at least E bind /e (e is the electron charge) of an external or internal potential is required to dissociate the bound e-h pairs. In addition, because intraexcitonic spectroscopy can access the p-like dark excitons, one may design a scheme of coupling an infrared (IR) light to the 2D TMDC materials, via below-gap two-photon excitation, for the light-harnessing applications.
Here we explore the 1s intraexcitonic transient dynamics in monolayer MoS 2 by using time-resolved mid-IR spectroscopy. Inspired by a theoretical GW-Bethe-Salpeter result 19 , where the fundamental 1s-2p transitions are predicted to be 0.32 and 0.3 eV for the A and B exciton in isolated, suspended monolayer MoS 2 , we employed an ultrafast mid-IR spectroscopy (0.23-0.37 eV probe) in conjunction with an ultrafast white-light continuum spectroscopy (Fig. 1a). The mid-IR measurements show that there are two 1s-3p transitions for A and B exciton and 1s-2p between 1s A and 2p B exciton. The time-dependent IR absorption rapidly subdues over broad probe-photon energies, representing the transient absorption from the 1s to the quasi-continuum states after pump excitation.

Results
Time-resolved intraexcitonic and band-to-band dynamics. The samples used in our experiment were monolayer MoS 2 , grown by chemical vapour deposition method, and were transferred to a CaF 2 substrate (see Supplementary Note 1 for the sample characterization). As schematically shown in Fig. 1a, the sample was non-resonantly excited by a 70 fs, 3.1 eV pump pulse, and the corresponding differential-transmission changes DT/T 0 were measured in a vacuum cryostat (Methods). The 3.1 eV pump excites carriers into the quasi-continuum of the A and B excitons 37,38 or into the band-nesting C-band near the G point 39,40 . The former generates the unbound e-h plasma above the A and B excitons and the latter case experiences a rapid inter-valley scattering into K and K 0 valley. Nevertheless, both cases generate carriers in much higher energy compared with the A or B exciton resonance. Figure 1b shows a direct comparison of two representative data measured by mid-IR probe (0.35 eV) and interband A-exciton probe (1.86 eV) with the same pump fluence F ¼ 24.4 mJ cm À 2 (equivalent to e-h pair density of 7.4 Â 10 12 cm À 2 given 15% absorption) 8,41 measured at 77 K. The polarization of pump and probe beam are linear and orthogonal with respect to each other, such that we do not account for the recently discovered valley-exciton-locked selection rule 32 . The fact that two DT/T 0 transients exhibit an opposite sign implies the kinetic origin of the photoresponses is indeed different. For the 1.86 eV dynamics, the increased probe transmission is typically attributed to the ground-state bleaching 35,42,43 , where the increased occupation probability of electrons in conduction band and holes in the valance band leads to the reduced probe absorption, that is, increased DT/T 0 40. On the other hand, given that the 0.35 eV probe is far below the band-to-band A-exciton energy, one may attribute the decreased DT/T 0 o0 (increased probe absorption) to the transition within the bands, that is, intraband free-carrier absorption. However, considering that the mid-IR peak signal is only 36.2% of the 1.86 eV one, we can exclude this possibility because the intraband oscillator strength is much smaller than the interband one, usually by an order of magnitude, as revealed by prior works on the quasi-2D quantum wells 44 or recent 2D MoS 2 (ref. 45); as discussed later in Figs 2-4, we provide compelling experimental evidences to support our rationale (see also Supplementary Note 2 (refs 46-48)). The increased probe absorption of the mid-IR suggests that there exists an occupied state below the electronic gap. We find that there exists a clear time departure between the two rising dynamics, where the onset of the 0.35 eV probe peak appears B0.2 ps later than the 1.86 eV probe (dashed line in Fig. 1b). Immediately after the pump, the 1.86 eV probe rapidly increases, while the 0.35 eV dynamics emerge rather slowly. We observed that this rapid upsurge of the 1.86 eV is not a local spectral behaviour, but being presented in a broad range of high-energy probes (Supplementary Notes 3 and 4), evidencing the quasi-instantaneous ground-state bleaching 35 . Understanding this high-energy dynamics has been a subject to debate; different investigations have proposed different kinetic origins of the 1s exciton, such as exciton linewidth broadening 35 , stimulated emission 42 , dynamic bandgap renormalization 49 and biexciton formation 38 . As discussed, more details in Supplementary Note 4, both earlier [50][51][52] and recent studies 35,42,53 , have shown that the 3.1 eV photoexcitation into the quasi-continuum of unbound states generates a significant amount of free-carriers. Because the exciton formation occurs after exciton-free carrier scattering, the initial decaying kinetics of mid-IR is slightly delayed compared with the rising transient of the interband one, explaining the observed time-delay between the two transients of Fig. 1b. Since the mid-IR probe can resonantly measure the internal exciton dynamics, the measured intraexcitonic transients are expected to provide pure population dynamics of the ground 1s exciton 33,54 .
