Abstract
Coupling degrees of freedom of distinct nature plays a critical role in numerous physical phenomena1,2,3,4,5,6,7,8,9,10. The recent emergence of layered materials11,12,13 provides a laboratory for studying the interplay between internal quantum degrees of freedom of electrons14,15. Here we report new coupling phenomena connecting real spin with layer pseudospins in bilayer WSe2. 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 valley15, 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 heterostructures16 through interlayer excitons.
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Exploring the consequences of the interplay between distinct quantum degrees of freedom has been an active theme in modern physics. A salient example is spinâorbit coupling (SOC), which is essential in renowned condensed matter phenomena such as the spin Hall effect1,2, topological insulators 3,4 and Majorana fermions5,6; in cold atom physics in the search for new condensate structures7; and in technological applications such as magnetoelectric coupling in multiferroics8 as well as optical and electrical control of spins for spintronics9,10. 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 recently12,13,17,18,19,20,21. The inversion symmetry breaking allows for an effective coupling between the real spin and valley pseudospin14 (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 graphene22,23,24,25,26 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 spinâvalley coupling and AB stacking, such as bilayer TMDCs, both spin and valley are coupled to layer pseudospin15. 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 pseudospins. Interlayer hopping thus has an energy cost equal to twice the SOC strength λ. When 2λ is larger than the hopping amplitude , 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 spinâlayer locking permits electrical manipulation of spins through gate control of layer polarization, which may lead to new magnetoelectric effects and quantum logic15.
Here, we report experimental signatures of coupling between this layer pseudospin and the spin and valley degrees of freedom in bilayers of WSe2 (bi-WSe2). In contrast to MoS2 (ref. 19), the high quality of WSe2, in addition to much larger SOC, provides an excellent system for observing spinâlayer locking. Although bi-WSe2 is an indirect-bandgap semiconductor, the near degeneracy between indirect and direct transitions permits us to efficiently monitor direct-gap photoluminescence from the K valleys12,13,27. Electrons in the conduction bands near the K valleys exhibit a spin splitting 2λâ¼30â40âmeV, which is two orders of magnitude larger than the interlayer hopping amplitude at the ±K points (see Supplementary Information 1). For holes, 2λâ¼450âmeV and (ref. 15). Large 2λ to ratios ensure that interlayer hopping for both electrons and holes is suppressed, achieving a spinâlayer locking effect.
We first identify the exciton states in bi-WSe2 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 (Vg) and photon energy. By comparing the gate-dependent patterns and emission energies of monolayer (Supplementary Section 2)29 and bilayer WSe2, we can identify the weak feature near 1.74âeV and Vgâ=â0 as neutral exciton (Xo) emission, whereas the peak near 1.71âeV at positive or negative Vg corresponds to negative (Xâ) or positive (X+) trions, respectively. The photoluminescence peak near 1.63âeV arises from impurity-bound excitons. Figure 2c shows photoluminescence spectra at three selected values of Vg. 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).
Next we show that large and electrically tunable exciton spin polarization can be generated in bi-WSe2 by optical pumping. Figure 3a shows the polarization-resolved photoluminescence under Ï+ excitation for Ï+ (black curve) and Ïâ (red curve) detection, at selected Vg. The degree of polarization is large for Xo, X+ and Xâ at all voltages, demonstrating the generation of large exciton spin polarizations. Interestingly, for Vg above 60âV, a doublet structure emerges in the Xâ spectrum for Ï+ (co-polarized) detection, with an increasing separation between peaks at higher Vg. We label the peaks I and II as shown in the bottom right of Fig. 3a. Note that the position of peak II coincides with the single peak present for Ïâ (cross-polarized) detection. The doublet can be fitted by a dual Lorentzian line shape (blue lines).
We define the degree of circular polarization as ηÏâ=â(PL(Ï+)âPL(Ïâ))/(PL(Ï+)+PL(Ïâ)), where PL(ϱ) is the detected photoluminescence with ϱ polarization. The extracted Î·Ï of the trion peak as a function of Vg is shown in Fig. 3b. For Vg below 60âV, the doublet separation is not resolved and Î·Ï is obtained at the peak position without fitting. The inset shows a zoomed-in view of Î·Ï centred at 0âV, where an enhancement of an already large Î·Ï for increasing |Vg| is observed. The doublet emerges for Vg above 60âV with differing degrees of exciton spin orientation for the two peaks. For simplicity, we plot just the Ï+ branch of ηÏ, with the black and blue dots indicating the polarization of trion peaks I and II, respectively, obtained from the peak fittings (see Supplementary Section 4 for fitting parameters). Figure 3c shows the peak splitting as a function of Vg under Ï+-polarized excitation (black squares).
