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# Enhancing and controlling valley magnetic response in MoS2/WS2 heterostructures by all-optical route

## Abstract

Van der Waals heterostructures of transition metal dichalcogenides with interlayer coupling offer an exotic platform to realize fascinating phenomena. Due to the type II band alignment of these heterostructures, electrons and holes are separated into different layers. The localized electrons induced doping in one layer, in principle, would lift the Fermi level to cross the spin-polarized upper conduction band and lead to strong manipulation of valley magnetic response. Here, we report the significantly enhanced valley Zeeman splitting and magnetic tuning of polarization for the direct optical transition of MoS2 in MoS2/WS2 heterostructures. Such strong enhancement of valley magnetic response in MoS2 stems from the change of the spin-valley degeneracy from 2 to 4 and strong many-body Coulomb interactions induced by ultrafast charge transfer. Moreover, the magnetic splitting can be tuned monotonically by laser power, providing an effective all-optical route towards engineering and manipulating of valleytronic devices and quantum-computation.

## Introduction

The investigation and control of the valley degree of freedom (DoF) are important topics in condensed matter physics and would give rise to new paradigms to encode and process information for future valleytronic and optoelectronic applications1,2,3,4. Two-dimensional (2D) transition metal dichalcogenides (TMDCs) with unique electronic band structure, such as direct band gap5,6, giant spin-orbit coupling (SOC), and entangled valley and spin DoF7,8, provide an unprecedented platform to manipulate the valley pseudospin through circularly polarized light excitation9,10,11,12 and electric field as well13,14,15,16,17. Moreover, due to valley-contrasting Berry curvature and magnetic moment8, magnetic field offers an effective opportunity to engineer the valley DoF. Recently, the valley degeneracy in TMDCs has been lifted via applying an external magnetic field, which is known as the valley Zeeman effect and plays a prominent role to manipulate valley polarization and valley coherence for logic valleytronic devices18,19,20,21,22,23,24,25,26. However, the valley splitting reported so far is relatively small, e.g. ~0.23 meV T–1, corresponding to a Lande g factor around 418,24,26,27,28. Such small valley splitting values strongly impede the practical application and development of valleytronics since magnetic control is almost impossible for a small external field.

In order to promote the information encoding and quantum-computing applications with valley DoF, great experimental efforts have been invested to enhance the valley splitting. An effective approach is to take advantage of an interfacial magnetic exchange field (MEF) from a ferromagnetic substrate29,30. Valley splitting with more than one order of magnitude enhancement is demonstrated in monolayer WSe2 by utilizing the proximity interfacial MEF from the ferromagnetic EuS or CrI3 substrate31,32,33,34. Another exotic way is doping which would induce the paramagnetic response of 2D Dirac fermions in TMDCs35 as proposed theoretically by T. Cai et al. in 2013. Recently, a giant and tunable valley exciton splitting induced by the strong electron-electron exchange interaction has also been uncovered in a wealth of atomically thin TMDCs through electrostatic gating21,25,36,37,38,39,40. In close analogy to electrostatic doping, ultrafast charge transfer in hetero-bilayers of TMDCs with type II band alignments, e.g., MoS2/WS2 heterostructures, generates electrons and holes separated in different layers and gives rise to the n-doping (p-doping) for MoS2 (WS2)41,42. Such ultrafast charge transfer induced doping would strengthen the Coulomb exchange interactions, leading to the strongly enhanced valley splitting and susceptibility. However, the greatly improved valley magnetic response has not yet been demystified in any heterostructures of TMDCs. Moreover, the efficient separation of holes and electrons guarantees the possibility to tune the doping concentration by the power of laser, providing an all-optical strategy to control magnetic related spin-valley phenomena43. In addition, monolayer TMDCs have short valley lifetime, which severely constrains their practical application44,45. In stark contrast, due to ultrafast charge separation in both real space and momentum space, the electron-hole exchange interaction is strongly suppressed in hetero-bilayers. Thus, heterostructures of TMDCs harbor ultra-long valley lifetime and are more promising for valleytronic applications46,47,48. Measurements of the valley magnetic response in heterostructures of TMDCs, brook no delay, which would provide a firm basis for the development of magnetic manipulation of valley DoF.

