Probing momentum-indirect excitons by near-resonance photoluminescence excitation spectroscopy in WS2 monolayer

Coulomb-bound electron-hole pairs (excitons) dominate the optical response of atomically-thin transition metal dichalcogenides (TMDs) semiconductors. The photoluminescence spectrum in W-based TMDs monolayers (i.e. WS2 and WSe2) at low temperature exhibits much richer features than Mo-based TMDs monolayers, whose origin is currently not well understood. Herein, by using near-resonant photoluminescence excitation spectroscopy, we probe the scattering events between excitons and phonons with large kˆ-momentum, which provides strong evidence for the momentum-indirect nature of the optical bandgap in monolayer WS2. The scattering between carriers and zone-edge phonons creates excitons at different valleys, among which, the lowest-energy is momentum-indirect. Our findings highlight that more efforts are required to solve the current debate on the inherent bandgap nature of TMD monolayers and the complex photoluminescence spectrum reported on W-based compounds.


Introduction
Atomically thin layers of group-VI transition metal dichalgcogenides (TMDs) such as MX 2 (M = Mo, W; X = S, Se) and hexagonal lattice feature prominent exciton properties and spin-valley physics. As a result of strong quantum-and dielectric confinement in single atomic layer of TMD materials, the photoexcited electrons and holes are tightly bound via Coulomb interaction to form excitons with the binding energy of hundreds meV [1][2][3][4][5][6]. The large exciton binding energies reinforce the stability of exciton complexes such as charged excitons (trions) [7][8][9][10] and biexcitons [10][11][12] that offers great opportunities to study many-body physics. In addition, the inversion symmetry breaking in TMDs monolayers gives rise to the energy-degenerate but non-equivalent K/K ′ valleys, which are coupled with electron spins [13]. This unique spin-valley coupling enables the use of light helicity to selectively excite valley excitons at K or K ′ valley [13], making TMD monolayers ideal candidates for opto-valleytronic applications [13][14][15]. The presence of neutral excitons and trions has been widely observed in previous optical studies on TMD monolayers [7,8,16]. The substitution of the metal element M, e.g. W into Mo, reverses the energetic order of the optically allowed (bright) and optically forbidden (dark) states at the K/K ′ valley [17].
In particular, W-based monolayers harness the dark exciton band lying at lower energy than the bright band, leading to the poor emission efficiency at low temperature [11]. Instead, the photoluminescence spectrum of WX 2 monolayer is dominated by several features arising at the low-energy side of the exciton energies, which is currently under intense debate among defects, bound excitons and biexcitons [10,11]. For example, the strongest peak that lies below the charged exciton (trion) was previously assigned to biexciton emission [10,11]. However, the discrepancy lies in that the PL intensity of that peak shows a sub-quadratic increase with excitation power and the binding energy (∼52 meV) [11] is much larger than the theoretically predicted value ∼20 meV [18][19][20][21][22]. In addition, the energies of lower energy features in WX 2 monolayers coincidently match the calculated momentum-indirect exciton transitions, which arises from the recombination of electrons and holes in different valleys [23][24][25][26][27][28][29], suggesting the more complicated nature of these low-energy peaks. Therefore, a detailed investigation on the exciton dynamics of WX 2 material is needed. In this work, by using photoluminescence excitation spectroscopy, we probe the momentum-indirect transition in WS 2 monolayers that could explain for the low-energy features in the photoluminescence spectrum of W-based compounds. Under nearresonant excitation condition, multiple scattering processes between excitons and phonons carrying non-zero wavevector are revealed, indicating the presence of indirect excitons whose constituent electrons and holes locate at different valleys, beside the wellunderstood direct excitons with their electrons and holes located at the same valley. Furthermore, we find that phonon scattering contributes to valley depolarization during hot exciton relaxation. Our results advance non-trivially the fundamental understanding of the photoluminescence spectra of W-based monolayers that can shed light to intrinsic exciton properties in TMD monolayer semiconductors.

