Negative circular polarization emissions from WSe2/MoSe2 commensurate heterobilayers

Van der Waals heterobilayers of transition metal dichalcogenides with spin–valley coupling of carriers in different layers have emerged as a new platform for exploring spin/valleytronic applications. The interlayer coupling was predicted to exhibit subtle changes with the interlayer atomic registry. Manually stacked heterobilayers, however, are incommensurate with the inevitable interlayer twist and/or lattice mismatch, where the properties associated with atomic registry are difficult to access by optical means. Here, we unveil the distinct polarization properties of valley-specific interlayer excitons using epitaxially grown, commensurate WSe2/MoSe2 heterobilayers with well-defined (AA and AB) atomic registry. We observe circularly polarized photoluminescence from interlayer excitons, but with a helicity opposite to the optical excitation. The negative circular polarization arises from the quantum interference imposed by interlayer atomic registry, giving rise to distinct polarization selection rules for interlayer excitons. Using selective excitation schemes, we demonstrate the optical addressability for interlayer excitons with different valley configurations and polarization helicities.

Top: Circular polarization-resolved PL spectra using σ excitation at 1.96 eV. Bottom: Positive circular polarizations for both of the intralayer and interlayer excitons are observed. The broad PL emission band between X and X is attributed to the emissions from defect-bound excitons in monolayer WSe2, since this PL band shows no valley polarization and exhibits the largest intensity when excitation at WSe2 exciton energy. The X PL shows positive , in contrast to the negative shown in Fig. 3b using σ excitation at 1.64 eV (MoSe2 exciton resonance). Figure 9: Polarization selection rule for bright X I states. a,b, AA stacking. c,d, AB stacking.

Supplementary Figure 10: Experimental setup for CD measurements.
A circularly-polarized pump beam from a cw Ti:Sapphire laser was used to create spin-valley polarized carriers in the MoSe2 and the WSe2 layers. A linearly-polarized probe beam from a wavelength-tunable supercontinuum laser was used as the probe for the pump induced CD spectra. Both the pump and probe were focused to the sample by an objective lens (OBJ). The   and   components of the reflected probe beam were separated by a quarter-wave plate (/4) in conjunction with a polarization beam splitter (PBS) and detected by a pair of balanced photodiodes. The pump beam signals were rejected by short-pass or long-pass filters (F). The pump beam was also modulated by an optical chopper in order to enable lock-in detection for the CD spectra. P: polarizer; /2: half-wave plate; BS: beam splitter; M: mirror. Figure 11: CD response. a,b, Co-polarized σ pump and σ probe leads to the band filling effect. c,d, Cross-polarized σ pump and σ probe leads to the trion formation. e, The CD spectra resulting from the difference between the co-polarized σ probe and the crosspolarized σ probe. g,h, The effects of band filling (g) and trion formation (h) for valley-polarized holes in WSe2. Figure 12: CD spectrum of monolayer WSe 2. Bottom: The CD spectrum (gray dots) measured at the monolayer WSe2 region using   pumping at 1.797 eV (690 nm). Top: the differential reflectance spectrum measured at the monolayer WSe2 region. Black solid lines are fitted curves using two Lorentzian functions (blue and orange lines), corresponding to the exciton and trion absorptions. Figure 13: CD spectra of AA and AB stacked hBLs. (a,b) Lower panel: Analysis of CD spectra (gray dots) measured from AA-stacked (a) and AB-stacked (b) hBLs using   pumping at 1.797 eV (690 nm). Black solid lines are fitted curves using two positive (blue) and two negative (orange) Lorentzian functions. Upper panel: the differential reflectance (black) and PL spectra (red). The positive (negative) peaks corresponds well with the exciton (trion) peaks X W (T W ) and X Mo (T Mo ) of WSe2 and MoSe2. (c,d). The CD spectra for AA and AB stacking measured using   pumping at different energies: 1.797 eV (red), 1.664 eV (blue) and 1.642 eV (green). Figure 14: The formation of bright X I states in AB stacked hBLs. a,b, The formation of bright (a) X and (b) X states using σ excitation at the MoSe2 layer. Red and blue lines are WSe2 and MoSe2 bands, respectively. Solid and dotted lines represent bands with different spins. Vertical arrows indicate optical excitations. Grey solid (dotted) arrows represent interlayer transfer to the lowest energy band without (with) spin flips. Green solid (dotted) arrows represent intralayer scatterings without (with) spin flips. c, The formation of bright X state using σ excitation at the WSe2 layer. Since the optical gap of WSe2 is higher than that of MoSe2, the σ excitation also injects +K polarized carriers into MoSe2 non-resonantly. The formation of X state involves spin-flip processes. Figure 15: PL spectra from ten hBLs with AA and AB stacking measured at 4 K. The PL intensity of X in AB stacking is generally weaker by a factor of 2-5 in comparison with that in AA stacking. Table 1: The helicity of circular polarization for the four possible valley configurations of bright X I states in hBL with AA and AB stacking.

