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Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin

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Science Advances  20 Dec 2019:
Vol. 5, no. 12, eaax7407
DOI: 10.1126/sciadv.aax7407


Excitons in monolayer semiconductors have a large optical transition dipole for strong coupling with light. Interlayer excitons in heterobilayers feature a large electric dipole that enables strong coupling with an electric field and exciton-exciton interaction at the cost of a small optical dipole. We demonstrate the ability to create a new class of excitons in hetero- and homobilayers that combines advantages of monolayer and interlayer excitons, i.e., featuring both large optical and electric dipoles. These excitons consist of an electron confined in an individual layer, and a hole extended in both layers, where the carrier-species–dependent layer hybridization can be controlled through rotational, translational, band offset, and valley-spin degrees of freedom. We observe different species of layer-hybridized valley excitons, which can be used for realizing strongly interacting polaritonic gases and optical quantum controls of bidirectional interlayer carrier transfer.


Van der Waals (vdW) bilayers composed of stacking two atomically thin two-dimensional (2D) layers have rapidly evolved into a variety of designer quantum materials with many fascinating properties that are not possessed by the constituent monolayers (112). The key control knob for designing new quantum materials is the stacking-dependent interlayer coupling, which determines the electronic structure of the vdW bilayer as a whole. One strategy is to harness the “moiré pattern”—a periodic variation of local stacking configuration (due to twist angle and/or lattice mismatch)—to form a 2D electronic superlattice. Such a moiré designer has led to the observation of the Mott insulating phase and, more intriguingly, the accompanying unconventional superconductivity in twisted bilayer graphene (13, 14). In semiconducting transition metal dichalcogenide (TMD) heterobilayers, this strategy has also been used to create interlayer moiré excitons, which have attractive properties such as tunable quantum emitters and spin-orbit–coupled superlattice (12, 1518). While the formation of the moiré exciton has been stated, an in situ structural confirmation is still needed to directly connect the observed excitonic features to the formation of excitonic moiré superlattice in the experiments (1518).

Here, we report structural and spectroscopic evidence that coherently shows how stacking configurations, band alignment, and valley-specific spin configurations work in concert to define the excitonic structures of the vdW bilayers. More specifically, using the above degrees of freedom, we tailor different species of layer-hybridized excitonic states in TMD hetero- and homobilayers that feature both a large optical dipole (comparable to that of monolayer exciton) and a large electric dipole (comparable to that of interlayer exciton), which are highly desired for realizing strongly interacting excitonic/polaritonic gases and can also be exploited for spin valley–selective interlayer quantum controls. In addition, we determine quantitatively important coupling parameters for future design of electronic structures of vdW bilayers.


The layer hybridization of electronic states in bilayers can be described by a two-level Hamiltonian: [εuttεl] (Fig. 1A), where the basis states ∣ψu⟩ and ∣ψl⟩ are the states from upper and lower layers before coupling. The off-diagonal element t is the interlayer hopping integral that conserves the spin. For the electronic states at the ±K valleys, the hopping integral t is strongly dependent on the stacking configuration (11). Noticeably at high-symmetry stacking, threefold rotational symmetry dictates t to be zero/finite at certain band edges, where interlayer hybridization is forbidden/allowed (c.f. Fig. 1, B to F). On the other hand, the offset 2δ = εl − εu between the band edges from the two layers is controlled by valley-spin splitting together with the valley pairing that is opposite in the R- and H-type stackings. The two layer-hybridized eigen vectors are ∣ψh+⟩ = α∣ψu⟩ + β∣ψl⟩ and ∣ψh−⟩ = α∣ψu⟩ + β∣ψl⟩, where β/α = t/(δ − Δ), β = t/(δ + Δ), and Δ=δ2+t2. The energy separation between the doublet is 2Δ, which, together with the spectral ratio ∣β/α∣2, can provide signature of the hybridization. The degree of layer hybridization is further defined as PH = ∣β/α∣.

Fig. 1 Interlayer hybridization of valence bands at K valleys for commensurate TMD heterobilayer.