Here we demonstrate the robust giant magnetic valley splitting of MoS2 in as-grown MoS2/WS2 heterostructures via circular polarization-resolved magneto-photoluminescence measurements. The large enhancement of magnetic response in MoS2 is attributed to the significantly enhanced strength of exchange interaction induced by ultrafast charge transfer, which leads to the Fermi level cross the spin-split upper conduction band. Furthermore, the enhanced Zeeman splitting of MoS2 exciton emission can be photo-controlled by varying the excitation power from 6.6 to 3.8 meV at 7 T, corresponding to g factor from 15.4 to 9.5. The large g factor reveals the strong interaction effects in the conduction band of MoS2 in MoS2/WS2 heterostructures. Meanwhile, we further demonstrate that the strongly enhanced valley splitting in MoS2/WS2 heterostructures make it possible to manipulate the valley polarization effectively through magnetic fields. Our results will stimulate the widespread development in general doping enhanced magnetic susceptibility of 2D electron gas system in van der Waals (vdW) heterostructures.

## Results

### Growth and characterization of MoS2/WS2 heterostructures

Our high-quality vertical heterostructure samples were synthesized directly on SiO2 substrates following two-step process of chemical vapor deposition (CVD)49. Initially, well-defined monolayer triangular WS2 were grown on 300-nm-thick SiO2/Si substrates. Then, using WS2 as the growth template, the top layer MoS2 with typical lateral size up to 10 μm were synthesized either with parallel or antiparallel stacking, as illustrated in Fig. 1a (See Method for more growth details). The atomically smooth surface of vertically stacked MoS2/WS2 heterostructures is shown by atomic force microscopy (AFM) image in Fig. 1b. Furthermore, Raman characterization (Fig. 1c) confirms that the top layer is monolayer MoS2 with typical in-plane and out-of-plane phonon vibration modes located at 385 cm−1 and 404.4 cm−1, while the center triangular region contains the Raman modes of both MoS2 and WS2. Figure 1d shows the room temperature PL for monolayer MoS2, WS2, and hetero-bilayers. The prominent peak at 1.85 eV (1.96 eV) corresponds to excitonic emission of monolayer MoS2 (WS2). For epitaxial heterostructures, the profile is dominated by the intralayer exciton of both monolayers with PL intensity quench by a factor of 50 (100) compared with MoS2 (WS2) which is attributed to efficient interlayer charge transfer between layers41,42. Note that interlayer exciton stemmed from the recombination of separated electrons and holes can also be observed at low energy regime from room temperature PL spectra (please refer to Supplementary Fig. 5 for more information). Up to now, interlayer excitons have sparked significant attention due to the fascinating physical properties50,51,52. However, only a few papers focused on the intralayer excitons in the heterostructures which would also possess excellent exotic phenomena and play a key role for valleytronics. In this work, we study the intralayer excitons of MoS2/WS2 heterostructures to demonstrate the interesting spin-valley related phenomena and their potential applications instead of interlayer excitons.

### First-principles calculations of MoS2/WS2 heterostructures

Figure 2a shows the top and side schematic of the representative 2H stacked MoS2/WS2 heterostructures, where Mo and S atoms of the upper MoS2 layer lie on top of the S and W of the bottom WS2 layer. The average interlayer distances are determined to be 3.156 Å. The calculated band structures of the heterostructures including the SOC is shown in Fig. 2b. More detailed information about first-principles calculations can be found in the method section. Via orbital analysis, it can be known that the conduction band minimum (CBM) and valence band maximum (VBM) at K point are predominantly from Mo-4d and W-5d orbitals. Although density functional theory (DFT) and related methods often underestimate the electronic bandgap, they can provide basic guidelines for distinguishing specific type of the heterostructures. Figure 2c demonstrates the band alignment diagram for the investigated MoS2/WS2 heterostructures at K valley. It shows typical type II heterostructure character with CBM and VBM located at MoS2 and WS2 monolayer, respectively. Note that the simulated energy gap for interlayer exciton is consistent with our observed peak at low energy regime of 1.4 eV (See Supplementary Fig. 5 for more details).