Results and discussion
Sample and Optical Characterization of WS 2 Monolayer. The high-quality monolayers of WS 2 were prepared by mechanical exfoliation onto a Si/SiO 2 substrate and extensively characterized by optical spectroscopy at cryogenic temperatures (T = 20 K). Figure 1(a) shows the reflectance-contrast spectrum, in which, three sharp resonances are clearly resolved. Specifically, the features arising at ∼2.09 eV and ∼2.50 eV are attributed to A-exciton (X A ) and Bexciton (X B ) whose constituent electrons and holes are excited at K or K ′ valleys in the Brillouin zone [1,14,16,30]. The energy splitting of ∼400 meV between A and B originates from the spin-splitting of the valence band at K and K ′ points [1,14,30]. In addition, the energy structure observed at ∼2.06 eV is ascribed to a charged exciton state (trion), which is formed by the neutral A-exciton and a free charge (electron or hole) [7][8][9][10]. A schematic of the energy structure of WS 2 monolayer is illustrated in figure 1(b). The energy positions of A-exciton and B-exciton are taken from the reflectance measurement. The continuum band of A-exciton is located at ∼2.44 eV [3], which is close to the energy of B-exciton. The existence of different electronic states around the energy of Aexciton and B-exciton suggests nontrivial exciton behaviors, especially under near-resonant excitation conditions. For example, with excitation energies of ∼2.5 eV (see the black arrows in figure 1(b)), excitons can be directly generated at B resonance or freecarriers are created at the continuum of A. In the first case, B-excitons can either radiatively recombine in a so-called hot luminescence process [16,[31][32][33], or relax non-radiatively to X Γ A (A-exciton with zero center-of-mass momentum). On the other hand, when free carriers are generated at the continuum of A, an electron and a hole can relax and later bind together to form exciton at A to result in photoluminescence. Alternatively, when the excitation energy is well below 2.45 eV (see the red, green, orange arrows in figure 1(b)), X Γ A excitons are directly generated and later radiatively recombine. Here the exciton formation, relaxation and recombination processes in WS 2 are intensively investigated by varying the excitation energy across the resonances. Figure 1(c) presents the low-temperature photoluminescence spectrum under ℏω exc = 2.707 eV excitation. Several optical features are resolved, including the radiative recombination of the neutral A-exciton (∼2.09 eV) and the charged state trion (∼2.06 eV). The energy positions are in good agreement with the reflectance contrast spectrum shown in figure 1(a). Interestingly, the PL spectrum is dominated by very intense features (P i ) at the low-energy side of the trion, where the light-absorption is negligible. The origin of the peaks P i (especially P 1 and P 2 ) is currently under debate, which will be discussed later in this work. On the other hand, when the excitation energy is tuned close to the resonance A (ℏω exc = 2.103 eV), additional sharp features are resolved on top of A-exciton with the linewidth of ∼0.4 meV. The behaviors of these emission features are carefully monitored while varying the excitation energy from 2.103 to 2.707 eV across the A and B resonances. In the case of the A resonance, up to eighteen excitation energies from a continuous tunable laser ranging from 2.103 to 2.173 eV (see Supporting Information figure S1 (stacks.iop.org/TDM/7/031002/mmedia)) are used to excite the WS 2 monolayer. Figure 2(a) shows PL spectra acquired with selected excitation energies of 2.103 eV, 2.111 eV, 2.125 eV and 2.136 eV. All the spectra are plotted relative to the energy position of the zero phonon line of X Γ A (ZPL X Γ A ), which corresponds to the direct transition of excitons with zero center-ofmass momentum and is independent of excitation energy. On the other hand, the narrow features clearly shift while changing the excitation conditions. For instance, while changing ℏω exc closer to the A resonance, from 2.136 eV (top panel) to 2.111 eV (middle panel), the peak marked by blue arrow (later identified as 2LA(M)) shifts in   accordance with the excitation. The rigid shift of the peak position with excitation energy together with the narrow linewidth approaching the resolution limit, are typically observed in scattering processes between carriers/excitons and phonons that is usually referred to as resonant Raman scattering [34]. We, therefore, attribute these features to near-resonant scattering events between exciton and different phonon modes of monolayer WS 2 , which exhibit much richer information than previous nonresonant Raman study [35][36][37]. In total, we identify up to eight modes shown in figure 2(b), whose energies match well with recent resonant Raman studies [38][39][40] and theoretical calculations [41]. The first-order optical modes A 1 g (Γ) and Dependence on Excitation Energy of Exciton-Phonon Scattering Intensity. In addition to the energy shift, the scattering intensity of the all phonon modes also varies drastically with the excitation energy. The lineshape of the PL spectrum has been fitted as shown in the bottom panel of figure 2(a) (2.103 eV excitation). For the fittings, we used Voigt functions to model each of the different peaks, where blue solid-lines refer to excitonic resonances. Specifically, the blue solid-curve centred at zero represents the ZPL X Γ A . Green solid-lines indicate scattering events between excitons and phonons, while red solid-curve is the cumulative fitting of all curves. From the fitting, the intensities of individual features are extracted (all the spectra are normalized by excitation power). The fitting procedure is repeated for all the spectra, from which the maximum of scattering intensity for each phonon mode among all excitation energies is given in figure 2 (1). The data points are plotted with excitation energies ranging from 2.114 eV to 2.173 eV, as in this energy range the resonance condition is achieved between 2LA(M) phonons and neutral X Γ A excitons.