Supplementary Note 1. Characterization of heterobilayers
Different types of heterostructure flakes were grown on the same substrate and have been characterized by PL and Raman spectroscopes. In Supplementary Figure 1a

Supplementary Note 4. Intralayer exciton energy and calculated bandgap energy in MoSe 2 and WSe2
From the differential reflectance spectra shown in Fig. 2e, the energy for intralayer excitons can be determined. Here we denote the A (B) exciton peak in MoSe2 and WSe2 as X and X (X and X ), respectively. In Supplementary Figure 7, we compare the measured intralayer exciton energy with the calculated bandgap energy in monolayer MoSe2, WSe2 and hBLs with AA (3R-like) and AB (2H-like) stacking. We found that the observed energy shifts of A-and B-exciton peaks in MoSe2 (X and X ) and the B-exciton peak in WSe2 (X ) agree quantitatively with the calculated band gap variation in hBLs with AA and AB stacking. However, we noted that Aexciton peak in WSe2 (X ) exhibits a significantly larger energy shift. The neutral and charged excitons can be distinguished in PL spectra. In Supplementary Figure 7b, we also include the energy of neutral A exciton determined from PL measurements. The energy variation agrees very well with the calculated bandgap energy, indicating that the X peak measured by ∆ / is dominated by trion absorption.

Supplementary Note 5. Theoretical analysis of interlayer dipole
Here we consider lattice-matched MoSe2/WSe2 commensurate heterobilayers with AA and AB stacking (without interlayer twist which is the superposition of the three dipoles associated with a distinct phase factor • .
According to the theory proposed by Yu et al. [1], the interlayer transition dipole also acquires contributions from coupling to intralayer excitons via interlayer hopping. Based on the symmetry analysis detailed in Yu et al. [1], the σ and σ components of are [1]:

Supplementary Note 6. Interlayer spin-valley transfer
We performed optical-pump-induced circular dichroism (CD) spectroscopy to study the interlayer spin-valley transfer processes. The experimental setup is shown in Supplementary   Figure 10.
According to Schaibley et al. [2], the spin and valley polarized carriers created by the circularly-polarized pump beam have two dominant effects on the probe beam: (1) band filling effect for co-polarized probe and (2) trion formation for cross-polarized probe, as illustrated schematically in Supplementary Figure 11. Consider the case of σ pump injecting +K polarized electrons in the MoSe2 layer, the exciton absorption measured by σ probe will be partially blocked and blue shifted due to the band filling effect (Supplementary Figure 11a,b). For σ probe at the opposite -K valley, the dominant effect is trion (X  ) formation, leading to increased trion absorption and reduced neutral exciton absorption (Supplementary Figure 11c,d). The difference between the σ and σ probes thus gives rise to the CD response, resulting in a CD line shape as shown in Supplementary Figure 11e, where the peak and dip are close to the exciton and trion resonances, respectively. For the case of injecting +K polarized holes in the WSe2 layer usingσ pump, the CD response also arises from the band filling effect and the trion (X + ) formation (Supplementary Figure 11f, g), which results in a similar CD line shape.
In Supplementary Figure 12, we show the CD spectrum measured from monolayer WSe2 regions using σ pump at 1.797 eV (690 nm). The observed CD spectrum is consistent with the line shape feature shown in Supplementary Figure 11. By using two Lorentzian functions to fit the CD line shape, we obtain a peak and a dip, which are close to the exciton and trion resonances of monolayer WSe2 measured by the differential reflectance. Since our CVD grown WSe2 is weakly p-type, the trion peak is attributed to the formation of positively charged excitons (X  ).
Now we discuss the CD response in the WSe2/MoSe2 hBLs. In Supplementary Figure 13a,b, we show the CD spectra for AA-and AB-stacked hBLs using above-gap σ excitation at 1. To gain insight on the interlayer spin-valley transfer, we used σ pump at MoSe2 and probe the CD response of WSe2 (Supplementary Figure 13c,d), which reflects the spin polarized holes transferred from the +K valleys of MoSe2 to the +K valley of WSe2. We found that the CD line shapes of WSe2 using σ pump at MoSe2 exciton energy (1.642 eV) are almost identical with that using above-gap σ excitation at 1.797 eV for both stacking. This result clearly demonstrates that the interlayer hole transfer is a spin-conserving process, regardless of the stacking orientation. We have also measured the CD response near the MoSe2 exciton resonance using σ pump at the MoSe2 layer (Supplementary Figure 13c,d). In the experiment, the excitation energy was increased slightly to 1.664 eV in order to reject the pump beam from the measurements. The CD line shape of MoSe2 using σ pump at the MoSe2 layer are also similar to that using above-gap excitation, indicating the generation of +K polarized electrons in the MoSe2 layer. Furthermore, we observed enhanced CD responses of MoSe2 by a factor of 3-4 when pumping at the MoSe2 layer, in comparison with that using above-gap excitations. This suggests that using resonant (near resonant) excitation at the MoSe2 exciton energy can significantly increase the electron valley polarization in MoSe2, in consistent with the enhanced of interlayer excitons shown in Fig. 3b.

Supplementary Note 7. Formation of bright X I states in AB stacked hBLs
According to the valley optical selection rule for AB stacking and the sign of measured shown in Fig. 4b, we determine the preferential valley configuration of bright X I state as X when using σ excitation at the MoSe2 layer and X when using σ excitation at the WSe2 layer.
According to Schaibley et al. [2], the interlayer charge transfer process is dominated by a spinconserving transfer to the lowest energy band, independent of the interlayer momentum mismatch.
Our CD measurements (see Supplementary Note 6) also support this picture. Therefore, using σ excitation at MoSe2 layer, a majority of dark interlayer state X is created in the steady state.
The formation of bright X state may meditated through a spin-conserving intervalley scattering in the MoSe2 layer (Supplementary Figure 14 a). When using σ excitation at the +K valley of WSe2 layer, the spin-conserving interlayer charge transfer also implies to form a majority of dark X in steady state. However, the formation of bright X state requires spin flip processes (Supplementary Figure 14 b), which is expected to be energetically unfavorable. Nevertheless, the low circular polarization for X I in AB stacked hBL suggest that there is a competing channel for the formation of X states. Further studies, such as using time-resolved Kerr rotation spectroscopy, is necessary to clarify which path is the dominant process.
The existence of lower-lying dark state in AB stacked hBLs will quench the emission from bright X states, particularly at low temperatures. Therefore, the PL emissions from AB stacked hBLs are less efficient than those from hBLs with AA stacking. As shown in Supplementary   Figure 15, the PL intensity for the investigated AB stacked hBLs is generally weaker by a factor of 2-5 in comparison with those of AA stacking, which may imply the presence of lower-lying dark state in AB stacked hBLs.