The gate-dependent photoluminescence in Fig. 2a shows the crossover between X+ and Xâ near Vgâ=â0, which demonstrates that the sample is nearly intrinsic, without substantial external doping from substrate effects or impurities. The inset in Fig. 3b shows that the polarization minimum is near Vgâ=â0. We also performed second harmonic generation measurements (Supplementary Section 5), which showed more than two orders of magnitude suppression of second harmonic generation in bi-WSe2 compared with monolayer30. These results imply the presence of inversion symmetry in unbiased bi-WSe2. Therefore, it is not possible that the circularly polarized photoluminescence near Vgâ=â0 stems from valley polarization, as demonstrated in single-layer materials17,18,19, which requires explicit inversion symmetry breaking14. Rather, it originates from exciton spin polarization, a consequence of the spin optical selection rules present for both inversion-symmetric and asymmetric bilayers with large SOC (ref. 15).
We attribute the large exciton spin polarization, together with the emergence of an Xâ doublet at high electric field, to the spinâlayer locking effect15, which leads to an enhanced spin lifetime and electrically induced spin splitting. Figure 3d shows the energy level diagram of AB-stacked bi-WSe2 without an applied electric field. Single and double arrows denote the spin configurations of electrons and holes, respectively. As there are many possible trion configurations, we show only electronâhole pairs that emit significant photoluminescence. Under Ï+ excitation, the transition involving spin-up hole states is excited in both +K and âK valleys with equal strength and no valley polarization is generated. As a result of the spinâlayer locking (Fig. 1b,c), intra-valley spin flips are suppressed as the spin-up and -down states are localized in opposite layers. Accordingly, the spin relaxation time can be long compared with the exciton lifetime, leading to large exciton spin orientation31.
A perpendicular electric field creates a potential difference between upper and lower layers, which lifts the energy degeneracy between spin-up and -down states localized in opposite layers for a given valley. The result is an electrically induced spin Zeeman splitting. The spin splitting for electrons, Îc, is larger by a few per cent than that for holes, Îv, owing to the larger ratio (Supplementary Section 6). This difference leads to two distinct emission frequencies, that is, a higher frequency Ï1 for electronâhole recombination in the upper layer and a lower emission frequency Ï2 for the lower layer (Fig. 3e). When Ï1âÏ2 becomes larger than the spectral linewidth, the trion peak splits into a doublet as shown in Fig. 3a.
With this doublet resolved at large gate values, we observe differing degrees of polarization for the two trion peaks, which further corroborates spinâlayer locking. Specifically, the polarization of peak I centred at the higher frequency Ï1 is larger than that of peak II centred at Ï2. As the spectra in Fig. 3a show, for Vg>50âV, the weak photoluminescence feature acquired under Ï+ excitation with Ïâ detection (red curves) is always centred at Ï2. Figure 3e depicts the mechanism for the reduced polarization of peak II compared with peak I. Considering Ï+ excitation, Ï+-polarized photoluminescence at Ï1 and Ï2 comes from electronâhole recombination in the upper layer in the âK valley and the lower layer in the +K valley, respectively. Through a spin-flip and dissipation of the energy Îc to the environment, the photo-excited electron in the upper layer of the âK valley can relax to the lower layer within the same valley, which leads to Ïâ photoluminescence at energy Ï2, corresponding to peak II (Supplementary Fig. 7). In contrast, Ïâ PL at energy Ï1 requires absorption of the energy Îc to flip the photo-excited electron spin from the lower to the upper layer in the +K valley. Such spin-flip processes are strongly suppressed as Îcâ«kBT under the applied field necessary to resolve the doublet. Therefore, photoluminescence at Ï1 exhibits larger Î·Ï than at Ï2.
In the light of the clear asymmetry of trion peak splitting with applied gate, we note that the energy difference between Ï1 and Ï2 also has a contribution from the different binding energies for each trion configuration. We consider only the lowest energy configurations of optically active trions, where the extra electron or hole is in the lowest energy band (Fig. 3e and Supplementary Fig. 8). For the Xâ configuration that emits at Ï1, the electronâhole pair is in the upper layer and the excess electron is in the lower layer (interlayer trion). Conversely, all three particles are localized in the lower layer for Xâ at Ï2 (intralayer trion). The larger wavefunction overlap in the latter case leads to larger trion binding energies for peak II than peak I. This effect enhances the Xâ energy splitting, that is, Ï1âÏ2â=â(ÎcâÎv)+|δ EB|, where δ EB denotes the binding energy difference between interlayer and intralayer trions. Similar analysis for the X+ trion shows that Ï1âÏ2â=â(ÎcâÎv)â|δ EB| (Supplementary Section 8). From the measured trion binding energy of â¼ 30âmeV, we estimate δ EB to be several milli-electron volts. Thus, the binding energy difference may cancel the electric-field-induced splitting and lead to the negligible splitting of X+ that we observe.
We also examined the degree of linear polarization of the photoluminescence under linearly polarized excitation, which provides clear evidence for the observation of intralayer and interlayer trions, in addition to further revealing the electrically tunable optical orientation of in-plane excitonic spin and confirming the spinâlayer locking effect. Figure 4a shows polarization-resolved photoluminescence spectra at selected Vg under vertically polarized excitation and for vertically and horizontally polarized detection. In contrast to the observation of linearly polarized photoluminescence for only neutral excitons in monolayer WSe2 (ref. 29), we observe strong linear polarization for both neutral and charged excitonic states in bi-WSe2 (see graph for Vgâ=â0, Fig. 4a). Measuring emitted photoluminescence for arbitrary incident polarization angles (green arrows) shows that the trion photoluminescence polarization direction always coincides with that of the incident light (Fig. 4b). This demonstrates insensitivity of the photoluminescence polarization to sample orientation and thus rules out crystal anisotropy as an explanation.