(A) Schematic showing the hybridization of electronic states from upper (∣ψu⟩) and lower (∣ψl⟩) layers. (B and C) High-symmetry R-type (B) and H-type (C) stacking configurations, where the top (side) view is shown in the upper (lower) panel. Rνμ (Hνμ) denotes an R-type (H-type) stacking with μ sites of the upper layer vertically aligned with ν sites of the lower layer, where μ, ν = M or X. (D and E) The interlayer hopping integral ∣tvv∣ as a function of interlayer translation r for R-type (D) and H-type (E) heterobilayers, where the dots correspond to the high-symmetry stacking configurations shown in (B) and (C), respectively. (F) ∣tvv∣ of R-type (blue) and H-type (red) heterobilayers along the dashed diagonal line are shown for comparison.

Our vdW bilayer samples include WSe2/MoSe2 and WS2/MoS2 heterobilayers with negligible lattice mismatch, and MoS2 homobilayers grown directly by chemical vapor deposition (CVD) (10). The fundamental characterizations can be found in figs. S1 to S3. Despite a slight lattice mismatch of ~0.2 to 0.4% between WX2 and MoX2 (X = S, Se), the top layer of the CVD-grown WX2/MoX2 heterobilayers tends to adopt the same lattice constant as the bottom layer (fig. S4) to form commensurate R (twist angle θ = 0°) and H stacking (θ = 60°), as schematically shown in Fig. 1 (B and C). The interlayer atomic registry has been examined by transmission electron microscopy (TEM). Only the HXM stacking configuration was observed in H stacking samples. TEM inspections on different locations of the same sample also confirm that the stacking has no interlayer translation (10). In R stacking samples, only the RXM or RMX stacking configurations were observed (Fig. 2, A and B). According to Fig. 1F, the hopping integral reaches the maximum in HXM stacking but vanishes in RXM and RMX stacking configurations.

Fig. 2 Layer-hybridized valley excitons in the WSe2/MoSe2 heterobilayer.

(A and B) TEM and Bragg-filtered (inset) images of RMX (A) and HXM (B) heterobilayers. The ideal atomic registry is illustrated for comparison, where the top (side) view is shown in the upper (lower) panel. Scale bars, 1 nm. (C) The differential reflectance (DR; upper panel) and second derivative (lower panel) spectra of an RMX (blue curves) and an HXM (red curves) heterobilayer, showing a clear splitting of XBW for the HXM heterobilayer. (D) The DR (upper panel) and second derivative (lower panel) spectra of an HXM heterobilayer shown with the spectra fitting (red curve). (E) Schematic showing the optical transitions of the HXM heterobilayer at K valley. Note that both XBW (blue) and XAMo (orange) transitions are split into two hybridized transitions (Xh±W and Xh±Mo), corresponding to the fitting curves in (D). The transitions form Λ-shape level schemes that allow the interlayer quantum control of electrons. (F) Schematics showing the wave functions in the out-of-plane direction for the four species of layer-hybridized valley excitons, featuring both large optical dipoles and large electric dipoles compared with that of monolayer and interlayer excitons. (G) A schematic showing the spin valley–selective interlayer quantum control of electron states by Xh±W and Xh±Mo transitions intermediated via an interlayer negative trion IX. a.u., arbitrary units.

The stacking-dependent interlayer coupling, the band alignment, and the valley-spin work collaboratively to determine the hybridization of electronic states at K point, leading to rich excitonic structures. Shown in Fig. 2C are the differential reflectance (DR) spectra acquired at 4 K for a HXM-stacked and a RMX-stacked WSe2/MoSe2 heterobilayer. The most notable difference emerges from the B exciton of WSe2 (denoted as XBW), which shows a single peak in R stacking, but becomes a doublet (referred to as Xh+W and XhW) in H stacking with a splitting of 92 meV and a spectral weight ratio of roughly 1:1. In addition, the oscillator strength of the XAMo (XAW) excitons is reduced (enhanced) in H stacking. This can be explained by the splitting of the XAMo exciton peak into a doublet (Xh+Mo and XhMo), where the split-off spectral feature merges with the XAW excitons. Curve fitting yields a splitting of 87 meV and a spectral weight ratio of nearly 1:1. These spectral features can be further enhanced by taking the second derivative of these spectra, as displayed in Fig. 2C. The measurements have been carried out on several samples with well-defined R or H stacking. In all cases, the HXM-stacked heterobilayers exhibit spectral splitting in XBW, albeit the splitting varies from 70 to 105 meV (fig. S5). In Fig. 2D, we show an example of spectral fitting for an H-type heterobilayer.