Temperally and spectrally resolved intraexcitonic dynamics. Figure 2 is the temporally and spectrally resolved mid-IR dynamics. Here we probed not only the broad mid-IR transients (0.23-0.37 eV), but also measured the IR dynamics (0.47-0.67 eV). This scheme affords a simultaneous access to the dynamic transitions from the 1s ground exciton to the higher lying np excitons or quasi-continuum states. The measured À DT/T 0 spectra show peculiar energy-dependent behaviours. At Dtr0.4 ps, the À DT/T 0 spectra are strongly reshaped, exhibiting a relatively small increase of differential absorption (not absolute absorption) near 0.27 eV compared with the increased absorption around 0.3-0.5 eV. The increased absorption is more prominent at Dt40.4 ps, where one can see that À DT/T 0 is gradually larger near 0.27 eV with increasing Dt, and the differential absorption at 0.3-0.5 eV is concurrently smaller with increasing Dt. Between 0.4oDtr0.9 ps, À DT/T 0 above 0.3 eV is rapidly vanished, while the absorption resonance below 0.3 eV is accordingly increased. After Dt40.9 ps, the absorption resonance below 0.3 eV keeps reserved and it slowly subdues with featureless IR spectra above 0.3 eV.
For a quantitative analysis of the observed transient spectra, we use the following model consisted of multi-oscillator components 55 : The term of summation represents the intraexcitonic absorption from 1s to either A or B excitonic np state and the second term Y(E À E bind ) is a step-like transition 21 from 1s to the continuum with E bind of 0.44 eV. In the equation, e ( ¼ 4.2) (refs 14,27) and e 0 are the dielectric constant of monolayer MoS 2 and the vacuum dielectric constant, respectively. There, the absorption amplitude S 1s-np , or the spectral weight of the intraexcitonic 1s-np transition, is proportional to the product of the oscillator strength f 1s-np and the ground exciton density n 1s (refs 39,40,55,56). Because the 3.1 eV pump excitation creates e-h plasma in the band nesting resonance, an accurate estimation of n 1s requires both theoretical study of intervalley scatterings and the corresponding ultrafast measurements, which is beyond the scope of our ultrafast mid-IR intraexcitonic spectroscopy. In fact, the spectral weight from 1s-np is not only proportional to the population, but also depends on the probability of finding an empty final np state. As discussed about the transient spectra dynamics above, the photoexcited unbound e-h pairs experience rapid relaxation and start to form a ground-state exciton within B0.4 ps. It is strictly true that the np exciton population is negligible only at DtZ0.4 ps. Similar studies on 1D and quasi-2D quantum-well structures have shown that the contribution from np-continuum is negligible 33,54,[56][57][58] . We found that the spectral fit matches well the measured data when we used up to three mid-IR oscillators, with the following transition energy E n of E 1 ¼ 0.27 eV, E 2 ¼ 0.31 eV, and E 3 ¼ 0.36 eV. On the basis that the observed E n s do not vary Dt, we fix E n to fit the time-resolved mid-IR spectra, but vary S 1s-np and the phenomenological exciton broadening parameter G. For the IR transients, the spectra are featureless representing the step-function-like 1s to the continuum transition 21 ; this featureless IR spectrum is Given that the magnitude of S 1s-np differs only by a factor of 2 for each E n , these transitions cannot simply be assigned to the phenomena taking place within single exciton Rydberg series of the A (or B) exciton branch. This is because even when the nonhydrogenic excitonic nature of a monolayer TMDC is considered, where a strongly (weakly) screened Coulomb potential is dominant when nr2 (nZ3) (ref. 21), the spectral weight should be substantially decreased by nearly an order of magnitude with increasing n, which is too large to account for our measurement results. Of course, care should be taken to estimate the precise strength of intraexcitonic transition in a monolayer TMDC because the nonhydrogenic exciton is dominant when nr2, thus the 1s-np transition can deviate from the hydrogenic excitonic nature for nZ3. This is because any intraexcitonic 1s-np transition depends both on the wavefunction of the nth exciton as well as the 1s exciton state, and the latter certainly deviates from the 2D-hydrogen model. Recent PLE 23 revealed that the energy levels of the exciton Rydberg series are 1.88 eV (1s), 2.05 eV (2s) and 2.15 eV (3s) for A exciton and 2.03 eV (1s), 2.24 eV (2s) and 2.34 eV (3s) for B exciton. By considering 0.15 eV energy splitting between A and B excitons and the difference of reduced exciton masses of 0.25m 0 (A exciton) and 0.28m 0 (B exciton) 18 , we estimated the intraexcitonic transition energies of 0.27 eV for E 1A-3A , 0.31 eV for E 1B-3B and 0.36 eV for E 1A-2B , which are exactly matched our measured intraexcitonic transition