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

We report the layer-hybridized valley excitons in 2D hetero- and homobilayers manifested by band alignment and valley spin.

Abstract

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.

INTRODUCTION

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 (1–12). 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, 15–18). 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 (15–18).

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.

RESULTS AND DISCUSSION

The layer hybridization of electronic states in bilayers can be described by a two-level Hamiltonian: $\left[\begin{array}{cc}{\mathrm{\epsilon }}_{\mathrm{u}}& -t\\ -t& {\mathrm{\epsilon }}_{\mathrm{l}}\end{array}\right]$ (Fig. 1A), where the basis states ∣ψ_u⟩ and ∣ψ_l⟩ 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 = ε_l − ε_u 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 ∣ψ_h+⟩ = α∣ψ_u⟩ + β∣ψ_l⟩ and ∣ψ_h−⟩ = α^′∣ψ_u⟩ + β^′∣ψ_l⟩, where β/α = t/(δ − Δ), β^′/α^′ = t/(δ + Δ), and $\mathrm{\Delta }=\sqrt{{\mathrm{\delta }}^2+t^2}$. 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 P_H = ∣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 (∣ψ_u⟩) and lower (∣ψ_l⟩) 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. ${\mathrm{R}}_{\mathrm{\nu }}^{\mathrm{\mu }}$ (${\mathrm{H}}_{\mathrm{\nu }}^{\mathrm{\mu }}$) 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 ∣t_vv∣ 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) ∣t_vv∣ 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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ 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 ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$ or ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ stacking configurations were observed (Fig. 2, A and B). According to Fig. 1F, the hopping integral reaches the maximum in ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ stacking but vanishes in ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$ and ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ stacking configurations.

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

(A and B) TEM and Bragg-filtered (inset) images of ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ (A) and ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ (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 ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ (blue curves) and an ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ (red curves) heterobilayer, showing a clear splitting of ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$ for the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer. (D) The DR (upper panel) and second derivative (lower panel) spectra of an ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer shown with the spectra fitting (red curve). (E) Schematic showing the optical transitions of the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer at K valley. Note that both ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$ (blue) and ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ (orange) transitions are split into two hybridized transitions (${\mathrm{X}}_{\mathrm{h}\pm }^{\mathrm{W}}$ and ${\mathrm{X}}_{\mathrm{h}\pm }^{\text{Mo}}$), 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 ${\mathrm{X}}_{\mathrm{h}\pm }^{\mathrm{W}}$ and ${\mathrm{X}}_{\mathrm{h}\pm }^{\text{Mo}}$ 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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$-stacked and a ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$-stacked WSe₂/MoSe₂ heterobilayer. The most notable difference emerges from the B exciton of WSe₂ (denoted as ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$), which shows a single peak in R stacking, but becomes a doublet (referred to as ${\mathrm{X}}_{\mathrm{h}+}^{\mathrm{W}}$ and ${\mathrm{X}}_{\mathrm{h}-}^{\mathrm{W}}$) 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 ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ (${\mathrm{X}}_{\mathrm{A}}^{\mathrm{W}}$) excitons is reduced (enhanced) in H stacking. This can be explained by the splitting of the ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ exciton peak into a doublet (${\mathrm{X}}_{\mathrm{h}+}^{\text{Mo}}$ and ${\mathrm{X}}_{\mathrm{h}-}^{\text{Mo}}$), where the split-off spectral feature merges with the ${\mathrm{X}}_{\mathrm{A}}^{\mathrm{W}}$ 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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$-stacked heterobilayers exhibit spectral splitting in ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$, 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 ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$ (${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$) exciton state into a doublet ${\mathrm{X}}_{\mathrm{h}+}^{\mathrm{W}}$ and ${\mathrm{X}}_{\mathrm{h}-}^{\mathrm{W}}$ (${\mathrm{X}}_{\mathrm{h}+}^{\text{Mo}}$ and ${\mathrm{X}}_{\mathrm{h}-}^{\text{Mo}}$) 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 ($2\sqrt{{\mathrm{\delta }}^2+t^2}$) 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 t_vv = 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 P_H ≈ 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 ($\mid {\mathrm{\psi }}_{\mathrm{e}}^{\text{Mo}}\rangle$) and the WSe₂ ($\mid {\mathrm{\psi }}_{\mathrm{e}}^{\mathrm{W}}\rangle$) layers, which can be connected by an intermediate state of interlayer negative trion (IX⁻) through optical excitations. Considering the initial state $\mid {\mathrm{\psi }}_{\mathrm{e}}^{\text{Mo}}\rangle$ (i.e., an electron in the MoSe₂ layer), the IX⁻ can be created by a π-pulse resonant excitation of ${\mathrm{X}}_{\mathrm{h}+}^{\mathrm{W}}$. By using another π-pulse excitation in resonance with ${\mathrm{X}}_{\mathrm{h}+}^{\text{Mo}}$, the trion state will be forced to recombine, leaving behind the final state $\mid {\mathrm{\psi }}_{\mathrm{e}}^{\mathrm{W}}\rangle$ (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 ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$, ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$, and ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ 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 ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$ 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 t_vv = 36 ± 4 meV, band offset 2δ = − 7 ± 20 meV, and P_H ≈ 90% in WS₂/MoS₂ heterobilayers. For the ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ and ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$ 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 (20–23). 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 ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ (A), ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$ (B), and ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ (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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer exhibits interlayer hybridization. (E) A comparison of ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ and ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayers (upper panel), showing a clear splitting of ${\mathrm{X}}_{\mathrm{B}}^{\mathrm{W}}$ for the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer. The second derivative spectrum (lower panel) of the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer with spectral fitting (red curve).

The ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayers demonstrated above exemplify the interlayer hybridization in the regime with t > δ. The ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ and ${\mathrm{R}}_{\mathrm{X}}^{\mathrm{M}}$ 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 ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ - and ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ 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 (${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$) and B-exciton (${\mathrm{X}}_{\mathrm{B}}^{\text{Mo}}$) transitions in all samples. Because of the small spin splitting in the conduction band of MoS₂, the energy splitting between ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ and ${\mathrm{X}}_{\mathrm{B}}^{\text{Mo}}$ 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 ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ 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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ bilayer is increased to 164 meV. The same A-B exciton separation between twisted and ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ bilayers is a confirmation on the absence of interlayer hybridization in the ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ bilayer, as discussed above. On the other hand, the enlarged energy splitting indicates the presence of partial interlayer hybridization in the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ 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 $2\sqrt{{\mathrm{\lambda }}^2+t^2}$ (2λ) for the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ (${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$) bilayer. Comparing the A-B exciton separation in ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ bilayers and in twisted bilayers without interlayer hopping, we determine the interlayer hopping integral in the MoS₂ bilayer to be t_vv = 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 P_H ≈ 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 ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ and ${\mathrm{X}}_{\mathrm{B}}^{\text{Mo}}$ as a function of θ, where the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ bilayer is a singular point featuring a separation larger by ~20 meV. (C) Schematic showing the optical transitions of spin-up excitons in the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ heterobilayer at K valleys, where both ${\mathrm{X}}_{\mathrm{A}}^{\text{Mo}}$ and ${\mathrm{X}}_{\mathrm{B}}^{\text{Mo}}$ transitions are split into hybridized transitions (${\mathrm{X}}_{\mathrm{h}+}^{\uparrow o,e}$ and ${\mathrm{X}}_{\mathrm{h}-}^{\uparrow o,e}$). Note that the valence band spin splitting in the ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ bilayer is increased from 2λ to $2\sqrt{{\mathrm{\lambda }}^2+t^2}$ by the presence of finite interlayer hopping (t), whereas in the ${\mathrm{R}}_{\mathrm{M}}^{\mathrm{X}}$ 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 ${\mathrm{X}}_{\mathrm{h}}^o$ have large optical dipoles (moderate electric dipoles) of ~97% (~25%) compared with that of monolayer (interlayer) exciton. The other four ${\mathrm{X}}_{\mathrm{h}}^e$ 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 ${\mathrm{X}}_{\mathrm{h}}^o$ 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 ${\mathrm{X}}_{\mathrm{h}}^e$ have large electric dipoles (~97% compared with that of interlayer exciton) and moderate optical dipoles (~25% compared with that of monolayer exciton). The ${\mathrm{X}}_{\mathrm{h}}^o$ and ${\mathrm{X}}_{\mathrm{h}}^e$ 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.

CONCLUSION

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 t_vv ≈ 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.

MATERIALS AND METHODS

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 MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/12/eaax7407/DC1

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 ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ WSe₂/MoSe₂ heterobilayer.

Fig. S6. Temperature-dependent DR spectra of ${\mathrm{H}}_{\mathrm{X}}^{\mathrm{M}}$ 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.

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