Identification of Exciton-Phonon Scattering Processes Under Near-Resonant Excitation of A-
where ℏ is the reduced Planck constant, C is the amplitude of the resonant-scattering event, ℏω exc is the excitation photon energy, ℏω det the detected/scattered photon energy, ℏω ZPL the exciton resonance energy, Γ ZPL is a damping constant that is related to the radiative lifetime of the exciton transition. The intensity of the scattering event is maximal at the resonant condition when the difference between the excitation laser and detection photon energy matches the phonon energy (ℏω ph ), i.e. ℏω exc − ℏω ZPL X Γ . The fitting parameters are C and Γ ZPL , while the resonance energies of excitons and phonons obtained from the modelling in figure 2(a) are fixed. The fitting results in Γ ZPL = (4±1) meV corresponding to an exciton radiative lifetime of ∼1 ps, which is in excellent agreement with experiments [42] and theoretical calculations [43,44]. Moreover, the strongest scattering intensity among different phonon modes comes from the scattering with zoneedge phonons (M-point) (see figure 2(b)). Therefore, we highlight that most of the scattering features resolved in our optical spectra involve zone-edge phonons, suggesting that they originate from the collisions between real excitonic states and phonons.
Evidences of Indirect Excitons in WS 2 Monolayer. Figure 3(a) demonstrates the exciton-phonon scattering processes in single-particle (left panel) and exciton (right panel) representations. Excitons are composed of electrons and holes, both of which can be scattered by phonons. The exciton momentum is defined by center-of-mass momentumQ i X given by the momentum difference between the electrons and holesQ i X =k i e −k i h , while the phonon momentum isq i ph (i corresponds to the position in the Brillouin zone). During the events of exciton-photon (light absorption) and exciton-phonon collisions,  momentum is conserved and obeys the relationship k photon =Q i X +q i ph . In monolayers TMDs, direct photoexcitation of electron and holes takes place at K and K ′ valleys, generatingQ Γ X excitons (see figure 3). In the following, the generated carriers are scattered by phonons, involving the zone-center (the Γ-point,q Γ ph ∼0) and the zone-edge (the M-point,q M ph ̸ =0) of the Brillouin phonon zone (see blue hexagon at figure 3(a). Phonons at Γ-point (q Γ ph ∼0) scatter the electron-hole pairs generated at the light cone into the zone-centre (Γpoint) of exciton dispersion (see orange symbol and parabola at figure 3(b) and (c)). When only a single phonon mode is involved in the collision, either an electron or a hole is scattered after the photoexcitation. As both electrons and holes have similar effective masses (m ∼ 0.42 m 0 ) [45,46], their first-order phonon-scattering probability is likely comparable, in clear contrast to conventional semiconductors such as II-VI and III-V, where exciton scattering is normally dominated by lighter electrons [34]. More interestingly, phonons at the M-point have non-zero momentum (q M ph ̸ =0), which implies that the virtually generated excitons are scattered out of the light cone to their dispersion at other high-symmetry points in their Brilluoin zone to satisfy the momentum conservationq M ph ∼ −Q X (see bluish parabolas at figure 3(c)).