The WSe2/MoSe2 heterobilayer is known to exhibit a type II band alignment, where the valence band maximum of WSe2 is lying above that of MoSe2, as schematically shown in Fig. 2E. We label the two valence bands split by spin-orbit coupling (SOC) as v1 and v2 for WSe2, and v1′ and v2′ for MoSe2. Because of the larger SOC splitting in WSe2 and the type II alignment, the v2 band aligns closer to the v1′ and v2′ bands of MoSe2 (19). Spin conservation of interlayer hopping, on the other hand, ensures that the v2 band of WSe2 only coupled to the v1′ band of MoSe2 in H stacking (Fig. 2E). Such a coupling hybridizes v2 and v1′ bands into the doublet h+ and h−, as depicted in Fig. 2E. Conduction band hybridization, however, is not allowed in this high-symmetry stacking (11). Interband optical transition can excite either of the hybridized valance states (h+ and h−) to the conduction band localized in the WSe2 (MoSe2) layer, leading to the splitting of the XBW (XAMo) exciton state into a doublet Xh+W and XhW (Xh+Mo and XhMo) as shown in Fig. 2E. These four exciton species, all consisting of a layer-hybridized hole and an electron confined in an individual layer (Fig. 2F), feature a large optical dipole that is one-half of the monolayer exciton one and a large electric dipole in the out-of-plane direction. They, therefore, combine the advantage of both intralayer excitons (for strong light coupling) and interlayer excitons (for electric tunability of resonances and strong dipole-dipole interaction).

According to the coupled two-level model, the band offset 2δ and the hopping integral t can be deduced from the measured energy splitting (2δ2+t2) and the spectral weight ratio (∣β/α∣2). Measurements conducted on several samples show that the spectral weight ratio is in the range of 1.1 to 1.5, and the splitting ranges from 70 to 105 meV, which determines a hopping integral of tvv = 43 ± 9 meV and a band offset of 2δ = 12 ± 2 meV between the v2 and v1′ bands. We, thus, obtained a very high degree of layer hybridization of PH ≈ 87% for holes. We have also performed temperature-dependent measurements from 4 to 300 K. We found that the splitting and spectral ratio are temperature independent, indicating that the band offset and interlayer hopping integral remain invariant in this temperature range (fig. S6).

The layer-hybridized excitonic states further enable the possibility of interlayer quantum control. As depicted in Fig. 2 (E and G), the excitonic transitions form a three-level Λ-system that would allow the interlayer quantum control of electrons via the layer-hybridized holes. The schematic shown in Fig. 2G is an example of two states with a layer-confined electron in the MoSe2 (ψeMo) and the WSe2 (ψeW) layers, which can be connected by an intermediate state of interlayer negative trion (IX) through optical excitations. Considering the initial state ψeMo (i.e., an electron in the MoSe2 layer), the IX can be created by a π-pulse resonant excitation of Xh+W. By using another π-pulse excitation in resonance with Xh+Mo, the trion state will be forced to recombine, leaving behind the final state ψeW (i.e., an electron in the WSe2 layer). Note that this quantum control process is bidirectional with spin-valley selectivity through helicity-dependent optical excitations.

Similar interlayer hybridization has also been observed in WS2/MoS2 heterobilayers at room temperature. For this sample set, we also performed measurements on samples with different twist angles. We have identified several commensurate heterobilayers with the RMX, RXM, and HXM stacking configurations based on TEM analyses (Fig. 3, A to C), and some twisted bilayers using second harmonic generation (SHG) microscopy. Figure 3D shows the second derivative spectra for heterobilayers with different twist angles. The doublet of the XBW exciton is observed only for θ = 60° (H stacking). The splitting is smaller (74 ± 6 meV for the spectrum shown in Fig. 3E) than that of the WSe2/MoSe2 heterobilayers, indicative of a weaker interlayer hopping in WS2/MoS2 heterobilayers. From the measured splitting and fitted spectral weight, we determine the interlayer hopping to be tvv = 36 ± 4 meV, band offset 2δ = − 7 ± 20 meV, and PH ≈ 90% in WS2/MoS2 heterobilayers. For the RMX and RXM heterobilayers (Figs. 1F and 3, A and B), layer-hybridized valley excitons are absent since the interlayer hopping is dictated to be 0 for both the conduction and valance band edges. On the other hand, the absence of interlayer hybridization at the K point in twisted bilayers can be understood from two factors. First, the K valleys of the two layers in momentum space are misaligned by the twist angle θ (Fig. 3D, inset), where the interlayer hopping is inhibited by the large momentum mismatch. Second, since the interlayer hopping decreases exponentially with the interlayer spacing d, the enlarged interlayer spacing in twisted heterobilayers, thus, further suppresses the interlayer hopping (2023). Nevertheless, the interlayer hybridization of the Γ and Q points in twisted bilayers is also possible and has been reported previously (24, 25).

