Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe 2 (original) (raw)

Coupling degrees of freedom of distinct nature plays a critical role in numerous physical phenomena 1-10. The recent emergence of layered materials 11-13 provides a laboratory for studying the interplay between internal quantum degrees of freedom of electrons 14,15. Here we report new coupling phenomena connecting real spin with layer pseudospins in bilayer WSe 2. In polarization-resolved photoluminescence measurements, we observe large spin orientation of neutral and charged excitons by both circularly and linearly polarized excitation, with the trion spectrum splitting into a doublet at large vertical electrical field. These observations can be explained as a locking of spin and layer pseudospin in a given valley 15 , where the doublet implies an electrically induced spin splitting. The observed distinctive behaviour of the trion doublet under polarized excitation further provides spectroscopic evidence of interlayer and intralayer trion species, a promising step towards optical manipulation in van der Waals heterostructures 16 through interlayer excitons. Exploring the consequences of the interplay between distinct quantum degrees of freedom has been an active theme in modern physics. A salient example is spin-orbit coupling (SOC), which is essential in renowned condensed matter phenomena such as the spin Hall effect 1,2 , topological insulators 3,4 and Majorana fermions 5,6 ; in cold atom physics in the search for new condensate structures 7 ; and in technological applications such as magnetoelectric coupling in multiferroics 8 as well as optical and electrical control of spins for spintronics 9,10. All of these phenomena arise from the coupling of the motional degree of freedom of a particle with its real spin. A pseudospin describes another discrete internal degree of freedom of electrons, and in most systems has an orbital origin and can therefore couple to the real spin by SOC as well. An excellent example is found in monolayer transition-metal dichalcogenides (TMDCs), which have attracted a significant amount of interest recently 12,13,17-21. The inversion symmetry breaking allows for an effective coupling between the real spin and valley pseudospin 14 (the latter indexes the degenerate extrema of the electron energy dispersion in momentum space). In the presence of mirror and time-reversal symmetry, SOC can be manifested as an out-of-plane spin splitting with a valley-dependent sign (Fig. 1a). Bilayer two-dimensional materials (for example, bilayer graphene 22-26 and bilayer TMDCs; ref. 15) possess another distinct degree of freedom known as the layer pseudospin. An electronic state localized to the upper or lower layer can be labelled with pseudospin up or down, respectively, which corresponds to electrical polarization. In a layered material with spin-valley coupling and AB stacking, such as bilayer TMDCs, both spin and valley are coupled to layer pseudospin 15. As shown in Fig. 1a, because the lower layer is a 180 • in-plane rotation of the upper layer, the out-of-plane spin splitting has a sign that depends on both valley and layer pseu-dospins. Interlayer hopping thus has an energy cost equal to twice the SOC strength λ. When 2λ is larger than the hopping amplitude t ⊥ , a carrier is localized in either the upper or lower layer depending on its valley and spin state. In other words, in a given valley, the spin configuration is locked to the layer index. This is schematically illustrated in Fig. 1b,c. This spin-layer locking permits electrical manipulation of spins through gate control of layer polarization, which may lead to new magnetoelectric effects and quantum logic 15. Here, we report experimental signatures of coupling between this layer pseudospin and the spin and valley degrees of freedom in bilayers of WSe 2 (bi-WSe 2). In contrast to MoS 2 (ref. 19), the high quality of WSe 2 , in addition to much larger SOC, provides an excellent system for observing spin-layer locking. Although bi-WSe 2 is an indirect-bandgap semiconductor, the near degeneracy between indirect and direct transitions permits us to efficiently monitor direct-gap photoluminescence from the K valleys 12,13,27. Electrons in the conduction bands near the K valleys exhibit a spin splitting 2λ ∼ 30-40 meV, which is two orders of magnitude larger than the interlayer hopping amplitude t ⊥ at the ±K points (see Supplementary Information 1). For holes, 2λ ∼ 450 meV and 2λ/t ⊥ ∼ 7 (ref. 15). Large 2λ to t ⊥ ratios ensure that interlayer hopping for both electrons and holes is suppressed, achieving a spin-layer locking effect. We first identify the exciton states in bi-WSe 2 through gate-dependent photoluminescence measurements (see Methods) 28,29. Figure 2a shows the photoluminescence intensity from direct-gap exciton emission as a function of backgate voltage (V g) and photon energy. By comparing the gate-dependent patterns and emission energies of monolayer (Supplementary Section 2) 29 and bilayer WSe 2 , we can identify the weak feature near 1.74 eV and V g = 0 as neutral exciton (X o) emission, whereas the peak near 1.71 eV at positive or negative V g corresponds to negative (X −) or positive (X +) trions, respectively. The photoluminescence peak near 1.63 eV arises from impurity-bound excitons. Figure 2c shows photoluminescence spectra at three selected values of V g. The peaks here coincide with the lowest energy absorption feature shown in Fig. 2b, the gate-dependent differential reflectivity obtained by white-light reflection (Supplementary Section 3).