### Enhanced valley splitting in MoS2/WS2 heterostructures

Due to the type II band alignment of MoS2/WS2 heterostructures, electrons and holes would separate in different layers through ultrafast charge transfer (Fig. 2d), leading to the n-doping and p-doping for MoS2 and WS2, respectively. Since the spin-splitting for the conduction band of MoS2 is relatively small (ΔCB ≈ 3 meV)53,54,55, the ultrafast charge transfer induced n-doping in MoS2 could enhance the many-body Coulomb interactions strongly. As a result, the optical transitions of MoS2 will deviate significantly from the simple non-interacting particle picture and possess a largely enhanced magnetic response. To confirm this view, we performed circular polarization dependent PL measurements under an out-of-plane magnetic field (Faraday geometry) with 532 nm (2.33 eV) excitation laser at 4.2 K. The middle image in Fig. 2f shows the polarized PL for co-circularly polarized detection under right-circularly (σ+, blue curve) and left-circularly (σ, red curve) polarized light excitation in the absence of magnetic field. It is known that, the σ+/σ can selectively excite the electrons in K/−K valley. There is no obvious energy shift at zero magnetic field due to the energy degeneracy of these two valleys. The two peaks located at 1.94 eV and 2.08 eV correspond to the direct band transition for monolayer MoS2 and WS2, respectively. Note that the interactions of the optically excited excitons with the surrounding Fermi sea of electrons would give rise to complex many-body states, such as trions, biexcitons and Fermi polarons27,56,57,58. Here we refer to them as the direct optical transitions simply. In contrast, at high field of ±7 T, the valley degeneracy is broken with higher energy for σ+/σ component at −7 T (bottom in Fig. 2f)/7 T (top in Fig. 2f). The valley splitting energy can be measured from the excitonic energy difference from the σ+ and σ polarized emission. It can be observed obviously in Fig. 2f that the valley splitting energy for MoS2 is much larger than that of WS2. Zeeman splitting energy as a function of magnetic field is plotted in Fig. 2g. According to ΔE = BB, g factor for MoS2 and WS2 in heterostructures, extracted by linear fitting, can be calculated to be $$g_{{\mathrm{MoS}}_{\mathrm{2}}} = 11.03 \pm 0.3$$ and $$g_{{\mathrm{WS}}_{\mathrm{2}}}^{} = 4.93 \pm 0.12$$, respectively.

For WS2, the g factor is ~4 which is consistent with the previous results59. In stark contrast, g factor for the optical transition of MoS2 is increased dramatically and clearly violates the simple non-interacting independent particle picture. Such strong enhanced g factor for the optical transition of MoS2 can be understood as a combination of the relatively small spin-splitting for the conduction band of MoS2 and electron-doping of MoS2 induced by ultrafast charge transfer (Fig. 2e). First, the spin-splitting for the conduction band of MoS2 is only 3 meV53,54,55, the corresponding electron density, that is required to dope electrons into the upper conduction band, is ~2.5 × 1011 cm−2, an order of magnitude smaller than that for WSe2 (refer to Supplementary Discussion for more calculation details). Second, TMDCs usually possess a high density of sulfur vacancies up to 1013 cm−2, leading to electron-doping ~ 1011 cm−259. Due to the large built-in interfacial electric field in type II MoS2/WS2 heterostructures, most of the electrons stemmed from sulfur vacancies of both MoS2 and WS2 will be localized in MoS2, resulting in a high electron-doping. Therefore, the Fermi level of MoS2 in MoS2/WS2 heterostructures is basically located in the spin-split upper conduction band, which can be clearly seen from the results of electric measurement (refer to Supplementary Fig. 3 for more details). Crossing the spin-polarized upper conduction band would lead to the change of spin-valley degeneracy (lslv) from 2 to 4, as illustrated in Fig. 2e. For the exchange interaction, it is dependent on the spin-valley degeneracy strongly. And the strength of the exchange interaction is encoded in a dimensionless parameter $$r = \sqrt {\frac{{l_sl_v}}{2}} r_s$$, where the Wigner-Seitz parameter $$r_s = \frac{1}{{\sqrt {\pi n} }}\frac{1}{{a_B}}$$ denotes the strength of Coulomb repulsion energy and aB is the effective Bohr radius. When the Fermi level crosses the upper conduction band, the doubling of spin-valley degeneracy could dramatically enhance the exchange interaction and causes the anomalously enhancement of g factor, as shown in Fig. 2g and Fig. 3. In this way, we could achieve strong magnetic response in MoS2 based on as-grown MoS2/WS2 heterostructures by intrinsic band alignment and ultrafast charge transfer doping.

