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:
(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.
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
(A and B) TEM and Bragg-filtered (inset) images of
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
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
According to the coupled two-level model, the band offset 2δ and the hopping integral t can be deduced from the measured energy splitting (
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 (
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
(A to C) TEM and Bragg-filtered (inset) images of
The
(A) The second derivative spectra of bilayer MoS2 as a function of twist angle θ. (B) The energy separation between
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
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 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.
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
Fig. S6. Temperature-dependent DR spectra of
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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REFERENCES AND NOTES
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