Sequential order dependent dark-exciton modulation in bi-layered TMD heterostructure

We report the emergence of dark-excitons in transition-metal-dichalcogenide (TMD) heterostructures that strongly rely on the stacking sequence, i.e., momentum-dark K-Q exciton located exclusively at the top layer of the heterostructure. The feature stems from band renormalization and is distinct from those of typical neutral excitons or trions, regardless of materials, substrates, and even homogeneous bilayers, which is further confirmed by scanning tunneling spectroscopy. To understand the unusual stacking sequence, we introduce the excitonic Elliot formula by imposing strain exclusively on the top layer that could be a consequence of the stacking process. We further find that the intensity ratio of Q- to K-excitons in the same layer is inversely proportional to laser power, unlike for conventional K-K excitons. This can be a metric for engineering the intensity of dark K-Q excitons in TMD heterostructures, which could be useful for optical power switches in solar panels.

Dark exciton peaks (SQ or SeQ) were exclusively observed from the clean interface.To confirm this, we fabricated one heterostructure (Supplementary Fig. S4a) as described in the method section, where the interface remained inert during transfer.Meanwhile, another heterostructure, where the bottom layer was transferred with polypropylene carbonate (PPC) to the target substrate and then cleaned the polymer by the conventional acetone-IPA-ethanol cleaning process, followed by the top layer transferred on top of it.Even though polymers were cleaned, still some contamination remained.As a consequence, we did not find a clear signature of a Q-band-related dark exciton peak (SQ) in this case (Supplementary Fig. S4b).ii.A 2 1g peak at heterostructure A 2 1g Raman mode becomes active in homo-bilayer or thicker layers and remains inactive in monolayer.It is noteworthy that, active A 2 1g mode of the WSe2 layer was clearly observed in a strongly coupled heterostructure (Supplementary Fig. S5a), whereas it became less intense in a weakly coupled heterostructure (Supplementary Fig. S5b).Previously, a similar result was reported for MoS2/WSe2 heterostructure, where A 2 1g mode was inactive before annealing and A 2 1g mode become active after annealing (at 300 °C) due to strong coupling between the layers. 1 However, in our case, we observed A 2 1g (309 cm -1 ) without annealing the sample, which again confirms the strongly coupled cleaned interface of our heterostructure.

iii. Homogeneous topography image via AFM
Homogeneous AFM topography image of the heterostructure region (Supplementary Fig. S6a,b) with corresponding low height fluctuation with distance (Supplementary Fig. S6c) represents a bubbles/contaminations-free clean interface.Meanwhile, the trap bubbles/contaminations are rich in a weakly coupled interface, which shows large root mean square surface roughness (Supplementary Fig. S6d,e) with large fluctuations of profile roughness (Supplementary Fig. S6f).

iv. Modulation of A1g intensity of WS2 in heterostructure
The relative intensity of A1g mode is always smaller in monolayer and increases with layer numbers as observed previously. 2,3In our investigation we also observed similar properties in monolayer and bilayer WS2 as shown in Supplementary Fig. S7a.Now, we also observed highly intense A1g peak at hetero-bilayer (such as WS2/MoSe2 and WSe2/WS2) heterostructure as well, similar to homo-bilayer WS2 (Supplementary Fig. S7b,c), compared to individual monolayer WS2.Furthermore, to clarify it in detail, we took the intensity ratio of the bilayer with monolayer for three significant peaks (2LA, E 1 2g, and A1g) (Supplementary Fig. S7a, right), which shows a high A1g intensity, compared to other modes.This property is further followed by heterogenous bilayer cases as well (Supplementary Fig. S7b,c right), which again confirms the strong coupling between the hetero-bilayer.

Note 7. Stacking angle measurements
We performed second harmonic generation (SHG) measurements on seven different samples to determine the stacking angle between the layers (Table S1), where we observed the indirect K-Q peaks, as illustrated in Supplementary Fig. 11.Based on the observations, we conclude that our newly observed K-Q intralayer peak is independent of the stacking angle, making it more robust compared to moiré or interlayer excitons.