### Optically controlled valley DoF in MoS2/WS2 heterostructures

Beyond significantly enhanced Zeeman splitting for MoS2 in MoS2/WS2 heterostructures, electron-doping in MoS2 can be controlled via varying the laser excitation power because of the ultra-long exciton recombination lifetime and the giant interfacial electric field. The manipulation of Coulomb repulsion energy and g factor through optical pumping provides an exceptional all-optical route towards tailoring the spin-valley properties in TMDCs heterostructures. Recently, tunable electron-doping caused by optical pumping has been demonstrated in bilayer WSe2 under an out-of-plane electric field60. Note that the band alignment of bilayer WSe2 under an out-of-plane electric field also belongs to type-II, being akin to the MoS2/WS2 heterostructures. Since the interfacial electric fields in MoS2/WS2 heterostructures is larger than the maximum applied electric field in bilayer WSe2, we can estimate the electron-doping caused by optical pumping in MoS2/WS2 heterostructures via using the results of the reference60 under the largest electric field, which is ~0.4 × 1010 cm−2/μW. In this way, we can obtain the concentration of external electron-doping caused by optical pumping under different power. The g factor of MoS2 and WS2 in the heterostructure versus the excitation power (bottom x axis) and the corresponding electron doping density (top x axis) is depicted in Fig. 3. As the power increases, the g factor of MoS2 goes through continuous decrease from 15.4 to 9.5 (refer to Supplementary Fig. 2 for more details), while the g factor of WS2 oscillates around 4 which corresponds to the value of undoped samples in previous studies56. Note that the g factor evolution of MoS2 with electron-doping in our work is in good harmony with the recent transport measurements61. For the continuous and monotonical decline in g factor of MoS2, it can be understood as the electron-doping tuned by optical pumping. As mentioned above, the Fermi level of MoS2 has crossed the upper of spin-polarized conduction band even without the optical pumping. When increasing the excitation laser power, the enhanced electron-doping would further lift the Fermi level within the upper conduction band of MoS2 and induce the drop of Wigner-Seitz radius rs. Thus, both the strength of the exchange interaction and Coulomb repulsion energy decrease, leading to decrease of g factor of MoS2 (Fig. 3). With the help of in-situ optical doping and efficient charge transfer in heterostructures, it could provide a unique picture of strong Coulomb interaction of 2D Dirac Fermions and a firm basis for the development of multi-bit optical computing. Such correlation between the magnetic, optical and valley coupling is important for potential applications of valley qubit for quantum computing, as the possibility of ultrafast generation and manipulation the valley pseudospin by coupling to photons. As for WS2, though it is strongly p-doped based on the band alignment, the large spin-orbit coupling energy (~400 meV) in valence band prevents the spin-valley degeneracy (lslv) for holes to be considerably tuned. Thus, the valley spitting of WS2 in heterostructure is relatively immune to the excitation power.

