Manipulating the valley degree of freedom in TMDs has aroused tremendous interests recently due to the large enough energy degeneracy lifting by spin-orbit coupling (SOC) in them^[1-5]. Valley Hall is a representative effect that can be probed by either transport or optical measurements due to the chiral nature of the propagation of the valley pseudo-spins^[6,7]. Even though monolayer TMDs are believed to exhibit rather weak valley Hall signals, studies revealed that electrical control of valley magnetizations are detectable by Kerr rotation microscopy in such as n- or p-doped monolayer WSe₂, and also in single-layer MoS₂ under a uniaxial stress with broken rotational symmetry^[8,9]. It thus makes the TMD materials very promising for future designing of valleytronic devices incorporated with light-matter interactions^[10].

AB stacked bilayer systems such as MoS₂ offer broken inversion symmetry that arises from the vertical electric field induced by electrostatic gating. It hence leads to a pronounced valley polarization effect that gathers ‘magnetized’ valley at the sample edge in the existence of a finite longitudinal electrical current^[6]. Indeed, by using Kerr rotation microscopy, such polarization was found to be present only near the edges of the device channel with opposite sign for the two edges, and was out-of-plane and strongly dependent on the gate voltage in AB-stacked bilayer MoS₂, similar to that observed in the spin Hall effect manifested in conventional thin magnetic or antiferromagnetic films with large SOC^[11,12]. This behavior is also believed to be consistent with symmetry-dependent Berry curvature and valley Hall conductivity in bilayer MoS₂^[6].

Nevertheless, a twisted bilayer of TMD, which yields a variety of fundamental physics including flat bands and strong e–e interactions^[13,14], have been overlooked thus far in regard to the investigation of valley Hall effect in them. Especially, when constructed with a certain twist angle, the symmetry breaking spontaneously takes place, which should be more favorable in terms of the detection of valley degree of freedom in those moiré systems^[15].

Here, we show the study of the valley Hall effect (VHE) in 40°-twisted chemical vapor deposition (CVD) grown WS₂ moiré transistors, using optical Kerr rotation measurements at 20 K. We observe a clear gate tunable spatial distribution of the valley carrier imbalance induced by the VHE when a current is exerted in the system. Further, our results demonstrate that TMD moiré heterostructure can offer an attractive platform for probing and manipulating valley degree of freedom.

To fabricate the WS₂ moiré transistors, the twisted bilayer WS₂ with different angles were first grown on the SiO₂/Si substrates by an improved CVD method with the assistance of heteroatom tin (Sn) for reducing stacking energy. The details of the process of growth can be found in our former article^[16]. Systematic characterizations using optical spectroscopy of the studied devices are carried out, with the details shown in Supplementary Fig. S1. To further confirm local atomic configuration and interlayer stacking induced moiré superlattice, scanning transmission electron microscopy (STEM) characterization of typical twisted WS₂ double layers (0° and 40° twisted, for example) are shown in Supplementary Fig. S2.Fig. 1(a) shows the schematic of twisted bilayer WS₂ and the spin-split conduction band minima and valence band maxima near the K⁺ and K⁻ valleys. The spin and valley degree of freedom can be selectively operated using circularly polarized light due to the optical selection rule^[17,18]. Thus, with linearly polarized light, we can probe the accumulation of spin-polarized and valley-polarized carriers using the measurement of magneto-optic Kerr rotation (KR)^[19]. The signal of Kerr rotation should be opposite for the K⁺ and K⁻ valleys due to the opposite sign of the Berry curvature around the two valleys. To obtain a better sample quality and enhance the mobility of WS₂, we transferred multi-layered h-BN flakes onto the top of twisted bilayer WS₂. The van der Waals heterostructures were then shaped into rectangular geometry by using standard electron-beam lithography and dry etching in a plasma system. The edge contact electrodes (5 nm Cr/50 nm Au) to WS₂ were deposited by electron-beam evaporation. The corresponding optical images of a typical device for every step are shownFigs. 1(c)–1(e). For this device, the twist angle of the as-grown bilayer WS₂ is about 40°.Fig. 1(b) shows a schematic of the final device structure.