Note 8. Interlayer exciton
We rarely observed the interlayer exciton (ILE).5][6] However, in most of the cases, we have not observed any signature of interlayer excitons.The reason behind this is listed below: ][9][10][11] However, in our case, heterostructures are not fabricated with specific angle alignment.
2,13 Nevertheless, in this work, all the experiments have been conducted at room temperature.

Note 10. Other TMD combinations
We further investigated several hetero-bilayers with other types of TMDs, for example, MoS2-WSe2, MoSe2-WSe2 and MoS2-WS2 (Supplementary Fig. S16) heterostructures.In top-WSe2/bottom-MoS2 hetero-bilayer case, we have observed a similar SeQ peak as earlier, due to the Q band of the WSe2 layer being downshifted at the hetero-bilayer region (Supplementary Fig. S16a, left).On the other hand, top-MoS2/bottom-WSe2 hetero-bilayer does not show any appreciable peak.This could be due to the Q-band of MoS2 being located far away from the K band, 14 becoming difficult to renormalize to form the hybrid K-Q state or could be inferred to the overlap of the energy range with the WSe2 band gap (Supplementary Fig. S16a, right).
In the WSe2-MoSe2 hetero-bilayer case, we have not observed any kind of dark exciton-related PL peak (Supplementary Fig. S16b).This can be explained with WSe2 as the top layer that the SeQ generally emerges at lower energy than WSe2 A-exciton and thus this energy is again also overlapped with MoSe2 A-exciton (Supplementary Fig. S16b, left).Similarly, MoSe2 as a top layer is expected to have an emerging dark exciton at higher energy than MoSe2 A-exciton in analogy with what was observed for MoSe2/WS2 hetero-bilayer (Fig. 1f).Similarly, the dark exciton peak is likely overlapped with WSe2 A-exciton peak in this case (Supplementary Fig. S16b, right).Nevertheless, we have not observed such a peak for both stacking sequences, which can be considered as an exception since other tested bilayer heterostructures generally revealed the clear emergence of dark exciton peaks on the top layer.
In WS2(top)/MoS2(bottom) case, the notable SQ peak has been observed as WS2 as the top layer with an energy of 1.89 eV, similar to other TMDs combinations (red color peak in Supplementary Fig. 16c, left).On the other hand, in MoS2(top)/WS2(bottom) heterobilayer case, we have not observed any dark exciton-related PL peak (Supplementary Fig. S16c, right).This can be explained with MoS2 being in the top layer where the K-Q peak for Mo-based material then emerges at higher energy than MoS2 A-exciton (as we observed for the MoSe2 case: Fig. 1f) and this K-Q energy overlaps with inlayer WS2 exciton.Another reason could be the energy of the Qband, which is located far away from the K-band, 14 subsequently incapable of band renormalization for K-Q excitons.The B-exciton of MoS2 is also indistinguishable for the same overlapping energy with inlayer WS2 exciton.We note that a similar PL peak to our SQ peak has been observed previously in WS2/MoS2 heterobilayer. 15

Note 11. Effect of nano-bubbles
To distinguish between the localized excitons originating from nano-bubbles 16 and the K-Q exciton in the heterostructure, we performed PL mapping on WS2/MoSe2 heterobilayer, which contains several bubbles (indicated by the arrow in Supplementary Fig. S17a,b) at the interface.We found that on top of the nanobubble, the WS2 inlayer peak underwent a red shift due to strain, while the MoSe2 peak remained unaffected (Supplementary Fig. S17c).Conversely, on the flat surface, we observed a prominent and highly intense SQ peak.Additionally, the relative intensity of the bottom MoSe2 layer increased at the flat surface, indicating strong coupling between the layers, which is deemed necessary for a high SQ peak.Supplementary Fig. S17d,e, represents the deconvolution of each spectrum from the flat and nanobubble region, confirming the presence of a strong SQ peak on the bubble-free flat surface.This finding again supports the conclusion that the SQ peak is not originated from an interfacial bubble but rather arises due to strong interlayer coupling between the layers.

