Directional interlayer spin-valley transfer in two-dimensional heterostructures

Van der Waals heterostructures formed by two different monolayer semiconductors have emerged as a promising platform for new optoelectronic and spin/valleytronic applications. In addition to its atomically thin nature, a two-dimensional semiconductor heterostructure is distinct from its three-dimensional counterparts due to the unique coupled spin-valley physics of its constituent monolayers. Here, we report the direct observation that an optically generated spin-valley polarization in one monolayer can be transferred between layers of a two-dimensional MoSe2–WSe2 heterostructure. Using non-degenerate optical circular dichroism spectroscopy, we show that charge transfer between two monolayers conserves spin-valley polarization and is only weakly dependent on the twist angle between layers. Our work points to a new spin-valley pumping scheme in nanoscale devices, provides a fundamental understanding of spin-valley transfer across the two-dimensional interface, and shows the potential use of two-dimensional semiconductors as a spin-valley generator in two-dimensional spin/valleytronic devices for storing and processing information.

from the main text when pumping the WSe2 heterostructure resonance near 1.710 eV, and probing the MoSe2. We note that although we are plotting the same data as shown in Fig. 3a, a different aspect ratio is used to highlight the dip feature. By fitting the co-(a) and cross-(b) polarized DT spectra to a sum of three and two independent Lorentzians respectively, we compare the relative signal from the negative (dip) feature (shown in blue) centered near 1.59 eV, which corresponds to the energy of the negatively charged MoSe2 exciton (X -). Curve fitting reveals that the ratio of the areas for this dip feature is approximately 1: 0.37, yielding a spin-valley polarization of (1-.37)/(1+.37) = 46%.

Measuring the Monolayer Crystal Axes by Polarization-Resolved and Phase-Sensitive Second-Harmonic Generation
To determine the relative crystal orientation between the monolayers in the heterostructure, we performed polarization-resolved and phase-sensitive second-harmonic generation (SHG) measurements. Here, we detail the measurement procedure for the heterostructure in the main text (Supplementary Figure 1a).
First, the orientation of the armchair axes of each monolayer was determined using co-linear polarization-resolved SHG as shown in Supplementary Figure 1b 1-4 . Since this technique is not sensitive to the phase of the SHG, it only determines the twist angle up to 60°. In this case, the relative angle between the lobe maxima is 1 ± 1°, which means the twist angle is close to 0° or 60°.
To resolve this ambiguity, we performed a SHG spectral interference experiment modelled after Ref 5-7. An optical parametric amplifier, pumped by an amplified mode-locked Ti:sapphire laser, launched tunable ~200 fs pulses at (typically ~0.83 eV) into the setup shown in Supplementary  Figure 1c. The excitation was focused onto a z-cut quartz reference, which was oriented to generate horizontally polarized 2 reference pulses (collinear to and co-polarized with the pulses). A time delay ( t) was generated as the and pulses travelled through the dispersive optics in the setup. A 50X objective focused the pulses onto the sample, generating an additional sample signal (time-delayed from the 2 reference). The sample was oriented so an armchair axis, determined by the 6-fold pattern, was parallel to the 2 reference and polarization. The backreflected signals were diverted with a 50/50 beamsplitter through a 1 m short-pass filter, into a spectrometer, and detected by a Si CCD. The time-delayed 2 sample and reference signals produce spectral interference as shown in Supplementary Figure 1d. The period of the fringes is set by the time delay between the pulses (~2 ps) and the phase of the interference fringes is determined in part by the phase of SHG generated by the sample 5 . Therefore, this technique can distinguish between armchair axes 60° apart, which shows up as a phase shift in the interference spectrum. The fringes can be separated from the broad background SHG through Fourier transforms, as shown in Supplementary Figure 1e-f 6,7 .
Due the different resonances of MoSe2 and WSe2, it can be difficult to find a single excitation energy for direct comparison of the relative phase. To circumvent this issue, we also performed the interference experiment using a reference sample of z-cut quartz. When focusing on the front surface of the quartz, the allowed second-order susceptibility elements are the same as those of the monolayer MX2. Thus, as before, we oriented the quartz with its "armchair" axis parallel to the excitation and reference pulses to get a similar interference spectrum (Supplementary Figure 1d, black). This was done for two orientations of the quartz, 60° apart. The WSe2 and MoSe2 interference experiments were then compared with the quartz experiment (Supplementary Figure  1e-f, respectively). In the case of the sample shown in Supplementary Figure 1, both the WSe2 and MoSe2 SHG fringes align well with the quartz(0) direction, which confirms the orientation is close to AA-like stacking.