Fig. 3 Layer-hybridized valley excitons in the WS2/MoS2 heterobilayer.

(A to C) TEM and Bragg-filtered (inset) images of RMX (A), RXM (B), and HXM (C) heterobilayers. The ideal atomic registry is illustrated for comparison, where the top (side) view is shown in the upper (lower) panel. Scale bars, 0.5 nm. (D) The second derivative spectra as a function of twist angle θ. Only the HXM heterobilayer exhibits interlayer hybridization. (E) A comparison of RMX and HXM heterobilayers (upper panel), showing a clear splitting of XBW for the HXM heterobilayer. The second derivative spectrum (lower panel) of the HXM heterobilayer with spectral fitting (red curve).

The HXM heterobilayers demonstrated above exemplify the interlayer hybridization in the regime with t > δ. The RMX and RXM heterobilayers, on the other hand, represent the example of vanished interlayer hopping t = 0 (11). In principle, one can tune the band offset 2δ by a vertical electric field to tune the degree of hybridization (26). However, fabricating the device to achieve such tunability is not straightforward, especially when the heterobilayer area is small. Here, we show that H-stacked MoS2 homobilayers can be a model system to investigate the interlayer hybridization of valance bands in the regime with δ > t. The MoS2 bilayers investigated here include commensurate RMX - and HXM stacking and twisted bilayers, as characterized by TEM and SHG measurements (fig. S7). Figure 4A shows the second derivative spectra for bilayer MoS2 as a function of θ, showing A-exciton (XAMo) and B-exciton (XBMo) transitions in all samples. Because of the small spin splitting in the conduction band of MoS2, the energy splitting between XAMo and XBMo thus represents a good measure of the valence band spin splitting at the K valley. As depicted in Fig. 4B, the A-B exciton splitting for RMX and twisted bilayers are around 144 meV, which is very close to the value of 148 meV for monolayer MoS2 and insensitive to the twist angle. The slightly reduced energy splitting in bilayers could be caused by the enhanced dielectric screening. On the contrary, the energy splitting of the HXM bilayer is increased to 164 meV. The same A-B exciton separation between twisted and RMX bilayers is a confirmation on the absence of interlayer hybridization in the RMX bilayer, as discussed above. On the other hand, the enlarged energy splitting indicates the presence of partial interlayer hybridization in the HXM homobilayer. Figure 4C depicts the optical transitions at the K valley of the H-type bilayer. Here, we denote the valence band spin splitting of monolayer MoS2 as 2λ. The presence (absence) of interlayer hopping t thus modifies the spin splitting to 2λ2+t2 (2λ) for the HXM (RMX) bilayer. Comparing the A-B exciton separation in HXM bilayers and in twisted bilayers without interlayer hopping, we determine the interlayer hopping integral in the MoS2 bilayer to be tvv = 39 meV, which is close to the theoretical calculation (6) and similar to those for the WX2/MX2 heterobilayers. From the measured λ and t, the degree of layer hybridization of hole is obtained to be PH ≈ 26%, which is much smaller than that of heterobilayers and forms a partially layer-hybridized hole.

Fig. 4 Partially layer-hybridized valley excitons in bilayer MoS2.