Note 13. Heterogeneous layer effect
We have investigated the heterostructures with different numbers of layers (Supplementary Fig. S19), which interestingly follow similar stacking sequence behavior.Supplementary Fig. S19a represents the PL measurement at 1L-WS2/2L-WSe2 heterostructure.SQ (red color peak) is present at WS2/WSe2 heterostructure interface.SeQ is also present in this system as well, as this heterostructure consists of bilayer WSe2.Other than the nearest neighbor such as X T , SQ T or SeQ T peaks represents corresponding trion peaks.Supplementary Fig. S19b represents the PL at 2L-WSe2/1L-WS2 heterostructure.Here SQ peak is absent, as WS2 is situated at the bottom.However, the SeQ peak is still observed due to the top-WSe2 layer in the heterostructure as well as the bilayer of WSe2.In this case, their energy is very close to each other.We cannot distinguish these two types of SeQ peaks.Again, we measured the PL at 2L-WS2/1L-WSe2 (Supplementary Fig. S19c).In this case, we have two SQ peaks, one appearing due to the WS2/WSe2 interface (SQ1: red) and another emerging due to the bilayer nature of WS2 (SQ2: yellow).Since these peaks are well separated, we can detect them individually.The violet color peak (SQ T ) near the red-SQ peak is ascribed to the trion state of SQ.Further PL spectrum measured at an even number of hetero-bilayer such as 2L-WS2/2L-WSe2 (Supplementary Fig. S19d) and shows one SeQ peak and two SQ peaks; the first SQ peak (SQ1: red) emerges at WS2/WSe2 interface and second SQ (SQ2: yellow color peak) originates from the bilayer of WS2.Similar to these experiments, we also measured the PL spectrum from the 2L-WS2/3L-WSe2 heterostructure (Supplementary Fig. S19e), where only the SQ1 peak is visible at WS2/WSe2 interface.However, the SQ2 peak becomes ambiguous because of the low signal-to-noise ratio.One SeQ peak is also visible due to bottom 3L-WSe2.We note that this SeQ peak is downshifted compared to previous case due to its tri-layer nature.From all these various layers-dependent PL measurements we confirm that SQ or SeQ peak does not depend on inversion symmetry or mirror symmetry of the system as these peaks are observed for both even and odd layer numbers of the heterostructure.

Note 14. Confirmation of SeQ and SQ peaks at different circumstances i. Low-temperature and high-vacuum PL measurements
We further confirmed the similar dark exciton peak SQ or SeQ depending on the corresponding stacking sequence at low temperature (77K) and high vacuum (⁓10 -6 Torr).The green and blue dotted lines represent the individual monolayer PL peak of WS2 and WSe2, respectively.For each case, the PL peak was slightly upshifted compared to the room temperature measurement similar to previous studies. 12,17In the WSe2/WS2 stacking sequence, we again observed the SeQ peak present even at low temperatures (Supplementary Fig. S20a).There is another PL peak observed with even lower energy than the SeQ peak at low temperatures that could be related to the associated trion state.Similarly, in the WS2/WSe2 stacking sequence, SQ still appeared at low temperatures as well (Supplementary Fig. S20b).

ii. Annealing effect
We annealed our hetero-bilayer samples at 250° C for 12 hours in helium (He) environment to improve the interlayer distance as well as to remove the polymeric residues. 12,15Therefore, we measured PL spectra after fabricating the heterostructure and before annealing the sample.We annealed the heterostructure and again measured the PL of the same sample (Supplementary Fig. S21).We observed that before and after annealing, the same SQ (SeQ) exists for the WS2/WSe2 (WS2/WSe2) stacking sequence with a slight peak shift.From these results, we confirm that these peaks originate from the intrinsic material properties and are not related to any defect or contamination-generated photoluminescence.

iii. Doping effect
We have increased the number of carriers by intrinsic Fermi level doping and again checked the stacking sequential properties of the WS2-WSe2 hetero-bilayer.In this case, we have used rheniumdoped WS2 (Re-WS2) for increasing more n-type carriers and niobium-doped WSe2 (Nb-WSe2) to increase the p-type carrier.Afterward, we fabricated Re-WS2/Nb-WSe2 with opposite stacking (Nb-WSe2/Re-WS2) and measured the PL for each case.We observed similar peaks (SQ or SeQ) on dopped material (Supplementary Fig. S22) as well for their corresponding stacking sequences analogous to undoped hetero-bilayers.