### Effective magnetic control of valley polarization

The strongly enhanced Lande g factor and valley splitting in MoS2/WS2 heterostructures, in principle, would enable the manipulation of the valley polarization effectively through magnetic field. To confirm this view, we measured the magnetic field dependent valley polarization of the direct optical transition in MoS2/WS2 heterostructures under both σ+ and σ excitations (Fig. 4a–f). The degree of valley polarization is defined as $$\rho {\mathrm{ = }}\frac{{I_{{\mathrm{co}}} - I_{{\mathrm{cross}}}}}{{I_{{\mathrm{co}}} + I_{{\mathrm{cross}}}}}$$ where Ico and Icross are the intensities for co- and cross-circularly polarized detection, respectively. Figure 4g presents the magnetic field driven evolution of valley polarization for the direct optical transitions of both MoS2 (blue) and WS2 (red) in MoS2/WS2 heterostructures. It can be seen clearly that the valley polarizations of both MoS2 and WS2 are linear in magnetic field, with a negative (positive) slope for σ+ (σ) excitation. Strikingly, the slope for the optical transitions of MoS2 (2.49) is obviously larger than that of WS2 (0.92), indicating that the valley DoF of MoS2 in MoS2/WS2 heterostructures can be manipulated more easily by magnetic fields. These phenomena can be understood as the combination of magnetic tuning of the dispersion of valley excitons and strongly enhanced Lande g factor in MoS2 induced by the enhanced exchange interactions. Due to exchange interactions between electrons and holes, the dispersion of valley exciton splits into two branches: the upper (lower) branch with a steep (smooth) dispersion18, as shown in Fig. 4h. For the zero-field case, the two branches touch at k = 0 and the two degenerate eigenstates are the excitons of K and −K, emitting σ+ and σ circularly polarized light, respectively (Fig. 4h, middle). Under a finite magnetic field, the degeneracy is lifted, opening a gap Δ(B) = BB18. Since the steeper dispersion of upper branch requires much smaller momentum transfers when exciton is scattering into the light cone, it will facilitate the formation of exciton relative to the lower branch. For positive magnetic fields, the center of the upper (lower) branch is the −K (K) valley exciton (Fig. 4h, right). Thus, valley-conserving rate γ1 (valley-flipping rate γ2) under σ+ excitation would possess a smaller (larger) value than that for σ excitation, leading to a smaller valley polarization for σ+ excitation under positive magnetic fields (Fig. 4i). Similarly, it can be known that valley polarization under σ+ excitation would yield a larger value than that under σ excitation for negative magnetic field. For the slope which represents the ability of the magnetic field to tune the dispersion of valley excitons, it is determined by the gap Δ(B) between the upper and lower branches induced by the valley Zeeman effect. Due to the strongly enhanced valley magnetic response for MoS2 induced by strongly enhanced exchange interaction, the gap Δ(B) is much larger for MoS2 than that of WS2 (as illustrated in Fig. 2d). Therefore, we would observe a much larger slope for the optical transitions of MoS2 in Fig. 4g. This different magnetic response indicates the potential applications in storing multiple valley indexes as information bits with magnetic writing and optical readouts, opening exciting possibilities for valleytronic memory devices.

## Discussion

To summarize, we demonstrate the strongly enhanced valley Zeeman splitting and magnetic tuning of polarization in MoS2/WS2 heterostructures through all-optical logic gates. The strong enhancement of valley magnetic response is due to the doubling of the spin-valley degeneracy and strongly enhanced electron-electron exchange interactions induced by ultrafast charge transfer. In addition, we show that significantly enhanced valley susceptibility can be tuned monotonically by optical pumping, offering a unique strategy for valleytronic applications. This heterostructure based approach designates a novel way for future exploration in strongly charged exciton polariton and spin-polarized Landau levels in TMDCs. Our results provide compelling evidence for band alignment induced intrinsic many-body interaction effects and establish a fertile ground for exploring the strongly correlated phenomena and ferromagnetic instability of massive Dirac electrons based on all-optical logic gates.