(A) The second derivative spectra of bilayer MoS2 as a function of twist angle θ. (B) The energy separation between XAMo and XBMo as a function of θ, where the HXM bilayer is a singular point featuring a separation larger by ~20 meV. (C) Schematic showing the optical transitions of spin-up excitons in the HXM heterobilayer at K valleys, where both XAMo and XBMo transitions are split into hybridized transitions (Xh+o,e and Xho,e). Note that the valence band spin splitting in the HXM bilayer is increased from 2λ to 2λ2+t2 by the presence of finite interlayer hopping (t), whereas in the RMX bilayer, the interlayer hybridization is absent by symmetry. (D and E) Schematics showing the wave functions in the out-of-plane direction for the eight species of partially layer-hybridized excitons per valley with spin up (D) and spin down (E). Note four of them Xho have large optical dipoles (moderate electric dipoles) of ~97% (~25%) compared with that of monolayer (interlayer) exciton. The other four Xhe have large electric dipoles (moderate optical dipoles) of ~97% (~25%) compared with that of interlayer (monolayer) exciton.

We note the fact that, in bilayer MoS2, the interlayer hybridization enables a total of eight transitions of partially layer-hybridized valley excitons as shown in Fig. 4 (D to E), with both spin-up and spin-down holes becoming relevant in each valley. Four of them Xho have large optical dipoles (~97% compared with that of monolayer exciton) and moderate electric dipoles (~25% compared with that of interlayer exciton). The other four Xhe have large electric dipoles (~97% compared with that of interlayer exciton) and moderate optical dipoles (~25% compared with that of monolayer exciton). The Xho and Xhe exciton transition energies differ by the conduction band spin splitting, not resolvable here due to the small splitting in MoS2 (~3 meV), while the much larger splitting in other TMDs shall allow separate access of these exciton states. Two Λ-shape level schemes are enabled in the spin-up and spin-down subspaces, respectively, by these layer-hybridized excitons, allowing the interlayer quantum control of both spin species in each valley.


Our work has demonstrated the first observation of the interlayer hybridization of K valleys in TMD hetero- and homobilayers, which is consistent with the symmetry-dictated registry dependence. The interlayer hopping integral of the valence band is determined to be tvv ≈ 36 to 43 meV, depending on the material combinations. While most research has focused on the band-edge moiré excitons in TMD heterobilayers, the obtained interlayer hopping strength at high-symmetry points provides a measure for the upper limit of confinement potential in a TMD-based moiré superlattice. By using the interlayer hybridization, creating a moiré potential up to ~100 meV becomes feasible in TMD hetero- and homobilayers. Moreover, our work points out a more notable moiré modulation effect in electronic structures, where the layer distribution of out-of-plane wave function can strongly depend on in-plane locations in the moiré. It can become a brand new control knob to engineer excitons in the bilayer, paving the way toward the next-generation artificial platform for exploring exciton physics and engineering moiré quantum dot arrays. In addition, the layer-hybridized valley excitons can be used for realizing strongly interacting excitonic/polaritonic gases, as well as spin valley–selective optical quantum coherent controls of bidirectional interlayer carrier transfer with either upper conversion or down conversion in energy.


Growth of bilayer TMD heterostructures and homostructures

Single-crystal WSe2/MoSe2 heterobilayers, WS2/MoS2 heterobilayers, and MoS2 homobilayers were grown on sapphire substrates in a horizontal hot-wall CVD chamber using the one-pot synthesis process (27, 28). The high-purity WO3 (99.995%, Aldrich), MoO2 (99%, Aldrich), Se (99.5%, Alfa), and S (99%, Aldrich) powders were used as the source precursors. The sapphire substrate and metal-oxide powder were placed at the central heating zone, while the chalcogen powder was heated by a heating belt at the upstream end. For WSe2/MoSe2 heterobilayers, the heterostructures were grown at 880°C in Ar/H2 flowing gas with flow rates of 60/6 sccm at low pressure (5 to 40 Torr) (10). For WS2/MoS2 heterobilayers, the growth temperature was set to 920°C in Ar/H2 flowing gas with flow rates of 60/6 sccm at low-pressure conditions (5 Torr). The MoS2 homobilayers were grown at 650°C in Ar flowing gas at ambient pressure.