energy E n . Interestingly, these values are somewhat deviated from the GW-Bethe-Salpeter prediction 19 , possibly due to the substrate dielectric screening effect. Nevertheless, our measurements agree well with the experimental PLE investigation due to similar dielectric constant of CaF 2 and fused silica 23 as a substrate. Although there is a small difference (B20 meV) for the A exciton energy between PLE (1.88 eV) and our photocurrent spectra and ultrafast absorption measurement (1.86 eV, Supplementary Notes 1 and 3), the difference is very marginal 19,28,30,31 and the intraexcitonic spectroscopy can measure the energy difference between 1s and np, regardless of the A-exciton resonance. In accordance with PLE and our mid-IR measurements, we expect the fundamental 1s-2p would be 0.17 eV for the A exciton and 0.21 eV for the B exciton, and this is beyond our capability of tuning the mid-IR spectrum. Therefore, as schematically shown in Fig. 3a, we understand our intraexcitonic transition energy of E 1 as 1s ,A -3p ,A within A exciton, E 2 as 1s ,B -3p ,B within B exciton and E 3 as 1s ,A -2p ,B between A and B exciton. Indeed, our energy assignment well-corroborates a recent many-body Bethe-Salpeter prediction on the nonhydrogenic characters of excited excitons 19,20,28,30,31 , underscoring a distinct capability of our intraexcitonic spectroscopy in measuring the relative energy difference between 1s and np. For the exciton broadening parameter G, since the effective mass of A and B exciton is different, G ( ¼ 28.2 meV) for 1s ,A -3p ,A , G ( ¼ 37.4 meV) for 1s ,B -3p ,B and G ( ¼ 30 meV) for 1s ,A -2p ,B are slightly different due to the different exciton dispersion.
Dynamics of 1s-np intraexcitonic spectral weights. For further analysis, we show the temporal dynamics of S 1s,A-3p,A (Fig. 3c, blue), S 1s,B-3p,B (Fig. 3d, orange) and S 1s,A-3p,A (Fig. 3e, green). We identify three different kinetic regimes: immediately after the pump, the rising transients of all three spectral weights show similar behaviours, representing the hot-carrier relaxation from the quasi-continuum to the A and B exciton branch. This kinetics clearly differs from the dynamics of 1.86 eV probe (Fig. 3b), where the latter arises from the quasi-instantaneous bleaching dynamics. At 0.4rDtr0.7 ps, the dynamics of S 1s,B-3p,B rapidly decrease, while the peak S 1s,A-3p,A and S 1s,A-3p,B emerge B0.3 ps later. Because the 1s B exciton is 0.15 eV higher than that of A exciton (Fig. 3a), the 1s B exciton serves as a population supplier to the energetically lower 1s A exciton, thereby the two transients show a complementary dynamics. At longer Dt40.7 ps, because the 1s A excitons are thermalized and reaches a quasi-equilibrium condition, the dynamics of S 1s,A-3p,A nearly follows that of S 1s,A-2p,B . This highlights that although S 1s,A-3p,A and S 1s,A-3p,B are spectrally separated apart, that is 0.27 and 0.36 eV, respectively, both transients are closely interrelated because these absorptions originate from the same 1s ,A ground state exciton.

Discussion
At an elevated temperature, the free-carrier absorption from 1s, 2s, 2p, 3s, 3py may contribute to the increased probe absorption with DT/T 0 o0. This scenario typically shows a strong temperature dependence of the relaxation rate, in which the higher temperature the larger the electron-phonon scattering rate, resulting in the dynamics to be highly temperature dependent. Here given that the formation time scale of the 1s exciton is very fast within 0.4 ps (see Figs 2 and 3) and the Drude scattering rate cannot be extended to the mid-IR range (Supplementary Note 2), the contribution of np-continuum transition may be very insignificant to the temperature-dependent mid-IR intraexcitonic response. Figure 4a shows that our mid-IR transients, fitted by a biexponential function, exhibit nearly temperature independent of the relaxation components (Fig. 4b,c). This implies that the effect of free-carrier absorption is negligible. We additionally show in Fig. 4b that the recombination of excitons arises on sub-ps and tens of ps time scale. At T ¼ 77 K, the mid-IR peak |DT/T 0 | linearly increases with F up to 32.5 mJ cm À 2 (equivalent to e-h pair density of 9.86 Â 10 12 cm À 2 ) (refs 8,41). The linear F-dependence reflects that there exists no high-order nonlinear excitonic interaction, ensuring that our mid-IR transients represent the first-order population dynamics. A recent below-gap-probe study 45 reported very similar relaxation times to our results. These time components were explained using defect-assisted exciton recombination. Given that we observed negligible F-dependent relaxation dynamics (Fig. 4e,f), we can infer that our mid-IR decay transients do not arise from the photoinduced absorption of filled e-h pair in the localized states, but arise from the exciton capture into the defects.