## Methods

### Growth of vertically stacked MoS2/WS2 heterostructures

Growth process was carried out in home-made three-zone CVD system with 1-inch quartz tube using WO3 (Alfa Aesar 99.999%), MoO3 (Alfa Aesar 99.999%) and S (Alfa Aesar 99.9%) powder as precursors. Each of the temperature zone was heated to preset values at a rate of 25 °C/min and kept stable for 20 min prior to growth. The precursor powders were pre-placed outside of the furnace and rapidly loaded from outside into each zone to start the growth. During the growth, Argon was used as carrying gas at a flow rate of 130 sccm and the vacuum pressure was kept at 0.7 Torr. The typical temperature for each three zones are 115 °C, 560 °C, and 800 °C, respectively for MoS2 growth.

### Optical characterization and magneto-PL measurements

The Raman and PL spectra in Fig. 1c, d were measured using a confocal microscope system (WITec, Alpha 300) with a frequency doubled YAG 532 nm laser at room temperature. For the magneto PL, we used a custom-designed attocube confocal micro-PL spectroscopy/imaging system with sample stage consisting of x-, y-, and z- axis positioners and a x-, y- scanner. The excitation light was a continuous-wave laser of 532 nm through a ×50 objective (laser spot size ~1 μm diameter). As for the configuration of circularly resolved PL, we inserted a quarter wave plate along incident laser to obtain circular polarized light excitation. The accuracy of the circular polarization degree for our setup was >93.0%. The emission light went through the same quarter wave plate plus a linear polarizer to be filtered by left/right helicities before CCD collection. A 600 lines/mm grating was used for PL measurements. Magnetic fields in the range of +7 T to –7 T were applied perpendicular to the plane of the heterostructure and monolayer samples.

### First-principles calculations

Our calculations are performed based on the density functional theory (DFT) as implemented in the Vienna Ab-initio Simulation Package (VASP)62. We utilize the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)63 realization for the exchange-correlation potential. To properly take the vdW interactions into consideration, the recent developed vdW density functional (i.e., SCAN + rVV10)64 is employed. The plane-wave cutoff energy is set to be 400 eV. The Monkhorst-Pack k-point mesh of size 21 × 21 × 1 is used for the Brillouin zone (BZ) sampling65. The thickness of the vacuum layer is set to be 25 Å, which is adequate to simulate two-dimensional materials. The convergence criteria of the total energy and the force on each atom were set to 10−5 eV and 10−3 eV Å−1, respectively. The SOC effect is included for the band structure calculation.

## Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

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## Acknowledgements

This project is supported by Singapore Ministry of Education (MoE) under the grant No. Tier 1, RG199/17(S) and National Natural Science Foundation of China (NSFC) under the grant No. 11774170. G.Z. thanks the finical supports from NSFC under the grant No. 11834017 and 61888102, the Strategic Priority Research Program of CAS under the grant No. XDB30000000, the Key Research Program of Frontier Sciences of CAS under the grant No. QYZDB-SSW-SLH004, and the National Key R&D program under grant No. 2016YFA0300904. S.A.Y. thanks the Singapore MoE AcRF Tier 2 (MOE2017-T2-2-108). B.Z. thanks Singapore Ministry of Education under grant No. MOE2018-T2-1-022(S). J.Z. thanks Ahmet Avar and Alberto Ciarrocchi for useful discussions and assisting in data analysis.

## Author information

Authors

### Contributions

J.Z., L.D., G.Z. and T.Y. conceived the experiments. J.Z. and L.D. prepared the as-grown samples and performed AFM characterization. J.Z., S.F. and Y.C. conducted the room temperature Raman and PL measurements. J.Z and S.F. performed the magneto-PL measurements, assisted by B.C. and C.Z. The first-principles calculations were conducted by. R.Z. and S.A.Y. J.Z., L.D., and S.F. discussed and analyzed the data. M.L. and B.Z. helped in analyzing the data and organizing the figures. J.Z., L.D., S.F., G.Z. and T.Y. co-wrote the paper. All authors discussed the results and commented on the manuscript.

### Corresponding authors

Correspondence to Guangyu Zhang or Ting Yu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work.

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Zhang, J., Du, L., Feng, S. et al. Enhancing and controlling valley magnetic response in MoS2/WS2 heterostructures by all-optical route. Nat Commun 10, 4226 (2019). https://doi.org/10.1038/s41467-019-12128-2

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