TEM characterizations

Annular dark-field scanning TEM imaging was performed in a spherical aberration-corrected TEM (JEOL-2100F). The CVD-grown samples were transferred onto the TEM grids using the conventional wet-transfer process. The TMD/sapphire samples were capped with a layer of poly(methylmethacrylate) (PMMA) (950K A4) by spin coating, followed by baking at 100°C for 60 min. The PMMA-capped sample was then immersed into a buffered oxide etch (BOE) solution at 80°C for 20 min. After diluting etchant and residues in deionized water, the PMMA film was exfoliated from the sapphire substrate and transferred onto a Cu grid with carbon nets (Ted Pella). Then, the top PMMA film was removed by acetone, and the sample was cleaned by isopropyl alcohol and deionized water.

Optical measurements

Room temperature optical characterizations, such as photoluminescence (PL), Raman, and SHG spectroscopies, were performed using a back-scattering optical microscope. The light sources were focused on the sample by a 100× objective lens [numerical aperture (NA), 0.9], and the signal was sent to a 0.75-m monochromator and then detected by a nitrogen-cooled charge-coupled device camera. For PL and Raman measurements, a 532-nm solid-state laser was used as the excitation source. For SHG measurements, the fundamental laser field was provided by a mode-locked Ti:sapphire laser at 880 nm. The polarization of the fundamental laser (SHG signal) was selected (analyzed) by the individual linear polarizers and half-wave plates (29).

For low-temperature DR measurements, the sample was cooled down to T = 4 K by a cryogen-free low-vibration cryostat equipped with a three-axis piezo positioner and a 50× objective lens (NA, 0.82). A fiber-coupled tungsten halogen lamp was used as the light source. To improve the spatial resolution, the confocal optics were set up in front of the monochromator, resulting in a final spatial resolution of ~0.5 μm. The integration time per spectrum was around 4 s, where the signal-to-noise ratio was further improved by averaging >100 spectra. The second derivative spectra were numerically smoothed using the Savitzky-Golay method, resulting in an overall energy resolution of ~5 meV.


Supplementary material for this article is available at

Fig. S1. Room temperature characterizations of WSe2/MoSe2 heterobilayers by Raman and PL spectroscopies.

Fig. S2. Room temperature characterizations of WS2/MoS2 heterobilayers by Raman and PL spectroscopies.

Fig. S3. Room temperature characterizations of MoS2 homobilayers by Raman and PL spectroscopies.

Fig. S4. Strain effect of commensurate WSe2/MoSe2 heterobilayers.

Fig. S5. Optical transitions of HXM WSe2/MoSe2 heterobilayer.

Fig. S6. Temperature-dependent DR spectra of HXM WSe2/MoSe2 heterobilayer.

Fig. S7. TEM characterizations of bilayer MoS2.

Fig. S8. Low-temperature PL of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.

Fig. S9. Scanning TEM images at different locations of WSe2/MoSe2 heterobilayer with R-type and H-type stackings.

Fig. S10. DR spectrum of WS2/MoS2 heterobilayer with H-type stacking.

Note S1. Low-temperature PL measurements.

References (3033)

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Acknowledgments: Funding: This research was supported by grants from the Welch Foundation (F-1672), the NSF (DMR-1808751), the NSF MRSEC program (DMR-1720595), and the U.S. Air Force (FA2386-18-1-4097). W.-T.H. acknowledges the support from the Ministry of Science and Technology of Taiwan (MOST-107-2917-I-564-010). W.-H.C. acknowledges the support from the Ministry of Science and Technology of Taiwan (MOST-105-2119-M-009-014-MY3 and MOST-107-2112-M-009-024-MY3). W.Y. acknowledges the support from the Research Grants Council of HKSAR (HKU17312916). Author contributions: C.-K.S. and W.-T.H. conceived the idea and designed the experiment. W.-T.H. and B.-H.L. performed the spectroscopy measurements and analyses. The CVD samples were grown and characterized by L.-S.L. under the supervision of L.-J.L. and W.-H.C. M.-H.L., W.-T.H., and L.-S.L. performed the TEM measurements, assisted by M.-W.C. W.-T.H., W.-H.C., W.Y., and C.K.S. developed the model to interpret the spectroscopic data. C.K.S. and W.-T.H. wrote the paper, with key inputs from W.-H.C. and W.Y. All authors discussed the results and commented on the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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