Note 15. Absorption measurements
Measuring the indirect bandgap through the absorption spectrum in TMD heterostructures poses a challenging task due to the involvement of both direct and indirect bandgaps, along with the band renormalization effect.This is well contrasted with PL, where indirect exciton also exhibits prominent features due to carrier transfer between different valleys (such as K to Q valley).
9][20] However, no indirect peak (Q-exciton) was observed unlike that in PL. 21 first measured absorption on the SiO2 substrate (Supplementary Fig. S23a) to make a direct comparison with our PL data.We found that each peak is redshifted in WS2/MoS2 heterostructures compared to monolayer peaks, analogous to the redshift observed in bilayer compared to monolayer, as reported previously, [21][22][23] and this behavior has been attributed to the transition from a direct to an indirect bandgap.We note that no additional peak related to K-Q exciton was observed in this case and such an absence of K-Q peak from absorption may originate from indirect nature.Similar K-Q peak from absorption not appeared from quartz substrate (Supplementary Fig. S23b) as well, although K-Q exciton in PL was observed (Supplementary Fig. S14a).Therefore, we conclude that K-Q peaks cannot be observed from absorption, congruent with previous reports as well. 21

Note 16. Charge transfer and the related exciton dynamics
The charge transfer at the heterostructure is the key to explain the intensity modulation of K and Q-excitons.The PL intensity of neutral excitons of WSe2 at heterostructure was greatly reduced compared to the individual WSe2 monolayer region (Supplementary Fig. S24a) due to efficient charge transfer from WSe2 to WS2.Meanwhile, Q-exciton intensity was remarkably developed, whereas the intensity of WS2 K-exciton was also reduced at the heterostructure due to further charge transfer from K to Q-band (Supplementary Fig. S24b).Supplementary Fig. S24c shows two relaxation times of fast relaxation τ1 (WS2: ⁓0.974 ns and WSe2: ⁓1.406 ns) due to presumably exciton scattering or electron-phonon scattering 24 and slow relaxation time τ2 (WS2: ⁓2.624 ns and WSe2: ⁓3.326 ns) due to trions and/or traps. 25Such behaviors of two relaxation times of individual WSe2 and WS2 monolayers are similar to each other.Notably, additional faster relaxation (⁓0.587 ns) appears at the heterostructure.This can be explained again by the efficient charge transfer from WSe2 to WS2 and further from K to Q-band in WS2.This is consistent with the previous report on faster relaxation time in multilayered WS2 compared to monolayer. 26In this report, we focused solely on the K-K and K-Q excitons in the heterostructure.To accomplish this, we need to perform simultaneous measurements of each K-K and K-Q peak separately and their corresponding relaxation time.However, simultaneous measurements of such discrete peaks cannot be possible, primarily due to their close proximity (as wavelength less equal to 50 nm).As a result, performing such precise measurements are beyond the scope of the current work and requires further investigations.

Note 18. Scanning tunneling spectroscopy (STS) measurement
From Fig. 1 we observed that the energy difference between SQ peak and WS2 A-exciton is less than 100 meV, which implies that the thermal broadening of room temperature STS measurement will heavily interfere in resolving such a small energy gap. 27However, 2L-WS2/1L-WSe2 heterostructure provides an SQ peak (SQ2 peak in Supplementary Fig. S19c) that is greater than 100 meV gap from the nearest A-exciton peak.Thus, we fabricated our heterostructure in such a way that it consists of a few regions 2L-WS2/1L-WSe2 and the rest of the 1L-WS2/1L-WSe2 area to ensure a certain signature of SQ peak from room temperature STS measurement.The additional density of states near the conduction band edge (red peak) was clearly visible at the 2L-WS2/1L-WSe2 heterostructure region (Supplementary Fig. S26).

