Introduction

Using excitons in transition metal dichalcogenides (TMDs) to store and manipulate information in their valley degree of freedom is argued to be an appealing alternative to charge-based information processing1,2,3,4,5. Especially heterostructures made from two different, semiconducting TMDs, like WSe2/MoSe2-heterobilayers, are of great interest as excitons in these heterobilayers can be controlled by electrical means6,7,8,9 and exhibit recombination and valley lifetimes in the nanosecond range10,11,12,13,14. The possibility to manipulate these excitons via the twist angle between the two TMD layers15,16,17,18 and the appearance of spin-valley and many-body physics19,20,21,22,23,24 made TMD-based heterobilayers even more interesting in the emerging fields of both valleytronics and twistronics1,2,3. However, most studies focus on pure exciton physics and do not address the questions, if and how valley-polarized excitons in such heterobilayers can transfer their valley polarization to free charge carriers in either their conduction or valence bands, and if such a transfer mechanism can be controlled by parameters like the twist-angle or the position of the Fermi level. Answers to these questions are crucial for the realization of opto-valleytronic devices, in which the optically excited valley polarization may be extracted and measured by electrical means.

In this article, we report on an optical excitation mechanism that transfers the valley polarization from excitons in WSe2 to free charge carriers in MoSe2 via an interlayer charge transfer in twisted WSe2/MoSe2-heterobilayers. We show that this transfer of valley polarization significantly depends on both the twist angle and the position of the Fermi level. In devices with large twist angles (LTAs), the interlayer valley transfer becomes most efficient when crossing the band edges of both the MoSe2 valence and conduction band. This behavior is explained by twist angle-dependent scattering mechanisms that involve the Q- and Γ-valleys, where the latter is probed by angle-resolved photoemission spectroscopy (ARPES). To measure both the valley polarization and the respective valley lifetimes, we employ an all-optical, time-resolved Kerr rotation (TRKR) measurement technique that has proven to be a powerful tool to investigate the valley dynamics25,26,27,28,29,30,31,32,33,34,35. In TRKR, circularly polarized laser pump pulses are typically used to resonantly excite valley-polarized excitons, while their temporal dynamics is being probed by linearly polarized laser probe pulses measuring the Kerr rotation angle. If the energy of the probe pulse is tuned to the trion (charged exciton) energy of the TMD material, TRKR is able to detect a valley polarization of free charge carriers in the corresponding TMD layer, as demonstrated in ref. 36 and discussed in the Supplementary Note 2. Therefore, for all measurements in this study, the pump and probe energies are the trion energies of the specified TMD unless stated otherwise.

We investigate five WSe2/MoSe2-heterobilayer devices (see schematic device layout in Fig. 1a and details on the device fabrication in the Method section) with varying twist angles, which were determined by polarization-dependent measurements of the second harmonic generation (see Supplementary Note 1 and 37). The devices can be divided into two subgroups, which, as we will show, have substantially different valley dynamics: The first subgroup has a small twist angle (STA) towards a well-defined crystallographic stacking order (an R-type stacking order for a twist angle of zero, an H-type stacking order for a twist angle of 60°18,24,38,39), while the second subgroup has a LTA with respect to these stacking orders.

Fig. 1: Photoluminescence and time-resolved Kerr rotation measurements on WSe2/MoSe2 heterobilayers with small twist angles towards a crystallographic stacking order.
figure 1

a Schematic device structure of the heterobilayer devices. Only STA device #1 and LTA devices #1 and #3 have a graphite gate, whereas STA device #2 is gated via the Si++/SiO2 (285 nm) wafer. c Calculated band structure in case of the RhX-stacking (i.e., a twist angle of zero), in which the amount of hybridization is color-coded. The bands at the K-point only show negligible hybridization and a type-II band alignment. The bands at the Q- and Γ-valleys are strongly hybridized and, depending on parameters like stacking order or twist angle, shift in energy with respect to the band maxima at the K-point (see Supplementary Note 4). b, g Photoluminescence (PL) spectra as a function of gate voltage Vgate for two different devices plotted with a logarithmic color scale and (d, f) respective line-cuts plotted on a linear scale along the black dashed lines in (b) and (g) (white dashed lines are guides to the eye). The features with the highest PL intensities are the intralayer neutral exciton (X0) and the trion (X−) emission of MoSe2. For STA device #1, the interlayer exciton (IX) emission consists of several sub-peaks (see fits in the inset of d), which can be attributed to transitions involving Q- and Γ-valleys. As these features are absent in STA device #2 (see inset in f), we assume that in STA device #2 both Q- and Γ-valleys are energetically further away from the K-valleys decreasing phonon-assisted scattering between the valleys (see schematic in the inset of e). This assumption is consistent to the TRKR data shown in (e, h). For STA device #1, we observe surprisingly short lifetimes of around 200 ps and extremely small amplitudes. Instead, Kerr rotation lifetimes and amplitudes of STA device #2 are one order of magnitude larger. All measurements were conducted at 10 K, pump and probe energies are the trion energies of the specified TMD unless stated otherwise.