In summary, we report the experimental observation of the 1s intraexcitonic transition. Recently, Poellmann et al. 47 investigated a similar investigation of intraexcitonic transition in monolayer WSe 2 , reporting the presence of strong absorption in a 2D TMDC, whose fundamental optical absorption originates from the 1s ground exciton. Our ultrafast mid-IR measurements reveal twofold 1s-3p transition energies to be 0.27 eV and 0.31 eV for A and B exciton, respectively. We additionally uncover an intraexcitonic relaxation channel of 1s-2p to be 0.36 eV between 1s A and 2p B exciton. The large exciton-binding energy due to the non-local dielectric screening ensures not only 1s-2p transition 47 to be observable, but also a higher-order transition of 1s-3p in a monolayer 2D TMDC at an elevated temperature, which cannot be accessible using conventional interband spectroscopy, or any in quasi-2D quantum-well structures. In addition, looking to the future, the availability of electric-gate tuning may enable to investigate the coherent many-body inter-excitonic correlations among exciton, biexciton 38,59 and trion 12,13,18,48 in a time-resolved controlled manner, which is non-trivial to study in other low-dimensional inorganic semiconductor structures.

Methods
Ultrafast optical pump-probe spectroscopy. Using 250 kHz, 50 fs Ti/sapphire laser system (Coherent RegA 9050), optical parametric amplifier (Coherent OPA 9850) yields signal (0.77-1.12 eV) and idler (0.47 eV-0.67 eV) pulses that are used to generate mid-IR pulse (0.23-0.37 eV) via difference frequency generator (Coherent DFG). The idler and DFG output serve as the probe pulse in the IR and mid-IR range, respectively. The chirp of mid-IR pulse is discussed in Supplementary Note 5. High-energy interband response was measured by using a white-light continuum (1.76-2.03 eV) generated by focusing 1.55 eV pulses into a 1 mm sapphire disk. For the group-delay dispersion (GDD) of the white-light continuum pulse, we compensated using a pair of prism, and further checked the GDD-induced delay via cross-correlation of the white-light pulse and 1.55 eV pulse, whose details are explained in the Supplementary Note 3. The 3.1 eV pump pulse was created by second harmonic generation of 1.55 eV pulse in a 1-mm-thick beta barium borate (BBO) crystal. Due to the combination of OPA and DFG, where both signal and idler from OPA were used to generate the mid-IR DFG output, the only available seed pulse for 3.1 eV pump pulse was 1.55 eV in our system, so that the mid-IR measurement with resonant pump excitation at either A or B 1s exciton was not possible in our current system. For the each mid-IR or IR measurement, pump pulse and probe pulse are simultaneously focused on the sample in the NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10768 ARTICLE NATURE COMMUNICATIONS | 7:10768 | DOI: 10.1038/ncomms10768 | www.nature.com/naturecommunications cryostat equipped with two CaF 2 windows, and pump-probe delay is controlled by a mechanical delay stage (Newport M-IMS300LM). The spot size of our pump and probe beams were 100 mm, and 50 mm, respectively, which were simultaneously focused using f ¼ 50 mm lens before the temperature-controlled vacuum cryostat. In our optical geometry, the 3.1 eV pump passes through a mechanical delay stage, so called 'pump delay'. Because the pump delay is recorded in a computer as an absolute length, we performed cross-correlation measurement to estimate the probe delay using BBO (visible upconversion) and KTA (mid-IR upconversion) crystals. More detailed information for determining the pump-probe 'time-zero' is explained in Supplementary Note 6. Differential transmission signal (DT/T 0 ) was recorded in a lock-in amplifier (Stanford Research Systems SR850) with 10 kHz chopping frequency (Scitec 300CD). The schematics of mid-IR and IR setup are illustrated in the Supplementary Fig. 9.