Note 20. SQ intensity mapping
PL intensity mapping may give a more detailed view of SQ peak distribution in real space.As shown in Supplementary Fig. 28a, the integrated PL intensity of WS2/WSe2 heterostructure is plotted.Since the PL intensity of WS2 is quite high compared to WSe2, the WS2 PL intensity is dominant compared to the heterostructure as well as the WSe2 region.To alleviate this difficulty, we normalized the SQ intensity with respect to WS2 PL intensity and plotted it in Supplementary Fig. 28b.This gives the distribution of the SQ peak over the heterostructure region, where the SQ population is well represented compared to the intrinsic inlayer WS2 intensity.The SQ intensity is dominant at the heterostructure region as shown in Supplementary Fig. 28b (yellow to the red region: scale >1).Furthermore, the intensity ratio changes from position to position, as described in Fig. 4c due to the variation of coupling strength between the layers.

Note 21. Raman spectra at different positions
We investigated Raman spectra to gain the nature of the possible interlayer strain effect by monitoring the E 1 2g Raman modes for both stacking sequences.In our scenario, we mainly focused on the interlayer coupling-induced strain effect (without application of external strain), which can alter the vibration of the phonon modes in the heterostructure compared to the monolayer region.However, we found that the in-plane E 1 2g modes of the heterobilayer show strong positiondependent phonon shifts (Supplementary Fig. S29), like -blue shift (compressive strain) or redshift (tensile strain) depending on the position.This result suggests complicated inhomogeneous local strain profiles that vary with positions.The excitonic energies are microscopically evaluated starting from the unstrained single-particle dispersion 28 and including their strain-dependent variations 29 .These values are then used to numerically solve the Wannier equation by introducing a generalized Keldysh potential for the Coulomb interaction.
In Supplementary Fig. S31 top, we show the resulting excitonic center-of-mass dispersion of K-Q excitons for the WS2 case, considering SiO2/air as a dielectric environment.Already in the unstrained case (blue), the minimum K-Q energy is smaller than the bright-exciton energy EK-K.
In the presence of a compressive strain s=-0.30%, the energy separation increases by a factor of 3 from 30 meV up to almost 87 meV.In contrast, in MoSe2 the K-Q valley is energetically above the K-K valley as shown in Supplementary Fig. S31 bottom.In this case, compressive strain also leads to a blueshift of K-Q energies (redshift of EK-K).This reduces the energy separation between the K-Q and K-K excitons from 123 to 69 meV, while keeping K-K as the ground state.In Supplementary Fig. S32, we provide a theory-experiment comparison for the WS2-MoSe2 heterostructure (Fig. 4e-f for WS2-WSe2).In the presence of a strained top layer, we find a new peak in WS2/MoSe2 in accordance with the experimentally measured SQ, reflecting K-Q states with energy smaller than EK-K (Supplementary Fig. S31 top).In contrast, we find no new phononassisted peaks in MoSe2/WS2, as here the K-Q excitons are energetically above the bright ones (Supplementary Fig. S31 bottom).This implies their reduced occupation in comparison to the bright-exciton states, resulting in negligible phonon-assisted photoluminescence.Nevertheless, our prediction of a decreased EK-Q-EK-K separation with compressive strain (Supplementary Fig. S31 bottom) could potentially lead to a peak similar to SeQ in MoSe2/WS2, if an additional activation mechanism is present, e.g.via interplay of strain and defects. 30The microscopic evaluation of these mechanisms goes beyond the scope of this work.

Note 1 .Note 3 .
Fig. S1 | Schematic illustration of a stepwise fabrication process of TMDs hetero-bilayer via PMMA-assisted layer.Top flake preparation: exfoliation on PVA/PMMA substrate, bottom flake: direct exfoliation on the substrate Finally, the top flake is transferred onto the destinated bottom flake through align transfer method.

Fig. S4 |
Fig. S4 | Interface cleanness.a, Schematic representation of WS2/WSe2 heterostructure.A clear SQ peak was observed from the clean interface obtained by our transfer method.b, Schematic representation of contaminated WS2/WSe2 heterostructure and the SQ peak was not visible in this case.

Fig. S6 |
Fig. S6 | Homogeneous topography image via AFM.Optical images a and d, AFM images b and e as well as height profile c and f of WSe2-WS2 hetero-bilayer for strong and weakly coupled heterostructures, respectively.Bright yellow dot spots in e represent the air trap bubbles/contaminants.