Defining the degree of linear polarization as , where and indicate co-linear and perpendicular polarization detection, respectively, we extract the degree of polarization of trions as a function of gate, shown in Fig. 4c. We find that levels out to 0.25 for Vg<0, and increases monotonically for Vg>0. For Vg>60âV, the doublet emerges and the peak splitting matches that obtained under circularly polarized excitation (red squares, Fig. 3c). The polarization is calculated for each doublet peak after fitting. Interestingly, of peak I continues to increase monotonically whereas for peak II it hovers near zero. This can easily be seen by polarization-resolved photoluminescence under vertically polarized excitation at Vgâ=â150âV (Fig. 4a). We obtain the vertically polarized component at Ï2 (blue line) by fitting the data taken with vertically polarized detection (black curve). The extracted vertically polarized photoluminescence at Ï2 matches the measured horizontally polarized component (red dots), indicating negligible linear polarization of peak II. Applying the same procedure at other Vg, we determine that linearly polarized emission comes only from peak I.
As demonstrated in monolayer WSe2 (ref. 29), isotropic linear polarization can arise from the optical generation of a coherent superposition of excitonic states in the K and âK valleys, which must have identical emission energies and final electronic states on electronâhole recombination. For X+ in bi-WSe2, this is allowed only for the interlayer trion configuration (Supplementary Section 9). For Xâ, the lower panel of Fig. 4d shows the ground-state configuration for emission at Ï2, which is an intralayer trion with all three particles localized in the same lower layer. As the exchange interaction with the excess electron destroys the inter-valley coherence of the electronâhole pair, no linear polarization is observed at Ï2. Intralayer trion configurations are basically the same as those in monolayer WSe2, and our observation here is in agreement with the absence of linearly polarized Xâ photoluminescence in monolayers29. In contrast, for interlayer Xâ emission at Ï1 (upper part of Fig. 4d), the excess electron is in the layer opposite the electronâhole pair and the exchange interaction as a dephasing mechanism between Ï+ and Ïâ emission is largely suppressed. Our results thus provide spectroscopic means to distinguish intralayer and interlayer excitonic states and demonstrate optical generation of a coherent superposition of distinct valley configurations of interlayer trions.
Methods
WSe2 bilayers were obtained through mechanical exfoliation11 of bulk WSe2 crystals onto 300ânm SiO2 on a Si substrate. Patterning the bilayers into field-effect transistor geometries was done using an FEI Sirion scanning electron microscope with a Nabity nanometre pattern generation system. Device contacts consisting of 5ânm/50ânm V/Au were evaporated using an electron beam evaporator, followed by standard hot-acetone lift-off techniques. Polarized photoluminescence studies were performed with samples mounted in a low-temperature microphotoluminescence cryostat (Janis). Circularly polarized excitation and photoluminescence readout was accomplished using a Fresnel rhomb prism (CVI), and subsequently analysed with a linear polarizer. All studies were performed at a sample temperature of 30âK with 1.88âeV laser excitation and a 1.5âμm spot size, unless noted otherwise.
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Acknowledgements
The authors wish to acknowledge G. Liu and X. Wu for helpful information on the bilayer band structure, and D. Cobden for useful comments. This work is mainly supported by US DoE, BES, Division of Materials Sciences and Engineering (DE-SC0008145). A.M.J. is partially supported by a NSF graduate fellowship (DGE-0718124). H.Y. and W.Y. were supported by the Research Grant Council (HKU705513P) of the government of Hong Kong, and the Croucher Foundation under the Croucher Innovation Award. N.J.G., J.Y. and D.G.M. were supported by US DoE, BES, Materials Sciences and Engineering Division. Device fabrication was completed at the University of Washington Microfabrication Facility and NSF-funded Nanotech User Facility. Second harmonic generation is done at Garvey Imaging Core of the Institute for Stem Cell and Regenerative Medicine.
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X.X. and W.Y. conceived the experiments. A.M.J. performed the measurements. J.S.R. fabricated the devices, assisted by A.M.J. and P.K. H.Y., W.Y., A.M.J. and X.X. analysed the results. The WSe2 crystals were synthesized by N.J.G., J.Y. and D.G.M., who also performed characterization measurements of bulk crystals. A.M.J., X.X., H.Y. and W.Y. co-wrote the paper. All authors discussed the results and commented on the manuscript.
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Jones, A., Yu, H., Ross, J. et al. Spinâlayer locking effects in optical orientation of exciton spin in bilayer WSe2. Nature Phys 10, 130â134 (2014). https://doi.org/10.1038/nphys2848
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DOI: https://doi.org/10.1038/nphys2848
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