We find that the first-order scattering of electronholes pairs photoexcited at K or K ′ valleys takes place via two M-point phonons (see figure 2(b)), suggesting that both electrons and holes are scattered to their dispersions. There are several pathways to form an exciton from these carriers in monolayer WS 2 , depending on the exact valley where they reside after being scattered. Photoexcited electrons at K ′ (K)-valleys can be scattered into Λ (Λ ′ )-valleys by one M-phonon because the momentum conservation . Furthermore, since Λ-valley is an energy minimal [47], the electrons preferentially reside on this band. In other way, the M-phonon could scatter the electron from K (K ′ ) to the K ′ (K) valley. In this case, k e -momentum is not strictly satisfied, lowering the probabilities for this scattering channel. For photoexcited holes at K ′ (K)-valleys, the situation is slightly different. By considering just momentum, they could be scattered to the Λ (Λ ′ )-valley. However, this valleyextrema is hundreds of meV lower in energy that the  Figure 3(c) shows a schematic structure of the lowest-energy exciton bands as a function of the center-of-mass momentum Q X . The location of the excitonic valleys, the dispersion of the parabolas and relative energies are reproduced from calculations for excitons in TMD monolayers [27,28] and from our scattering features with phonons of non-zero wavevector (see figure 2). In W-based monolayers, forQ X = Γ, two kinds of exciton branches exist due to different spin configuration of electron and holes. When the electron and hole own the same spin orientation, the resultant exciton transition is spin-allowed (orange solid parabola). In contrast, the opposite spin orientation of the constituent carriers gives rise to the spinforbidden exciton band (grey dash parabola). For Q X = K (K-valley), the spin configuration is opposite to the exciton at the Γ-valley. Specifically, the spinforbidden band of X K energetically lies above the spin-allowed branch. The energy splitting between allowed and forbidden spin-states (∆E Γ a−f , so-called (spin) bright-dark splitting) varies for different compounds, being ∼50 meV as recently reported for W-based monolayers. [27,[49][50][51][52] The spin order of each band is reversed in Mo-based monolayers. [17,[49][50][51][52][53] ForQ Λ X (Λ-valley), the calculated lowestenergy exciton branch is spin-allowed. Interestingly, the momentum-indirect exciton X Λ lies energetically below the momentum-direct X Γ , which is due to the larger exciton effective mass at Λ-valley [27]. The energy separation between spin-allowed excitons at Γ-and Λ valleys (∆E Γ−Λ a−a ) in WS 2 monolayer has been calculated in the range of 70 to 100 meV [23,27]. The formation of the excitons at Λ-valley is elucidated by the observation of first-order intervalley scattering events assisted by M-point phonons in our near-resonance experiments.
The spin-allowed X Γ A branch possesses a giant oscillator-strength that allows for a transient decay (∼1 ps) of excitons. At the same time, the excitons decay into spin-or momentum-forbidden branches at lower energies of ∼50 meV [27,[49][50][51][52] and ∼70 meV [27] respectively, from which the luminescence is nominally forbidden. The complexity of the excitonic landscape determines the light emission properties of two-dimensional W-based semiconductors. The lineshape of the PL spectrum in figure 4 has been fitted by using Voigt functions to model each of the different peaks, where blue solidlines refer to excitonic resonances, green solid-lines indicate scattering events between excitons and phonons, while red solid-curve is the cumulative fitting of all curves. The parameters obtained from the fitting to the PL spectrum are listed in table S2 in the Supporting Information. The PL spectrum exhibits several features whose origin is currently under intense debate. An overall consensus exists on the high-energy structures, attributed to radiative recombination of the neutral X Γ A (∼2.09 eV) and its charge state trion T Γ A (∼2.06 eV), whose energy separation is ∆E X Γ A −T Γ A ∼30 meV. However, the largest contribution to the PL spectrum comes from the energy structures lying 50-100 meV below A-exciton (P 1 -P 4 ), at which the light absorption is negligible. They have been attributed to biexciton luminescence [10,11,54] and to localized exciton states [55][56][57]. Similar PL structures have been resolved in boron nitride encapsulated WS 2 (and WSe 2 ) monolayers, while only excitons and trions are present in MoS 2 (and MoSe 2 ) monolayers [54,58] that strongly suggests the contribution of intrinsic exciton-states emission into the energy features below the A-exciton. Intensity (arb. units) The PL energy is plotted relative to ZPL X Γ A . The raw PL spectrum is shown by the black solid-line, while the red-solid line is the global fitting by using multiple peaks with Voigt lineshapes, indicating for exciton-like (blue solid-lines) and exciton-phonon (green solid-line) scattering processes. The inset shows the relative energy of excitonic-like peaks with respect to the ZPL X Γ A . As obtained from the fitting, the height of the color bars indicates the relative contribution of each line to the total PL spectrum.