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Results

Heterobilayers with small twist angles

We start our discussion with a WSe2/MoSe2 heterobilayer that has a STA of 7 ± 3° towards an R-type stacking order (STA device #1). A photoluminescence (PL) measurement as a function of the gate voltage Vgate is shown in Fig. 1b, whereas Fig. 1d depicts a line-cut along the black dashed line of Fig. 1b. The two features with the highest PL intensities are the intralayer neutral exciton (X0) and trion (X−) emission of MoSe2. One observation that will get relevant as soon as we compare this device to ones that have larger twist angles is the absence of any intralayer PL emission from WSe2. We note that even the PL emission from MoSe2 is significantly reduced compared to the monolayer case, which can be attributed to an ultrafast charge transfer from intralayer into interlayer excitons15,40,41,42. In fact, a majority of the photo-excited electron-hole pairs must have been scattered into the interlayer exciton state (IX) to explain the appearance of its emission in Fig. 1b despite its very small oscillator strength43,44. The interlayer exciton appears between 1.3 and 1.4 eV and shows the expected gate-dependent energy shift due to its dipole moment7,20 (dashed white lines in Fig. 1b are guides to the eye).

In this device, the interlayer exciton emission consists of several sub-peaks (see fits in the inset of Fig. 1d) which exact origins are still a debated topic45. Some studies argue that these sub-features can be related to transitions involving Q- and Γ-valleys12,18,19,44,46,47. If this is the case, the appearance of these sub-features would imply a strong hybridization between the two TMD layers. To address this, we refer to band structure calculations that predict that the bands at the K-point of the heterobilayer only show negligible signs of hybridization, i.e., that the conduction band minimum at the K-point of the heterobilayer mainly consists of MoSe2 states, whereas the valence band maximum at the K-point mainly consists of WSe2 states, leading to a type-II band alignment44,46,47,48 (see Fig. 1c for the calculated band structure in case of the RhX-stacking). On the other hand, the bands at both the Q- and Γ-valleys are strongly hybridized and, depending on parameters like stacking order and twist angle, may shift in energy towards the band maxima at the K-point (see Supplementary Note 4 for more calculations). Interestingly, different studies significantly differ in the prediction of these energy shifts. Some of them claim a transition to an indirect semiconductor as either the Q-valley shifts below the K-point’s conduction band minimum, or the Γ-valley shifts above the K-point’s valence band maximum44,46,47,48,49. As we observe the sub-features in the interlayer exciton emission, we assume that both the Q- and Γ-valleys are energetically close enough to the K-valleys that phonon-assisted scattering can take place between these valleys (see schematic in the inset of Fig. 1e).

This finding is important for the interpretation of the TRKR data shown in Fig. 1e, where we plot the Kerr rotation amplitude ΘKerr vs the time delay between pump (circularly polarized) and probe (linearly polarized) pulses. Regardless where we set the pump and probe energies or which gate voltage we apply, we observe surprisingly short lifetimes of around 200 ps and small amplitudes of ΘKerr < 40 μrad. The only Kerr rotation signal with a good enough signal-to-noise ratio to be analyzed was obtained by tuning the pump and probe energies to the trion energies of WSe2 and MoSe2 (see Fig. 1e). Instead, no signal was detected at the interlayer exciton energies (not shown). This is highly surprising in two ways: On the one hand, these values fall significantly short compared to lifetimes of up to nanoseconds and amplitudes of up to several hundreds of μrad that are typically observed in TRKR measurements on monolayer TMDs25,26,27,28,29,30,31,32,33,34,36. On the other hand, and even more surprising, is the fact that the lowest valley lifetimes of interlayer excitons measured by time- and helicity-resolved PL measurements in WSe2/MoSe2-heterobilayers are also in the nanosecond range10,11,12,13,14. Although we observe interlayer excitons in PL (see Fig. 1b), we conclude that TRKR is in all likelihood unable to directly detect the interlayer exciton valley polarization (see further discussion in Supplementary Note 3). Moreover, the short lifetimes in TRKR probed at the trion energies (Fig. 1e) imply that any valley polarization of free charge carriers relaxes quite fast in this heterobilayer. We attribute this to the aforementioned presence of the Γ- and Q-valleys, which provide additional scattering channels for a valley polarization as soon as these valleys are energetically in the phonon-assisted scattering range (see inset in Fig. 1e). This indicates the importance of these valleys in the understanding of the overall spin and valley dynamics of free charge carriers in heterobilayers that have STAs near to a crystallographic stacking order, which is in accordance with previous theoretical and experimental studies based on optical measurement techniques other than TRKR4,40.

To support this notion, we studied another WSe2/MoSe2 heterobilayer (STA device #2) with a twist angle of 56 ± 3°, which is a STA of 4 ± 3° to an H-type stacking order. This device also shows interlayer excitons in the gate-dependent PL map (see Fig. 1g), but without any well separated sub-peaks (see inset in Fig. 1f, which is a line-cut along the black dashed line in Fig. 1g). This may imply that the Q- and Γ-valleys are energetically further separated from the K-valleys and therefore no longer play a key role in the interlayer exciton emission. The less pronounced hybridization compared to STA device #1 might be due to the different stacking order (see also our calculations in Supplementary Note 4), an increased separation between the layers, or strain50,51. If we assume a larger energy separation between the K-valleys and the Q- or Γ-valleys, we expect a less pronounced scattering rate between these valleys. This is in complete accordance to the results of the TRKR measurements on this device, which yield Kerr rotation lifetimes and amplitudes which are one order of magnitude larger than the ones of STA device #1 (compare Fig. 1e, h). Setting the energies of the pump and probe laser pulses to the trion energies of the respective TMD layers, we now observe a fast decaying Kerr rotation signal of several hundreds of picoseconds and a second smaller signal with a decay in the nanosecond range. Interestingly, we even observe a small Kerr rotation signal when the probe pulse is set to the interlayer exciton energy (see the inset of Fig. 1h). However, it must be the topic of further studies to clarify, if this signal really originates from the interlayer exciton or is rather caused by a low-energy tail of a bright, intralayer exciton resonance (see, e.g., the discussions to Fig. 2b, c later on).

Fig. 2: Photoluminescence and time-resolved Kerr rotation measurements on a WSe2/MoSe2 heterobilayer with a large twist angle of 23 ± 3° (LTA device #1).
figure 2

a The gate-dependent PL spectra that are plotted on a logarithmic color scale show no interlayer exciton emission, but instead the intralayer exciton (X0) and trion peaks (X− and \({X}_{-}^{{\prime} }\)) of WSe2. The latter were absent in Fig. 1b, g because of hybridization-induced scattering channels in devices with small twist angles. b Conversely, the appearance of the WSe2 intralayer emission in LTA device #1 implies the suppression of these scattering channels, resulting in TRKR lifetimes and amplitudes that are much larger than the ones of the previous devices. c An energy scan, where the pump pulse energy is set to the trion energy of WSe2 and the probe pulse energy is varied, only shows resonances at the bright intralayer exciton and trion energies. A Kerr rotation signal at the interlayer exciton energy, which is scaled-up by a factor of 100 in (b) for better visibility, is only due to the long tail of the bright exciton resonances. (d–f) Gate-dependent TRKR amplitudes and (g–i) lifetimes for different combinations of pump and probe energies, which reveal two different types of signals. The first signal (reddish colors) appears if the Fermi level lies in the band gap region of the probed TMD layer and can be linked to defect-bound exciton states. The second signal (blueish colors) appears as soon as the Fermi level is tuned either into the conduction (CB) or valence band (VB) of MoSe2 (compare to the appearance of the trion features in (a)) and can be attributed to a valley polarization of free charge carriers (see explanation in the text). All measurements were conducted at 10 K, pump and probe energies are the trion energies of the specified TMD unless stated otherwise.

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Heterobilayers with large twist angles

An even smaller impact of the Q- and Γ-valleys due to a larger energy separation to the K-valleys is expected for twist angles that are far away from a crystallographic stacking order (see calculations in Supplementary Note 4). Therefore, we now focus on a heterobilayer with a LTA of 23 ± 3° (LTA device #1). The gate-dependent PL map of this device is shown in Fig. 2a and reveals a significantly different coupling between the two TMD layers. This is evident not only in the absence of an interlayer exciton emission18, but also in the appearance of the intralayer exciton (X0) and trion peaks (X− and \({X}_{-}^{{\prime} }\)) of WSe252,53,54, which were completely quenched in the previous two devices (compare Fig. 2a to Fig. 1b, g). It is important to note that many studies about WSe2/MoSe2-heterobilayers that are showing interlayer exciton emission show a much stronger quenching of WSe2 intralayer excitons compared to the quenching of MoSe2 intralayer excitons7,11,13,17,23,47. This implies the existence of fast, hybridization-induced scattering channels for photo-excited electron-hole pairs away from the K-valleys of WSe2 in heterobilayers with STA (see Supplementary Note 4 for a more detailed discussion). Conversely, the appearance of the WSe2 intralayer emission in LTA device #1 implies the suppression of these scattering channels for larger twist angles and therefore a significant decrease in the coupling strength between the TMD layers.

The conclusion of a decreased coupling is further supported by the TRKR measurements on LTA device #1 (Fig. 2b) that exhibit lifetimes and amplitudes that are much higher than those of the STA devices (compare Fig. 2b to Fig. 1e, h). In fact, amplitudes of hundreds of μrad and lifetimes in the nanosecond range are reminiscent to values measured on monolayer TMDs25,26,27,28,29,30,31,32,33,34,36. The energy scan in Fig. 2c, in which the pump pulse energy was fixed at the trion energy of WSe2 and the probe pulse was tuned over the whole energy range of the PL measurements, only shows resonances at the bright intralayer exciton and trion energies. A small Kerr rotation signal at the interlayer exciton energy (between 1.3 and 1.4 eV in case of the STA devices), which is scaled-up by a factor of 100 in Fig. 2b for better visibility, is only due to the long tail of the bright exciton resonances in Fig. 2c.

Interestingly, two distinctly different TRKR signals can be revealed in the heterobilayer by tuning the Fermi level via a gate voltage and by varying the energies of both pump and probe pulses (see Fig. 2d–f for the respective amplitudes ΘKerr of the TRKR signals and the Supporting Information of ref. 36 for the used fitting procedure). The occurrence of these two signals depends on whether the Fermi level is tuned either in the band gap of the probed TMD layer (reddish colors in Fig. 2d–f) or in the valence or conduction band (blueish colors). For example, if we set the energies of both the pump and probe pulses to the trion energy of WSe2 (Fig. 2d), a Kerr rotation signal with a lifetime between 4 and 10 ns (Fig. 2g) appears as soon as the trion emission of WSe2 in Fig. 2a vanishes for gate voltages smaller than 0 V, i.e., as soon as we leave the conduction band and enter the band gap of WSe2. If the probe pulse energy is instead tuned to the trion energy of MoSe2 (see Fig. 2e, f, where we used different pump energies), a TRKR signal with similarly long lifetimes appears in the gate voltage range that also shows the appearance of the neutral exciton (X0) emission of MoSe2 in Fig. 2a, which in turn marks the gate range of the band gap in MoSe2. Similar long-lived states within the gate voltage range, in which emission of neutral excitons predominates, have been reported previously in both WSe2/MoSe2 heterobilayers55 and WSe2 monolayer devices36,56.

The corresponding amplitude of this long-lived signal is maximal within the band gap region and falls as soon as the Fermi level enters either the conduction band (VB) or valence band (VB) of MoSe2, where the band edges are determined by the appearance of the negatively or positively charged trion emission in Fig. 2a, respectively. Small shifts in the gate-dependent positions of the features in Fig. 2a compared to Fig. 2d–f are expected due to photo-induced gate screening effects that depend on both the energy and intensity of the used laser systems, which are different for TRKR and PL measurements (see ref. 57 and the Supporting Information of ref. 36). As we discuss further below in more detail, the band gap related TRKR signal results from defect-bound exciton states within the band gap. Accordingly, the corresponding TRKR signal has a lifetime similar to the recombination time of these bound exciton states, which spans the nanosecond to microsecond range at cryogenic temperatures58,59,60.

A distinctly different TRKR signal in the WSe2/MoSe2 heterobilayer appears when the Fermi level gets tuned into either the valence or the conduction band of MoSe2 and when the probe energy is tuned to MoSe2 (see blueish colors in Fig. 2e, f). The initial increase of the Kerr rotation amplitude indicates that this signal is linked to a valley-polarization of free charge carriers. Interestingly, such a gate-dependent TRKR signal is completely missing if both the pump and probe energies are set to the WSe2 energy (Fig. 2d). Remarkably, this result is exactly opposite to what was found in the respective monolayer cases, as some of us demonstrated in ref. 36. There, a valley polarization of free charge carriers could only be achieved in WSe2, where the polarization mechanism was explained by an intervalley scattering channel via dark trion states, which are not available in MoSe2 monolayers52. Comparing Fig. 2d, e instead reveals the existence of a mechanism that transfers the valley polarization from excitons in WSe2 to free charge carriers in MoSe2 via an interlayer charge transfer.

Deviation from the expected type-II band alignment

To explain this intriguing charge transfer process, we first discuss the PL data in Fig. 2a in more detail to determine the band structure of LTA device #1 and the gate-dependent position of the Fermi level. There is a striking gate-tunability of the WSe2 trion emission, which shows a pronounced red-shift and a transition from the X− to the \({X}_{-}^{{\prime} }\) trions, which is normally seen in monolayers of WSe261,62, but to our knowledge has not yet been reported in such clarity in WSe2/MoSe2-heterobilayers. The exact origin of the \({X}_{-}^{{\prime} }\)-feature is still under debate: Whereas in earlier publications it was attributed to the filling of the energetically higher, spin-split conduction band of WSe2, more recent publications explain this feature with a coupling between plasmons and excitons or the creation of many-body exciton states63,64,65,66. Whatever its exact origin is, the appearance of this feature is only expected if the conduction band of WSe2 at the K-point gets filled with electrons. However, this is unexpected in case of a type-II WSe2 to MoSe2 band alignment with well-separated conduction band minima of WSe2 and MoSe2 (see Fig. 1c)44,46,47,48,67. It was proposed that large displacement fields or high gate-induced charge carrier densities can reduce the energy separation between the conduction band minima of WSe2 and MoSe2 at the K-point, which eventually may even lead to a transition from a type-II to a type-I band alignment9,68,69. However, this explanation cannot be applied to LTA device #1 as the trion emission of both MoSe2 and WSe2 in Fig. 2a appear almost simultaneously at gate voltages that are only slightly larger than 0 V. Hence, it seems that the conduction band minima of MoSe2 and WSe2 are aligned close to each other, which allows the Fermi level EF to almost simultaneously enter both conduction bands (see schematics in Fig. 3a, d, the blue lines in the figures represent spin-up and red lines represent spin-down bands, slightly opaque rectangles represent the filling of the respective bands with charge carriers). We propose that this unexpected band alignment might be caused by a combination of the LTA together with a slight n-doping of both the WSe2 and MoSe2 (note that in all PL maps, i.e., Figs. 1b, g, 2a, and 4a, the strongest emission of the neutral exciton is observed at gate voltages Vgate < 0 V, especially in Figs. 1g and 4a it is clear that the negatively charged trion emission prevails over the neutral exciton emission at Vgate = 0 V). The donor states may originate either from chalcogenide vacancies or substitutional dopants70,71. Before stacking the TMD layers into a heterostructure, the respective Fermi level in each TMD layer is therefore not in the middle of the band gap, but somewhere between the donor states and the conduction band minimum. Similar to conventional bulk semiconductors, we expect that the band alignment in the TMD heterostructure will be determined in first order approximation (i.e., ignoring any charge transfer processes) by the alignment of these two Fermi levels. Assuming similar donor binding energies (black solid lines below the conduction bands in Fig. 3a, d represent donor states) we therefore conclude that the conduction band minima of both TMD layers must be close to each other.

Fig. 3: Band structure at the K-, Q- and Γ-valleys for LTA devices and the resulting transfer mechanism of a valley polarization from excitons to free charge carriers.
figure 3

a, d Band structure of LTA device #1 at the K-points derived from the gate-dependence of the bright exciton emission in Fig. 2a. Blue and red colors represent spin-up and spin-down states, respectively. Sightly opaque rectangles represent the filling of the bands with charge carriers. a The fact that the negatively charged trion features of WSe2 and MoSe2 appear almost at the same gate voltage in Fig. 2a hints to an alignment of the respective conduction band minima to each other. This deviation from the expected type-II band alignment may be caused by a combination of the large twist angle together with a slight n-doping of both TMD layers (black solid lines below the conduction bands in (a, d) represent donor states). d For negative gate voltages, the smaller band gap of MoSe2 prevents the Fermi level to enter the valence band of WSe2 within the applicable gate voltage range, explaining the absence of the positively charged trion emission of WSe2. b, e ARPES measurements of LTA device #2 for both s- and p-polarized light and (c, f) linecuts that are normalized and averaged over a small wave-vector range at the K-, K’-, and Γ-points demonstrate that in this device the Γ-valley is energetically close to the K-valleys. g–j Model that is based on the derived and measured band structure in (a–f) and that can explain both the energy and the gate dependence of the Kerr data in Fig. 2. See text for a detailed explanation.

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For the given band alignment we expect that for negative gate voltages the Fermi level first enters the valence band of MoSe2, due to the smaller band gap of MoSe2 compared to WSe2 (see Fig. 3d). Ignoring any type of band renormalization that might be caused by photo-exited or gate-induced charge carriers9,72,73, the valence band maximum of WSe2 in Fig. 3d cannot be reached within a technically achievable gate voltage range. This is indeed in accordance to the PL data of Fig. 2a that shows the appearance of the positively charged trion (X+) of MoSe2 for Vgate < − 1 V, but no clear tuning into the positively charged trion regime of WSe2 (note that we have chosen a logarithmic color scale for all PL maps, the very small emission in the trion energy range of WSe2 for Vgate < 0 V can be readily attributed to strain-induced band fluctuations at bubbles in the heterostructure74,75).

Whereas the PL measurements in Fig. 2a provide information about the respective band alignment at the K-valleys, we employ ARPES measurements to get further information about the relative position of the Γ-valley with respect to the K-valleys. Depending on stacking order, interlayer distance, or twist angle, theoretical studies come to different conclusions about whether the valence band maximum lies either at the Γ- or the K-valley44,46,47,48,49. Interestingly, even experimental ARPES studies come to different conclusions: Whereas one of the first reported measurements claims that the Γ-valley lies below the K-valley76, a more recent measurement claims the opposite77. As we cannot conduct ARPES measurements on the devices with a top hexagonal boron nitride (hBN) layer (see Fig. 1a), we fabricated another heterobilayer (LTA device #2) with a twist angle comparable to LTA device #1. We used the same crystals and fabrication methods that were used for the other devices and placed a MoSe2/WSe2/graphite-stack directly onto an n-doped silicon wafer (i.e., with MoSe2 on top, which therefore contributes most to the surface-sensitive ARPES measurements).

The ARPES measurements are shown in Fig. 3b, e for both s- and p-polarized light with a photon energy of 50 eV. The answer to the question in which valley the valence band maximum lies is made more difficult by the fact that the signal strength of an individual valley state depends on the polarization. Whereas the Γ-valley can be measured quite well with p-polarized light (Fig. 3b), the K-valleys are better visible with s-polarized light (Fig. 3e). Only considering linecuts that are normalized and averaged over a small wave-vector range at the K-, K’-, and Γ-points of the ARPES measurements with p-polarized light therefore may lead to the erroneous conclusion that the Γ-valley is slightly higher in energy than the K-valleys (see Fig. 3c). Instead, considering both the s- and p-polarized measurements and comparing linecuts that show the highest intensity for each individual valley demonstrates that the valence band maximum is rather located at the K-valleys (see Fig. 3f). However, Γ- and K-valleys are energetically close enough to each other that phonon-mediated scattering between these valleys is most likely more relevant than it already is in case of monolayer TMDs27,40,78,79,80,81,82.

Based on these ARPES results, we assume that in the other LTA devices the Γ-valley is also energetically lower than the K-valleys of MoSe2, however energetically close enough such that the Γ-valley lies in between the K-valleys of WSe2 and MoSe2 (see schematic in Fig. 3g). It is also important that our DFT calculations show that the Γ-valley is spin-degenerate, whereas the Q-valley is showing a small spin-splitting (see Fig. 1c and Supplementary Note 4), which is consistent to previous studies44,46,47,83.

Model of the interlayer transfer mechanism

With this knowledge, we now provide a model that explains the observed dependence of the valley polarization (Kerr rotation amplitude) in Fig. 2d–f on both the pump/probe energy and the gate. Figure 3g–j show the underlying dynamics for the case that the energy of the pump laser is set to WSe2 and the Fermi level enters the valence band of MoSe2, i.e., −6 V < Vgate < −1 V in Fig. 2. Under such conditions, the right circularly polarized pump pulse will excite charge carriers from the upmost valence band of WSe2 to its upper spin-split conduction band (see transition from Fig. 3g–h)52. It is likely that the predominant energy relaxation path for the photo-excited electrons involves an interlayer transfer from the upper spin-split conduction band of WSe2 to the lower spin-split conduction band of MoSe2, with the same spin-orientation and the same K-valley (see upper black dashed line in Fig. 3h). In contrast, the photo-excited holes can experience spin scattering caused by the spin-degenerate Γ-valley (see transition from Fig. 3h–i) leading to a population of the K’-valley’s valence band with photo-exited holes.

The different interlayer spin/valley-scattering paths and rates of the photo-excited electrons and holes lead to a situation where eventually more photo-exited electrons than photo-excited holes are in the K-valley of MoSe2, whereas the situation is reversed in the K’-valley (see Fig. 3i). During exciton recombination (see transition from Fig. 3i–j), photo-excited electrons also recombine with free holes in the K-valley, pushing the charge carrier density below the Fermi level (continuous dashed black line through Fig. 3g–j). As there are more photo-excited holes than electrons in the K’-valley, it now shows a surplus of holes after the recombination process. Overall, this mechanism transfers the valley polarization from excitons to free charge carriers by a valley selective interlayer charge transfer. The resulting valley polarization then relaxes back into the equilibrium state with the genuine valley lifetime \({\tau }_{{{{\rm{valley}}}}}^{{{{\rm{VB}}}}}\) (see Fig. 3j).

The same interlayer transfer mechanism can be readily applied to the case in which the Fermi level is tuned into the conduction band of MoSe2, resulting in a net valley polarization of free charge carriers in the conduction band. As the Q-valley plays a less significant role in the scattering process than the Γ-valley, we expect, however, that the respective valley lifetimes in the conduction band are longer than the ones in the valence band, which is indeed observed in our data (see Fig. 2h, i). Our model can also explain the great similarity between Fig. 2e, h on the one hand and Fig. 2f, i on the other hand, i.e., between setting the pump energy either to WSe2 or MoSe2. Creating electron-hole pairs directly in the K-valley of MoSe2 would lead to the exact same condition that is depicted in Fig. 3i, if we assume that the photo-excited holes will be subjected to scattering via the Γ-valley. Despite the energy separation of the Γ-valley from the K-valleys of MoSe2, this scattering is very likely to occur during the short timescale of the pump pulse because of photo-induced band gap renormalization effects and the amount of available phonons that are created by the scattering of photo-excited charge carriers into lower-energy states72,73,84,85.

Finally, the long-lived Kerr rotation signal that is present when the Fermi level lies within the band gap of one of the two TMD layers (reddish data points in Fig. 2d–f) can be explained by the mechanism that was discussed in ref. 36 and can be easily incorporated into our current model: A part of the photo-excited electron-hole pairs scatter into defect-bound exciton states (see Fig. 3h), which can have quite long recombination times \({\tau }_{{{{\rm{rec}}}}}^{{{{\rm{bound}}}}}\) from the nanosecond up to the microsecond range58,59,60 and also may create a valley polarization of resident charge carriers during their recombination process (Fig. 3j). As this polarization process is directly connected to the lifetime of the bound excitons, i.e., the polarization occurs during the full exciton recombination time, it does not allow the direct probing of the respective valley lifetimes (see rate equation model in the Supplemental Material of ref. 36 for a more detailed discussion).

We note that we simplified our model in Fig. 3g–j in the sense that we did only consider the most important scattering and recombination channels. However, the consideration of, e.g., additional spin-flip scattering processes or non-radiative recombination processes does not change the overall result, as long as the photo-excited electrons and holes undergo differently strong valley scattering processes. Here a simplified explanation for this necessary condition: If the photo-excited holes recombine with the photo-excited electrons in the same valley (either the valley in which they were created or in which both were scattered into) the system will end up in its initial state, which means that no net valley polarization of free charge carriers can be induced. Instead, with different scattering rates for electrons and holes, there will be an imbalance of photo-excited charge carriers in the conduction and valence bands of a specific valley and, therefore, their recombination necessitates the involvement of resident (free) charge carriers, which get polarized during the recombination process.

Counter-play of two different scattering channels

Finally, we explore another device with large twist angle (LTA device #3), which additionally allows for charge transport measurements as it was built with multiple graphite contacts. The gate-dependent PL map of this device (Fig. 4a) is quite comparable to the one of LTA device #1 in Fig. 2a, especially with respect to the appearance of the exciton emission of WSe2. When tuning both pump and probe energies to WSe2 we again observe the long-lived Kerr rotation signal (Fig. 4b, d) that is related to the bound exciton states and that has its largest amplitude at the gate voltage range where the neutral exciton of WSe2 is most pronounced in Fig. 4a.

Fig. 4: Photoluminescence and time-resolved Kerr rotation measurements on a third WSe2/MoSe2 heterobilayer with large twist angle (LTA device #3).
figure 4

a The gate-dependent PL map of LTA device #3 that is plotted on a logarithmic color scale is also showing intralayer exciton emission of WSe2, comparable to LTA device #1 in Fig. 2a. Because LTA device #3 was built with several graphite contacts, electrical transport measurements could be conducted on this device. The white line depicts the current at a bias voltage of 2 V. b The bound-exciton related Kerr rotation signal has the highest amplitude at the gate voltage range at which the neutral exciton emission in (a) indicates the position of the band gap. c The Kerr signal that can be attributed to a valley polarization of free charge carriers appears as soon as the current in (a) starts to rise at a gate voltage of around Vgate = 0 V. d, e Lifetimes of the signals in (b) and (c), respectively. All measurements were conducted at 10 K, pump and probe energies are the trion energies of the specified TMD.

Full size image

The white solid line in Fig. 4a depicts the source-drain current measured at a bias voltage of 2 V and shows that the current starts to rise at a gate voltage of around Vgate = 0 V. It is exactly at this gate voltage at which the TRKR signal that can be attributed to the valley polarization of free charge carriers appears when the probe energy is tuned to MoSe2 (see Fig. 4c). Its amplitude first increases almost linearly with the gate voltage (the more free charge carriers are induced by the gate, the more can be polarized), before it eventually decreases again for larger gate voltages, i.e., larger electron densities, which is in complete accordance to LTA device #1. The respective valley lifetimes are shown in Fig. 4e, whereas Fig. 4d shows the lifetime of the bound-exciton driven signal. As it was the case for LTA device #1 (see Fig. 2h, i), the valley lifetime of the free charge carriers (Fig. 4e) first increases for small carrier densities, then exhibit a maximum at intermediate densities, before it eventually decreases towards higher densities. We attribute this overall trend to an interplay of two different scattering channels that have opposite dependencies with respect to the Fermi level. Pushing the Fermi level further into the conduction band reduces the scattering via mid-gap or tail states. However, at the same time, wave-vector dependent electron-phonon and spin-orbit scattering mechanisms get stronger36,81,86,87.

We note that when probing at the MoSe2 energy, LTA device #3 does not exhibit any long-lived, bound-exciton related Kerr rotation signal when the Fermi level is tuned into the band gap. This indicates a low defect density in the MoSe2 layer. At the same time, we observe much longer valley lifetimes of free charge carriers compared to LTA device #1 (up to 12 ns instead of 2 ns). Combining these two observations supports the notion that mid-gap or tail states limit the genuine valley lifetime for small charge carrier densities.

Discussion

In summary, we have demonstrated that the twist angle has a significant impact on the dynamics of valley-polarized free charge carriers in WSe2/MoSe2 heterobilayers. For small twist angles near a crystallographic stacking order (an R-type stacking order for a twist angle of zero, an H-type stacking order for a twist angle of 60∘), scattering via Q- and Γ-valleys highly diminishes the valley polarization of free charge carriers, despite the simultaneous occurrence of interlayer excitons with their presumably long recombination and polarization times. For twist angles that lie between these stacking orders, we observe a substantial increase in both the magnitude and the lifetime of the valley polarization, hinting to a significant reduction in the scattering via the Q- and Γ-valleys. Gate-dependent measurements of these latter devices enable us to disentangle two different Kerr signals, one that is related to defect-bound states within the band gap region, and one that represents the actual valley-polarization of free charge carriers within either valence or conduction band. Interestingly, for these devices we also observe a deviation from the widely assumed type-II band alignment that we contribute to an alignment of the respective conduction bands by donor states. This observation could open the possibility of tailoring the band alignment in these heterobilayer devices, and thus the valley and spin dynamics, by using differently doped TMD layers. Most importantly, the unexpected band structure alignment in these devices enables an interlayer transfer of photo-induced, valley-polarized excitons from the WSe2 layer into a pronounced valley polarization of free charge carriers in the MoSe2 layer. This transfer is most efficient at the onsets of either valence or conduction band, demonstrating the possibility of extracting and utilizing this valley polarization by electrical means.

Methods

Device fabrication

The WSe2/MoSe2-heterobilayer devices are fabricated from exfoliated flakes with a dry-transfer method, protected by hBN from both sides and contacted via graphite electrodes (see schematic in Fig. 1a; detailed information about device fabrication can be found in refs. 36,88). For STA device #1 and LTA devices #1 and #3 we furthermore incorporated a graphite gate, whereas for STA device #2 we use the Si++/SiO2 (285 nm) wafer for gating. An exception from this general fabrication procedure is LTA device #2 that is used for the ARPES measurements and therefore cannot be protected by hBN. For this device we directly placed a MoSe2/WSe2/graphite-stack onto an n-doped silicon wafer.

Measurements

Detailed technical information about the TRKR and PL measurement techniques and the used fitting procedures can be found in the Supporting Information sections of refs. 27,34,36. We note that it is important to account for photo-induced screening effects of the gate electric field57 to unveil the true lifetimes and amplitudes of the Kerr signal that can be attributed to free charge carriers. In the Supporting Information of ref. 36 we show how the standard optical measurement techniques can be modified to account for the photo-induced gate screening and we demonstrate that disregarding this procedure can lead to erroneous conclusions drawn from gate-dependent measurements.

Time-resolved Kerr rotation

Two mode-locked Ti:sapphire lasers are used to independently tune the energies of both pump and probe pulses. An electronic delay between both pulses covers the full laser repetition interval of 12.5 ns. The pulse widths are on the order of 3 ps. The laser beams are focused onto the device by a 15 mm focal length aspheric lens (numerical aperture of 0.66 NA). Typical spot diameters are 6−8 μm measured as a full width at half maximum (FWHM) value. The laser power was around 500 μW for both pump and probe beams.

Photoluminescence

A microscope objective lens (numerical aperture of 0.5 NA) is used for the photoluminescence measurement. The resulting spot size is around 1–2 μm FWHM. A continuous wave laser with an energy of 2.33 eV and a power between 10 and 50 μW is used for these measurements.

Angle-resolved photoemission spectroscopy

The ARPES measurements have been performed at the NanoESCA beamline of Elettra, the Italian synchrotron radiation facility, using a FOCUS NanoESCA photoemission electron microscope (PEEM) in the k-space mapping mode operation89. The PEEM is operating at a background pressure p < 5 × 10−11 mbar and the photoelectron signal is collected from a spot size of about 5−10 μm. Before the experiment the sample was outgassed in UHV at T = 180 °C for 60 min. The measurements were conducted with a photon energy of 50 eV and an overall energy resolution of 50 meV using p- and s-polarized synchrotron radiation, while keeping the sample at 90 K.