Fig. S7 |Note 5 .Note 6 .
Fig. S7 | A1g peak intensity at hetero-bilayer.a, In WS2 bilayer, the relative intensity of A1g peak is higher compared to the monolayer.b,c, Similar high intensity of the A1g peak was observed in WS2/MoSe2 and WSe2/WS2 heterostructure.

Fig. S11 |
Fig. S11 | Twist-angle measurements using second-harmonic generation (SHG).a, Optical image of WS2/WSe2 heterobilayer b,c, Polarized SHG intensity polar diagram as a function of incident field polarization angle for WS2 and WSe2 respectively.The black dots correspond to experimental data and the red line is the fitting, which reveals the stacking angle between two layers is -7.09°.

Fig. S16|
Fig. S16| Stacking sequence effect with other TMD combinations.a, PL spectra of WSe2/MoS2 and inverted MoS2/WSe2 heterostructure.SeQ still emerges on the WSe2 layer of WSe2/MoS2 heterostructure, whereas the SQ peak in MoS2 is rather ambiguous.b, PL spectrum of MoSe2/WSe2 and WSe2/MoSe2 heterostructure.The dark exciton peak was not visible due to overlaps with the bandgap.c, PL spectra of WS2/MoS2 and inverted MoS2/WS2 heterostructure.SeQ still emerges on the WS2 layer of WS2/MoS2 heterostructure, whereas the SQ peak in MoS2 is indistinguishable.

Fig. S17 |
Fig. S17 | Effect of nano-bubble.a, Optical image of WS2/MoSe2 heterobilayer.Nano-bubbles are indicated by arrows.b, Spatial PL map of WS2/MoSe2 heterobilayer, revealing that bright spots are localized in spatially discrete regions corresponding to the presence of nano-bubbles.c, Comparison of PL spectra collected from flat (labeled as A: orange) and nano-bubble region (labeled as B: blue).d,e, Deconvolution of the spectrum from the flat and nano-bubble region.

Fig. S19 |
Fig. S19 | Various layer-dependent PL measurements for inversion symmetry effect test in heterostructures.a-e, WS2-WSe2 various layer-dependent PL spectrums with different stacking sequences.

Fig. S22 |
Fig. S22 | PL measurement of doping effect.a, PL spectra of the individual monolayer of Nb-WSe2 and Re-WS2 (blue and green dotted lines, respectively) along with the Nb-WSe2/Re-WS2 heterostructure region (yellow solid line).SeQ (cyan color peak) is still present in the doped sample.b, Similar to a for opposite stacking (Re-WS2/Nb-WSe2) measurement, where SQ peak (red color peak) persists analogous to undoped sample.

Fig. S24 |
Fig. S24 | Charge transfer at heterostructure.a,b, PL measured at individual monolayers (WSe2: blue-dotted line; WS2: green-dotted line) as well as WS2/WSe2 heterostructure (yellow solid line) at the same excitation power.PL intensity is drastically reduced on WSe2 side compared to WS2 at the heterostructure region, which indicates the majority of the charge transferred from WSe2 to

Note 17 .
Fig. S25 | Mechanical cleaning by contact mode AFM.After contact mode scanning a tapping mode image has been taken to check the surface cleanness.The pink marked box region indicates the cleaned area and the wall of collected residue is indicated by an arrow on the left side of the box.

Fig. S28 |
Fig. S28 | Intensity mapping.a, Integrated PL intensity of WS2/WSe2 heterostructure, where WS2 PL intensity is dominant compared to the heterostructure as well as the WSe2 region.b, Normalized SQ intensity with respect to WS2 PL intensity.

Fig. S32 |
Fig. S32 | Experimental and theoretical PL for MoSe2-WS2 heterostructure.a, In the case of top-WS2, a low-energy peak (SQ) stems from the phonon-assisted transition by assuming a 0.45 % compressive strain in the WS2 layer.b, In the case of the top-MoSe2 layer, we do not see a phonon sideband on the high-energy side of the bright MoSe2 exciton, as the occupation of the K-Q state is negligibly small.