Effect of Twist Angle on the CD Response
Additional pump-induced circular dichroism (CD) measurements were repeated in the reflection geometry on three MoSe2-WSe2 heterostructures on SiO2 substrates. The twist angles of these samples were not aligned ( ≠ ); however, we observed that both the sign and qualitative line shape (sign and amplitude) of the CD response were not significantly affected by the twist angle (Supplementary Figure 2).
It has been previously established that the heterostructure twist angle affects how the MoSe2 and WSe2 valleys line up in momentum space 4,8 (Supplementary Figure 3). Therefore, the independence of the CD response with respect to twist angle suggests that the interlayer spin transfer process does not require the valleys to line up in momentum space. Thus, we conclude that the interlayer CD response we measure arises from real spin conservation during the interlayer transfer process (as opposed to valley pseudospin conservation). In the simplest model, spinpolarized carriers transfer between layers and then relax into the lowest energy state in each layer while maintaining their spin polarization as depicted in Supplementary Figure 3. We note that this conservation of real spin polarization also leads to a valley polarization in each layer due to the spin-valley locking effect 9 .

Degenerate DT Line Shape and Doping Effects
In this note, we examine the degenerate DT spectrum (Fig. 1c) and discuss the effects of unintentional doping. In the heterostructure region, the MoSe2 (WSe2) resonance is fit by a difference of two Lorentzians which reveals a weaker dip feature centered at 1.594 eV (1.675 eV) and stronger peak feature centered at 1.625 eV (1.705 eV). For each resonance, the ~20-30 meV difference between the peak and dip is consistent the reported binding energies for charged excitons. We therefore attribute the positive DT signal peaks to reduced neutral exciton absorption and the negative DT signal dips to increased charged exciton absorption. Both effects can be explained by pump induced photo-doping which increases the oscillator strength for charged excitons and reduces the oscillator strength for neutral excitons.
We note that the low energy pump induced absorption feature is stronger for the MoSe2 layer. We attribute this difference between the WSe2 and MoSe2 response to the different species of charged exciton for each layer. As discussed in the main text, the WSe2 pump induced absorption arises from formation of positively charged excitons (X + ), whereas the MoSe2 pump induced absorption arises from negatively charged excitons (X -). One possibility is that the oscillator strength for the X + in WSe2 is weaker than that of the Xin MoSe2, which is consistent with previous studies showing that the X + in WSe2 has weaker PL 10 . We also note that PL measurements indicate that our MoSe2 is weakly electron doped, whereas the WSe2 is nearly intrinsic. However, since we are performing a differential measurement, we expect the effect of the background unpolarized doping to be small.

Effect of the Upper Conduction Band in MoSe2
In the main text, we use the relative amplitudes of the DT responses near the negatively charged exciton (X -), to estimate the electron spin polarization in the MoSe2 layer. The lowest energy Xcorresponds to an intervalley configuration where, for example, one electron is in the lowest conduction band of one valley (-K), and the exciton is in the other valley (+K), as depicted in Supplementary Figure 6a. An intervalley trion with two electron in the same valley is not allowed due to Pauli blocking. Therefore, a -K valley electron in the lower conduction band can only induce + polarized optical absorption at the Xresonance. The conduction band splitting has been calculated to be on order of 20 meV 11 .
However, there is also the possibility of an Xcomposed of an electron in the upper conduction band which can either be in an intravalley (Supplementary Figure 6b) or intervalley (Supplementary Figure 6c) configuration and couples to a + or -polarized photon. The photon energy is given by the Xenergy minus the upper conduction band electron energy, close to the lowest energy Xoptical absorption. We note that: (1) The upper conduction band electrons have higher energies, so they will relax to the lower conduction band with the same spin 12 . Thus, in the steady state, the upper conduction band population is expected to be small. (2) A small electron population in the upper conduction band does not significantly affect our results. For example, if there is a small population of electrons in the upper conduction band, it increases the oscillator strength both for intravalley and intervalley charged excitons as shown in Supplementary Figure  6b-c. This population would lead to increased absorption for both co-polarized ( / ( ) ) and cross-polarized ( / ( )) signals, which contributes to / ( ) / ( ). But to lowest order, these two contributions are equal in magnitude, so they give rise to a negligible CD response which is proportional to the difference, Supplementary References: