Ultrafast non-excitonic valley Hall effect in MoS2/WTe2 heterobilayers

The valley Hall effect (VHE) in two-dimensional (2D) van der Waals (vdW) crystals is a promising approach to study the valley pseudospin. Most experiments so far have used bound electron-hole pairs (excitons) through local photoexcitation. However, the valley depolarization of such excitons is fast, so that several challenges remain to be resolved. We address this issue by exploiting a unipolar VHE using a heterobilayer made of monolayer MoS2/WTe2 to exhibit a long valley-polarized lifetime due to the absence of electron-hole exchange interaction. The unipolar VHE is manifested by reduced photoluminescence at the MoS2 A exciton energy. Furthermore, we provide quantitative information on the time-dependent valley Hall dynamics by performing the spatially-resolved ultrafast Kerr-rotation microscopy; we find that the valley-polarized electrons persist for more than 4 nanoseconds and the valley Hall mobility exceeds 4.49 × 103 cm2/Vs, which is orders of magnitude larger than previous reports.


Point-by-point responses to the issues raised by the reviewers
General remarks and comment of Reviewer 1: The paper explores the valley hall effect for electrons in MoS2 by using a optical injection of electrons from an WTe2 layer. The authors use time and space resolved Kerr rotation to estimate the valley polarization lifetime and mobility of these optically injected electrons.
Overall, I find the paper interesting, and the results appear reasonable.

Response 1 general remarks:
We appreciate the time that Reviewer 1 took to consider our manuscript. Following the advice from Reviewer 1, we provided additional supplementary information in the revised manuscript by providing more data obtained from control.
We wish to point out that we have made a device label following Reviewer 1's advice; in the revised manuscript, device # 1 means the device we used for the most of experiments described in the main text, and device #2 indicates the auxiliary device shown in Supplementary Fig. 4. This is because Reviewer 1 suggested to provide data from another device to compare the injection efficiency of spin-polarized electrons. The additional experiments performed using the above devices are supplemented in the revised manuscript.
Accordingly, we have labeled the device number in the revised manuscript. We also wish to note that the term "non-local pump" is replaced with "remote pump" in the revised manuscript following comment from Reviewer 2.
Below we present our point-by-point response to Reviewer 1's comments.

Comments 1-1:
I would like to see the Kerr rotation data for both pump helicities in Figure 3, since the sign of the Kerr rotation signal should flip sign.
Response 1-1: Indeed, the Kerr rotation signal has an opposite sign when the pump helicity is reversed. The experiment result with such helicity dependence is provided in Supplementary Fig. 7 (also presented below). The 2D scanning Kerr rotation data with an opposite pump helicity (compared to the pump helicity shown in Fig. 3) clearly shows a sign flip of the signal, and the valley Hall transport flows in the opposite direction (compare to the pump helicity in Fig.  3). Figure R2. Supplementary Fig. 8. When an opposite pump helicity is used (compared to the pump used in Fig. 3), the Kerr rotation signal flips its sign.

Comments 1-2:
It is somewhat surprising to me that the optical injection scheme would work reliably. What is the estimated valley polarization injection efficiency? Data from another device would be useful to compare.

Response 1-2:
We estimate the valley polarization injection efficiency from PL and transport data of devices #1 and #2. In short, our estimation is based on the following procedure. First, the injected electron population affects the MoS2 Fermi level, resulting in changes in the PL spectrum. Then, the injected electron population was estimated by comparing the VG-dependent PL spectra with and without the remote pump. Figure R3 ( Supplementary Fig. 7) shows the effect of the remote pump on the PL spectrum. Qualitatively, we see that the exciton PL with a remote pump (red color line) similarly corresponds to the PL spectrum without the remote pump when VG is just below 3 V for both devices. Based on these observations, we can draw a conclusion that the effect of the remote pump would render the MoS2 PL spectrum to lie at most VG of 3 V. Here, we wish to note that although we show the PL data when VG is 2 V without the remote pump, this corresponds to 0 % injection efficiency because we measure the PL with the remote pump when VG is 2 V. Therefore, we can only estimate the upper bound of the injection efficiency.
For the quantitative estimation of the valley polarization injection efficiency, we use the Vgdependent transfer data ( Fig. R3b for device #1 and Fig. R3d for device #2). The change of electron population was inferred by calculating the ratio between the current I2V and I3V when VG = 2 V and 3 V, respectively. As for device #1, I2V = 0.695 nA and I3V = 0.761 nA so the upper bound of efficiency (I3V-I2V)/I2V is 11.2 %. Similarly, for device #2, I2V = 0.876 nA and I3V = 0.796 nA for device #2, thereby the upper bound of efficiency is 9.8 %. Figure R3. Experimental results for the efficiency estimation. a. PL spectra with the remote pump when VG = 2 V compared to the PL at VG = 2, 3 V without the remote pump, and b. VGdependent transfer curve of device #1. c and d show the same experimental results for device #2.
We have added the estimated efficiency of both devices to Supplementary Note 4.

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Added sentences -Supplementary Note4: (Supplementary Information, page 10, line 7) Supplementary Fig. 7 shows the effect of the remote pump on the PL spectrum (Supplementary Fig. 6c and Supplementary Fig. 1b are shown again for the better comparison.). Qualitatively, we see that the exciton PL with a remote pump (red color line) similarly corresponds to the PL spectrum without the remote pump when VG is just below 3 V for both devices. Based on these observations, we can draw a conclusion that the effect of the remote pump would render the MoS2 PL spectrum to lie at most VG of 3 V. Here, note that although the PL data when VG is 2 V without the remote pump is presented, this corresponds to 0 % injection efficiency because the PL with the remote pump is measured when VG is 2 V. Therefore, we can only estimate the upper bound of the injection efficiency. For the quantitative estimation of the valley polarization injection efficiency, we use the VG-dependent transfer data (Supplementary Fig. 7b for device #1 and Supplementary Fig. 7d for device #2). The change of electron population was inferred by calculating the ratio between the current I2V and I3V when VG = 2 V and 3 V, respectively. As for device #1, I2V = 0.695 nA and I3V = 0.761 nA so the upper bound of efficiency (I3V-I2V)/I2V is 11.2 %. Similarly, for device #2, I2V = 0.876 nA and I3V = 0.796 nA for device #2, thereby the upper bound of efficiency is 9.8 %. General remarks and comment of Reviewer 2: However, the authors should address the following comments before publications.

Response:
We appreciate the effort that Reviewer 2 provided us with valuable inputs. Reviewer 2 suggested to provide a control experiment of the VHE under linearly polarized light and pointed out a confusing term, namely "non-local pump". He/she additionally raised a few concerns about the effects of trions and excitons on the spectrally resolved PL and the dynamics of Kerr-rotation transients.
We fully agree with all Reviewer 2's comments; we have added extra data that were not presented in the previous manuscript and revised some of confusing statements. For the terminology, the term "non-local pump" is replaced with "remote pump" to prevent any confusion.
We wish to point out that we have made a device label following Reviewer 1's advice; in the revised manuscript, device # 1 means the device we used for the most of experiments described in the main text, and device #2 indicates the auxiliary device shown in Supplementary Fig. 4. This is because Reviewer 1 suggested to provide data from another device to compare the injection efficiency of spin-polarized electrons. The additional experiments performed using the above devices are supplemented in the revised manuscript. Accordingly, we have labeled the device number in the revised manuscript. Below we present our point-by-point response to Reviewer 2's comments.

Response 2-1:
We agree that the VHE should include not only the circular helicity dependence but also the effect of linearly polarized light excitation. Indeed, we performed the same experiment with a linearly polarized light but have excluded these data in the original manuscript. This was simply because the data did not reveal noticeable features.
In the revised manuscript, we have added the spatially resolved PL data with an 1.55 eV linearly polarized remote pump excitation, taken from device #1. The corresponding data is presented in Fig. R5. We have observed that the suppressed exciton PL is distributed uniformly along the edge with no noticeable valley Hall deflection. This implies the spatial distribution of K and K′ valley polarization is equally spread due to the balanced up and down spin-polarized electrons. Figure R5. Spatially resolved differential PL (taken from device #1) is presented when the remote pump is linearly polarized.
For the zero longitudinal bias voltage, we note that although the VHE is not expected to appear in the spatially resolved differential PL, our data ( Fig. R6) show that such differential PL is not completely absent. Instead, we see a signature of the VHE, though the magnitude is very weak (about 20 % of differential PL when the bias voltage is applied). The transverse spatial displacement of the VHE is quite short (~ 0. 2   In the absence of the applied longitudinal electrical field, we still observe a signature of the valley Hall transport. The data were taken from device #1 when the polarization of the remote pump is a.  + and b.  -.

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Added sentences -Supplementary Note 4 (Supplementary Information page 9, line 16) Supplementary Fig. 6c shows the spatially resolved PL data with an 1.55 eV linearly polarized remote pump excitation. We have observed that the suppressed exciton PL is distributed uniformly along the edge with no noticeable valley Hall deflection. This implies the spatial distribution of K and K′ valley polarization is equally spread due to the balanced up and down spin-polarized electrons. For the zero longitudinal bias voltage, we note that although the VHE is not expected to appear in the spatially resolved differential PL, our data ( Supplementary Fig. 6d, e) show that such differential PL is not completely absent. Instead, we see a signature of the VHE, though the magnitude is very weak (about 20 % of differential PL when the bias voltage is applied). The transverse spatial displacement of the VHE is quite short (~ 0.2 m) compared to the non-zero bias voltage (~ 0.4 m, see Fig

Response 2-2:
The valley polarization of exciton and trion can be investigated by exciting 'remote pump' in WTe2 and by measuring the changes of PL in MoS2; note that we inject a spatially separated 'pump' light in MoS2 layer to measure the PL.
In Fig. R7  The red line in Fig. R7 shows that the trion PL is enhanced while the exciton PL decreases. Of course, the amount of changes of trion PL is not as large as the exciton PL changes. This is because of the weak oscillator strength of the trion. Nevertheless, in our Response 1-2 to Reviewer 1, the spin-polarization injection effieicncy is qualitatively and quantitatively estimated; the results are 11.2 % for device #1 and 9.8 % for device #2. The newly added data of Fig. R7 implies the valley polarization of trion PL also follows the helicity of the remote pump. Because both the exciton and trion follow the same helicity, some part of the transferred electron population contributes to the suppressed exciton PL, and the others lead to the enhanced trion PL.

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Added  Figure R7 is added to the supplementary information as Supplementary Fig. 5d.

Comments 2-3:
3.In spatial resolved Kerr measurements, the authors used a "non-local pump" at a specific position and then probe was then scan through the area of interest. The "non-local pump" is very confusing. It is actually a local pump at a specific position. The authors should use a more suitable terminology.

Response 2-3:
The reason we used the notion of "non-local pump" was to indicate that the VHE induced in the monolayer MoS2 is caused by the spatially separated light excitation in the monolayer WTe2. The light excitation in WTe2 is sufficiently far away from the monolayer MoS2. To measure the MoS2 PL, we use another light excitation. Because there are two light excitations (one in WTe2 and another in MoS2), these two excitations should be distinguishable.
We understand that the "non-local" term would be confusing to the readers. In fact, the intended meaning of "non-local pump" is closer to the meaning of spatially separated (, or remote) light excitation. Therefore, we have changed the term "non-local pump" into "remote pump" to convey the proper intention. For the measurement of MoS2 PL, we keep the term "pump" since the light excitation in MoS2 is necessary to measure the differential PL.

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Edited terminology -The term "non-local pump" used in the main text and in the supplementary information is changed to "remote pump".

Comments 2-4:
4.The rise time of Kerr signal is explained as the transport of valley-polarized electron packet toward the probe position. To verify this, the authors should demonstrate at least another probe position at a different distance.

Response 2-4:
Indeed, it is important to verify the assumption that the rising time shown in the timeresolved Kerr rotation measurement is originated from the spatially moving valley-polarized electron packet. We should have measured the Kerr dynamics at another probe position away from the pump. While the data from another probe position would provide a convincing evidence of the VHE, we wish to note that since the spatial dimension of the observable area near the WTe2 edge (marked as dashed black line in Fig. 1 in the main text) is very similar to the probe spot size. It was extremely challenging for us to find another probe position. In fact, while preparing the revised manuscript, we have tried to measure at another spot with 0.7 m away from the pump. The evidence was quite marginal so that a conclusive argument cannot be made. In fact, this is one of the main reasons why we took so long time before submitting the revised manuscript.
We feel sorry that we could only measure the time-resolved Kerr rotation data at one specific position (Fig. 3 c in the revised manuscript). Although the transients were measured at one specific position, we believe that we have provided clear evidence for the dynamics of the valley-polarized electron packet by measuring both spatially and temporally resolved Kerr rotation (Fig. 3 a in the main text and Supplementary Fig. 8).

Comments 2-5:
5.The authors used gate dependent rise time of Kerr signal to demonstrate the change of Hall mobility with the Fermi energy (the occupied electron states). However, gating the MoS2 only increase the nonpolarized electrons in MoS2. How can it achieve a higher Hall mobility? To increase the spin-polarized electrons, increasing the excitation power at WTe2 would make more sense.

Response 2-5:
Before replying to this comment, we have realized that Reviewer 2 and Reviewer 3 raises almost the same concern (see Response 2-5 and Response 3-2). So, we simply address the same explanation here.
Both Reviewer 2 and 3 raised a concern about the role of VG on the valley Hall velocity. In our experimental regime, the different rising time likely arises from the Berry curvature variation rather than the electrostatically induced uniform charge carriers.
For the valley Hall mobility, we wish to note that it does not exactly mean that mobility is  As VG increases, the increased amount of electron injection and the higher Fermi surface lead the change of electron distribution after thermalization from (i) to (ii). Note that Berry curvature is concentrated near at K point. More electrons experience a larger Berry curvature in case (ii) compared to the case (i).
In our experiment, changing the electron density by VG controls the electron distribution in the MoS2 conduction band. The applied longitudinal electric field ⃗ makes the Fermi surface being tilted in momentum space, as schematically shown in Fig. R8. After the thermalization and cooling are finished, the injected group of electrons fills the conduction band from the point marked as a black dashed line in Fig. R8. When VG increases, the electron population at the K (or K′) point increases, whose effect is explained as the band filling from (i) to (ii). This appears as a faster rising dynamic component in our time-resolved Kerr rotation because the non-zero Berry curvature is concentrated at the K and K′ point of the band extrema in the momentum space, i.e. the tilted Fermi surface makes the injected electrons away from the K or K′ point.
We thank both Reviewer 2 and Reviewer 3 to point out this important issue. We have included the above discussion in the revised manuscript as well as in the revised Supplementary Note 8.

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Edited sentences -Main text: (Main text, page 6, line 22) where is the antisymmetric tensor, n is the band index in the 2D limit, ( ( )) is Fermi-Dirac distribution, and Ω C ( ) is the Berry curvature derived in equations (S3)  Hall mobility by rendering more or less electrons to be affected by a larger or smaller Berry curvature distribution in the momentum space.
Just to illustrate the main point, we reiterate once again that the intrinsic valley Hall velocity ⊥ depends on the Berry curvature (k) and the electric field E applied to the electron in the band as shown in equation (1). As long as the longitudinal electric field is constant, which for most of the cases are done by applying DC source-drain potential gradient [4,12,15], the transverse valley Hall velocity would not be changed. This is exactly the same as our case. In our experiment, changing the electron density by VG controls the electron distribution in the MoS2 conduction band. The applied longitudinal electric field ⃗ makes the Fermi surface being tilted in momentum space, as schematically shown in Supplementary Fig. 13. After the thermalization and cooling are finished, the injected group of electrons fills the conduction band from the point marked as a black dashed line in Supplementary Fig. 13. When VG increases, the electron population at the K (or K′) point increases, whose effect is explained as the band filling from (i) to (ii). This appears as a faster rising dynamic component in our time-resolved Kerr rotation because the non-zero Berry curvature is concentrated at the K and K′ point of the band extrema in the momentum space, i.e. the tilted Fermi surface makes the injected electrons away from the K or K′ point.
Added figure - Figure R8 is newly added to the supplementary information as Supplementary Fig.  13.

Comments 2-6:
6.How can the authors verify that the spin-polarized electrons are generated from the 1D helical edge of 2D WTe2, rather than the interior area of WTe2?
Response 2-6: Experimentally, it is very challenging to figure out the exact origin of the spin-polarized electrons, because the remote pump generates the photo-excited carriers both in the metallic edge as well as in the interior bulk. Here, we need to consider the following two factors.
First, although the photo-excitation area of the interior bulk is much larger than the 1D edge, the interior bulk would not generate highly spin-polarized electrons, because the bulk is lack of the distinct helical states. It implies that any carriers from the bulk interior would contribute to MoS2 PL as a small background signal for the helicity-resolved PL.
Second, the density of states of the edge is quite larger than that of the bulk. In Fig. 9, we provide experimental and theoretical investigation from published literatures. Figure R9a [Nat. Phys. 13 683-687 (2017)] shows the dI/dV spectra taken across the step edge of an 1T′-WTe2 monolayer using a scanning tunneling spectroscopy (STS). The STS result implies that the density of state is strongly confined near the 1D edge of the monolayer 1T′-WTe2, in which the localized conductance along the sample is highly visible. Figure R9b   Given the above two considerations, we see that the majority of spin-polarized electrons would originate from the edge with a small background signal from the bulk. These discussions are now included in the revised main text.

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Added sentences -Main text: (Main text, page 5, line 1) Here we note that although the remote pump area of the interior bulk is much larger than the 1D edge, the majority of spin-polarized electrons would originate from the edge with a small bulk background. This is consistent with the Ref. [19,20], where the bulk is lack of distinct helical states and the density of states of the edge is significantly larger than the bulk.

General remarks and comment of Reviewer 3:
This Note the term "non-local pump" is replaced with "remote pump" in the revised manuscript according to the comments of other reviewer.
We wish to point out that we have made a device label following Reviewer 1's advice; in the revised manuscript, device # 1 means the device we used for the most of experiments described in the main text, and device #2 indicates the auxiliary device shown in Supplementary Fig. 4. This is because Reviewer 1 suggested to provide data from another device to compare the injection efficiency of spin-polarized electrons. The additional experiments performed using the above devices are supplemented in the revised manuscript. Accordingly, we have labeled the device number in the revised manuscript. Below we present our point-by-point response to Reviewer 3's comments.

Comments 3-1:
(1) The sign of the electron Berry curvature, which determines the Hall velocity direction under a given in-plane electric field, is related to the valley but not the spin. The existence of a valley Hall effect then implies that the excited spin-polarized electrons are also valley polarized. A transport measurement has indicated that in MoS2 the conduction band spin splitting is extremely small (~0.8 meV, see Nat. Commun. 8, 1938(2017), thus it's hard to say that the electron's spin and valley indices are locked. So the authors should discuss how the spin polarization in WTe2 is converted to valley polarization in MoS2. Meanwhile from the experimental observation one can get the sign of the Berry curvature thus the electron valley index. Is the obtained spin-valley relation consistent with those in the other papers?

Response 3-1:
As Reviewer 3 pointed out, the spin splitting of the monolayer MoS2 conduction band is much smaller than the valence band. Despite such a weak correlation between the spin and valley, we have observed the spin polarization injection efficiency of 11.2 % for device #1 and 9.8 % for device #2; please see our Response 1-2 to the Reviewer 1's comment for the calculation of injection efficiency. We would like to note that it is experimentally challenging to address the exact conversion mechanism from the electron spin polarization in WTe2 to the valley polarization in MoS2. If the valley polarization is not originated from the injection of spin-polarized electrons due to the small spin splitting, our experiment results may purely arise from the spin-polarized electron regardless of the valley degree of freedom. However, we wish to emphasize that the transverse Hall transport observed in our experiments is a strong signature of the valley Hall effect rather than the spin Hall effect, due to the following reasons.
First, the Kerr rotation signal exhibit nanosecond-long decaying transients, denoting a slow dynamic process. On the other hand, the spin polarization of the MoS2 conduction band electron exhibits a lifetime far shorter than the nanosecond at 77 K [Nat. Phys. 11, 830-834 (2015)] because of the highly efficient Elliot-Yafet spin relaxation of the small spin splitting.  (2017)].
The above discussion is newly added to the revised manuscript to elaborate the effect of the small spin splitting of the conduction band.

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Added sentence

Comments 3-2:
(2) More details are needed to understand the relation between the rising time and the gate voltage in FIG. 4b. The magnitude of the valley Hall velocity is given by the product of the Berry curvature and the electric field, whereas the Hall conductivity also depends on the electron density. Is the different rising time here caused only by the Berry curvature's variation with the electron energy or wave vector k (given in Supplementary Note 7)? If so, what is the relation between VG and the Berry curvature? On the other hands, does the electron density play any role here?

Response 3-2:
Before replying to this comment, we have realized that Reviewer 2 and Reviewer 3 raises almost the same concern (see Response 2-5 and Response 3-2). So, we simply address the same explanation here.
Both Reviewer 2 and 3 raised a concern about the role of VG on the valley Hall velocity. In our experimental regime, the different rising time likely arises from the Berry curvature variation rather than the electrostatically induced uniform charge carriers.
For the valley Hall mobility, we wish to note that it does not exactly mean that mobility is proportional to the amount of injected electrons. Instead, changing VG, i.e. increase or decrease of the total electron population, leads to the changes of valley Hall mobility by rendering more or less electrons to be affected by a larger or smaller Berry curvature distribution in the momentum space [Phys. Rev. Lett. 99 236809 (2007)].
Just to illustrate the main point, we reiterate once again that the intrinsic valley Hall velocity Here, the Berry curvature is an intrinsic character determined by the lattice symmetry of the involved atomic structure. As long as the longitudinal electric field is constant, which for most of the cases are done by applying DC source-drain potential gradient [Science 344 1489-1492 (2014); Nat. Nanotechnol. 11 421-425 (2016); Nat. Commun. 10 611 (2019)], the transverse valley Hall velocity would not be changed. This is exactly the same as our case. Figure R11. Schematic diagram describing the effect of the longitudinal field ( ⃗ ⃗ ) on the electron distribution. K point of the momentum space is expressed as a red dashed line, and the bottom of the conduction band near the Fermi surface EF is marked as a black dashed line.
As VG increases, the increased amount of electron injection and the higher Fermi surface lead the change of electron distribution after thermalization from (i) to (ii). Note that Berry curvature is concentrated near at K point. More electrons experience a larger Berry curvature in case (ii) compared to the case (i).