Our PLE experimental results, otherwise, provide evidence for the indirect nature of the optical transition from P 1 to P 4 . At low temperature, most of the exciton population resides at the lowest-energy and momentum-indirect exciton at the Λ-point. This is confirmed by the observation of i) first-order scattering events with non-zero wavevector phonons and of ii) weak light emission from the zero-phonon-line X Γ A (ZPL X Γ A ) in our near-resonant excitation experiments. For radiative recombination to take place from the indirect-X Λ , the assistance of phonons, carrier doping or disorder scattering might provide additional momentum to the optical transition. For phononassisted recombination, different types and combinations of lattice vibrations might contribute [59], leading to various phonon-assisted features. As a result, several lines are expected at energies ∆E Γ−Λ a−a ∼70 meV below the ZPL X Γ A . A peak at energy ∼ ∆E Γ−Λ a−a − n∆ ph below the ZPL X Γ A , where n∆ ph is the energy of the n-phonon mode (n = 1, 2,...) assisting the optical transition.
For light emission arising from the indirect-X Λ , the constituent electrons of these indirect excitons located at the Λ-points (see figure 3(a)) need to be scattered into the light cone at K-or K ′ -valleys.
There could be two possible scenarios. Firstly, with the assistance of zone-edge phonons, electrons at Λ-valleys can be scattered to K ′ -valleys and then recombine with K ′ -valley holes. Due to strong exciton-(zone-edge)-phonon coupling, it might give rise to several phonon replicas. Interestingly, the energy ∆E 1 = E P1 -E P3 and ∆E 2 = E P3 -E P4 is ∼26 meV (1LA(M) ∼26 meV) as can be observed in figure 4, suggesting evidences for the phononassisted processes. Secondly, it is also possible that electrons at Λ-valleys are scattered to the nearest K-valley to recombine with resident K-valley holes via other type of phonons with non-zero momentum, which could lead to a different emission energy. A way to distinguish between the two recombination pathways would be by investigating the polarization response of the PL spectrum under nearresonant excitation and/or by external magnetic fields.
Interestingly, as reported in previous studies, different substrates could strongly alter the PL spectum of TMDs monolayers [60][61][62][63][64] and, especially, are important for phonon behaviours of twodimensional materials [61,[63][64][65][66][67][68]. Depending on the symmetry of the phonon mode, the substrate could modify both the vibrational energy and/or the electron-phonon coupling strength. It has been reported that the doping levels of the TMD monolayers could vary for different substrates, and such a change on the carrier concentration can influence the atomic motion, leading to slight variations in the phonon energy [61][62][63][64][65]. As a result, different carrier dopings and/or substrates might lead to energy shifts of the PL resonances related to the phonon-assisted indirect-exciton X Λ and a change of the energy separation among their phonon replicas. Another scenario is the modification of the phonon amplitudes by the damping induced by the mismatch in the acoustic impedance between the monolayer and the substrate. It will be particularly relevant for out-of-plane modes. Theoretical and experimental studies have reported the increase in the acoustic phonon relaxation times and charge mobility by ten times for suspended graphene, as compared to graphene on top of silicon dioxide [66][67][68]. Therefore, we expect different substrates to have dissimilar interfacial interaction, leading to distinct phononphonon and electron-phonon coupling strengths. Consequently, the change in the phonon and carrier dynamics might alter the spectral weights of the phonon-assisted resonances.
On the other hand, electrostatic doping might lead to the formation of a negatively charge state of the indirect Λ-exciton or intervalley Λ-trion (T Λ ). In a simple scenario, the additional charge would locate at either K or K ′ , depending on the spin-valley configuration (K or K ′ ) of the hole to which the Λ electron is bounded. The additional electron will lead to intervalley Coulomb scattering between carriers providing additional momentum and turn the optical transition brighter. The associated peak will appear at the energy of ∼∆E Γ−Λ a−a − ∆ T Λ below the ZPL X Γ A . The binding energy ∆ T Λ of the intervalley Λ-trion will be smaller than that of T Γ A , as the the k-overlap between T Λcarriers might be smaller.
Therefore, besides the features below ZPL X Γ A that have been attributed to luminescence from biexciton and localized states, we argue that a multitude of available radiative recombination pathways of the lowest-energy and indirect-exciton X Λ , might contribute to the low-energy peaks (P 1 to P 4 ) in the photoluminescence spectrum of WS 2 monolayer. We highlight that multiple phonon-scattering processes could contribute into lines with similar energies, leading to super-linear power-dependencies that are often observed in literature [11,54]. Biexciton emission with a nonquadratic power-dependence (I PL = P α , α ∼ 1.4) in WS 2 monolayers at energies of ∼50 meV below ZPL X Γ A , which largely deviates from theoretical predictions [69], might be reconsidered.