In the following, we show the electrical and optical properties of the t-WS₂ field effect transistor, being mounted in a close-cycle Montana Instrument cryostat. The transfer curves of the device forV_ds = 1 V at 20 K is presented inFig. 2(a), which clearly shows good n-type behavior of WS₂. With the help of the capping h-BN on t-WS₂, the hysteresis in the transfer curves is not remarkable.Fig. 2(b) shows the PL spectra of t-WS₂ at 20 K. The moiré transistor is excited by a 532 nm continuous-wave laser with a spot size of ~1µm focused by a high numerical objective. To obtain better signal-to-noise ratio, the excitation power is kept 300µW. From the PL spectra confocally collected by a monochromator and detected by a CCD camera, we can see four evident peaks. Experimental PL data are compared with simulations allowing the deconvolution of the PL spectra. The detailed fitting for different contributions is shown inFig. 2(b). In previous reports, the two distinguished peaks of high energies at about 2.02 and 2.04 eV were attributed to neutral exciton (X₀) and trion (X⁻), respectively^[20]. The trions observed in our experiments indicate intrinsic doping of the as-grown t-WS₂ flakes, as it is commonly observed in other TMDs grown by CVD^[21]. Apart from the peaks of exciton and trion, a very broad peak shows up around 1.85 eV. This broad peak can be recognized as the defect-trapped localized exciton (LX₂) emission and the broad bandwidth arises from the interaction between defect-trapped excitons and phonons^[22-25]. Note that the trion peak X⁻ develops a low-energy shoulder located ~ 1.97 eV. This new peak may possibly stems from defect-trapped localized exciton (LX₁) and biexciton (XX), which is beyond our scope of this paper^[20].

In the following part, we will study the emerging valley Hall effect in our t-WS₂ device. Spatially resolved magneto-optic KR is implemented to measure the microscopic spin-valley accumulation in real space. An ACV_ds = 2 V RMS is exerted to the device to generate oscillating longitudinal charge current. The out-of-plane spin-valley polarization is probed by a linearly polarized laser with photon energy optimized to the lower energy side of X₀. The reflected probe laser is analyzed by a polarization sensitive photoreceiver system. To mitigate possible heating effects, the optical power of probe laser is selected to 10µW. To further determine the spatial distribution and magnitude of the spin accumulation, the 2D lateral distribution of the KR is mapped by an electrically-driven X-Y scanner.Fig. 3 shows the KR map of the t-WS₂ device at different gate voltages. The magnitude of KR signals atV_g = –80 V have little change and the sign is the same across the channel, as shown in yellow squares ofFig. 4. This overall positive KR probably arises from the magnetoelectric effect induced by the strain in the sample^[9]. However, whenV_g varies from 0 to 20 V, we can clearly see that the sign of KR is opposite on the two edges across the channel, which is resulted from the accumulation of carriers with opposite valley and spin. Note that the offset of the KR peaks atV_g = 0 V and 20 V is almost the same, suggesting the saturation of the accumulated carriers atV_g = 0 V.

To analyze the KR maps more quantitively, we linecut the KR maps orthogonal to the electrical current direction, as depicted with dashed lines inFig. 3. The linecut data are plotted inFig. 4. We consider a diffusion-drift model to describe the spin accumulation at channel edge phenomenologically. And the net spin-valley distribution perpendicular to the direction of charge transport can be simply solved in

1s(y)∼−exp[−(y+y1)/lD]+exp[(y−y2)/lD],

wherel_D is the spin-valley diffusion length,y₁ +y₂ is the width of the channel^[8]. As mentioned above, the KR forV_g = –80 V remains unchanged across the transverse channel because of the lack of charge conductance of the n-type transistor. However,l_D are ~ 500 nm fit by Eq. (1) forV_g = 0 V andV_g = 20 V respectively (solid lines inFig. 4), indicating that KR distribution are almost the same in the regime of electron doping. It’s quite counterintuitive as KR is supposed to be linear with charge current density for a certain device with constant spin Hall angle, butI_ds increases 3 times fromV_g = 0 to 20 V fromFig. 2(a). We also note that the spin-valleys are maximized inside the channel, around 3µm far from the edge. It may be understood by some defect-induced scattering centers that prevent the complete separation of carriers with K⁺ and K^-.

In conclusion, we have firstly observed the gate-tunable valley Hall effect in twisted bilayer WS₂ transistor by measuring the spatial distribution of the KR induced by spin and valley imbalance. It seems that the CVD twisted bilayer WS₂ suffers from strains and/or defects, and the moiré superlattice played limited role in the valley Hall effect. Future studies in cleaner samples, and smaller twist angles will be needed. Our findings provide new insights into electrical control of the valley Hall effect in twisted bilayer TMDs and open up new possibilities for the study of spin and valley properties in moiré superlattice.

This work is supported by the National Key R&D Program of China (No. 2019YFA0307800). The work gratefully acknowledges financial support from the National Natural Science Foundation of China (Nos. 22175060, 21975067, 92265203, 11974357, 12004259, 12204287, U1932151), Natural Science Foundation of Hunan Province of China (Nos. 2021JJ10014, 2021JJ30092), and China Postdoctoral Science Foundation (Grant No. 2022M723215).

Supplementary materials to this article can be found online athttps://doi.org/10.1088/1674-4926/44/1/012001.