A superlinear emission with excitation power could also be attributed to the increase of the PL quantum efficiency with the increase of excitation power. It is due to the coexistence of nonradiative decay pathways and a non-linear increase of the radiative recombination efficiency. The non-linearity could result from the increase of the relaxation rates or from the saturation of the nonradiative channels [70]. Within the drawn picture, it is very likely that the non-linearity appears due to the saturation of the nonradiative recombination channel of the indirect-exciton X Λ . We believe that future powerdependent time-resolved PL experiments could distinguish the origin of the non-linearity in the power law of the low-energy structures (P 1 -P 4 ).

Exciton Relaxation and Valley Depolarization Under Near-Resonant Excitation of B-Excitons.
Besides the excitation near A-exciton, we also investigated the relaxation processes of excitons after resonantly creating B-excitons (see details in Supporting Information). We found that the relaxation from B to A is quite efficient and the lack of valley polarization (see figure S6) during fast cooling of B-to A-excitons suggests that intra-valley and inter-valley relaxation are equally probable, of which the later causes the valley-pseudospin depolarization of the PL emission. Therefore, the scattering of hot excitons with zone-edge phonons should be considered as a valley depolarization channel in addition to electron-hole exchange interaction [59].

Conclusion
In summary, by using near-resonant excitation experiments, we prove exciton-phonon scattering events with non-zero wavevector that provide strong evidences for the momentum-indirect nature of the optical bandgap in WS 2 monolayer. The scattering between carriers and zone-edge phonons creates excitons at different valleys, among which, the lowestenergy band is momentum-indirect. Our findings advance the understanding on the inherent bandgap nature of TMD monolayers and highlight that more efforts are required for a complete understanding of the complex photoluminescence spectrum reported on W-based compounds. In addition to biexciton and localized states, the low-energy emission features observed at low temperature could arise from momentum-indirect transitions. Moreover, future experiments might be considered on high-quality hBN-encapsulated TMD monolayers. We believe such samples will benefit the clear identification of the different PL resonances. Furthermore, by using a backgate the charge density could be tuned to clearly distinguish between charge-and phononassisted recombination pathways for momentumindirect excitons. Furthermore, photoluminescence excitation across the whole spectral range in combination with polarization-dependent experiments could provide further evidences on the formation and polarization properties of momentum-indirect excitons. Finally, one could use magneto-optical spectroscopy to obtain g-factors that might vary across different valley excitons. These further experiments will shed light on the origin of the low-energy features observed in the low-temperature PL spectrum in W-based monolayer semiconductors.

Methods
Monolayer WS 2 was obtained by mechanical exfoliation of a high-quality bulk crystal. The thin WS 2 flakes were first exfoliated by polydimethylsiloxane (PDMS) stamp attached onto glass slides. The monolayers were identified under an optical microscope by the optical contrast with the substrate and by fluorescent measurements at room temperature. After, the samples were transfered onto a Si/(300 nm)SiO 2 substrate. For low-temperature (T = 20 K) photoluminescence excitation spectroscopy (PLE) studies, the monolayer was loaded and cooled in a liquid-He continuous-flow optical cryostat. For PLE measurements on A-excitons, a very narrow excitation source (≤0.08 nm FWHM) was achieved, using a tunable jet-stream dye (Rhodamine 6G) laser with lines raging from 2.103 eV till 2.173 eV that was filtered by a 600 gr/mm single grating spectrometer with 300 mm focal length. The output monochromatic beam was directed to the cryostat and focused on the sample by using a microscope objective (N.A 0.45). The photoluminescence, collected by the same objective (so-called back-scattering configuration), was dispersed by a triple-grating spectrometer operating in the subtractive mode. The near-resonant PL emission was dispersed by the final stage, a 640 mm focal length spectrometer and by using a 1800 gr/mm grating and finally detected by a liquid nitrogen cooled CCD camera. Additionally, for polarizationresolved PLE measurements on B-excitons, all the lines (2.707 eV, 2.627 eV, 2.605 eV, 2.541 eV, 2.499 eV, 2.470 eV and 2.412 eV) of an Argon-Ion laser were used. The PL signal was dispersed by using a 600 gr/mm single grating spectrometer with 800 mm focal length and finally detected by a liquid nitrogen cooled CCD camera.

Author contribution
QX and AGDA. started the project, conceived and designed the experiments. SL prepared the TMD micro-sized semiconductor layers. AGDA and DB performed the optical measurements. TTHD and JP intensively discussed on the data and the manuscript. DB and AGDA analyzed, interpreted the data and wrote the manuscript with input from all co-authors. DB and AGDA contributed equally to this work.