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Frank Volmer, Manfred Ersfeld, Paulo E. Faria Junior, Lutz Waldecker, Bharti Parashar, Lars Rathmann, Sudipta Dubey, Iulia Cojocariu, Vitaliy Feyer, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Claus M. Schneider, Lukasz Plucinski, Christoph Stampfer, Jaroslav Fabian, Bernd Beschoten

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[Twist angle dependent interlayer transfer of valley polarization from excitons to free charge carriers in WSe2/MoSe2 heterobilayers](https://mdr.nims.go.jp/datasets/0600aa43-c619-4726-bcfb-86fd5470fdbd)

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Twist angle dependent interlayer transfer of valley polarization from excitons to free charge carriers in WSe2/MoSe2 heterobilayersARTICLE OPENTwist angle dependent interlayer transfer of valley polarizationfrom excitons to free charge carriers in WSe2/MoSe2heterobilayersFrank Volmer 1,2✉, Manfred Ersfeld1, Paulo E. Faria Junior3, Lutz Waldecker 1,4, Bharti Parashar5, Lars Rathmann1, Sudipta Dubey1,Iulia Cojocariu 5, Vitaliy Feyer 5,6, Kenji Watanabe 7, Takashi Taniguchi 8, Claus M. Schneider5,6, Lukasz Plucinski5,Christoph Stampfer 1,9, Jaroslav Fabian3 and Bernd Beschoten 1,10Transition metal dichalcogenides (TMDs) have attracted much attention in the fields of valley- and spintronics due to their propertyof forming valley-polarized excitons when illuminated by circularly polarized light. In TMD-heterostructures it was shown that theseelectron-hole pairs can scatter into valley-polarized interlayer exciton states, which exhibit long lifetimes and a twist-angledependence. However, the question how to create a valley polarization of free charge carriers in these heterostructures after avalley selective optical excitation is unexplored, despite its relevance for opto-electronic devices. Here, we identify an interlayertransfer mechanism in twisted WSe2/MoSe2 heterobilayers that transfers the valley polarization from excitons in WSe2 to freecharge carriers in MoSe2 with valley lifetimes of up to 12 ns. This mechanism is most efficient at large twist angles, whereas thevalley lifetimes of free charge carriers are surprisingly short for small twist angles, despite the occurrence of interlayer excitons.npj 2D Materials and Applications            (2023) 7:58 ; https://doi.org/10.1038/s41699-023-00420-1INTRODUCTIONUsing excitons in transition metal dichalcogenides (TMDs) to storeand manipulate information in their valley degree of freedom isargued to be an appealing alternative to charge-based informa-tion processing1–5. Especially heterostructures made from twodifferent, semiconducting TMDs, like WSe2/MoSe2-heterobilayers,are of great interest as excitons in these heterobilayers can becontrolled by electrical means6–9 and exhibit recombination andvalley lifetimes in the nanosecond range10–14. The possibility tomanipulate these excitons via the twist angle between the twoTMD layers15–18 and the appearance of spin-valley and many-bodyphysics19–24 made TMD-based heterobilayers even more interest-ing in the emerging fields of both valleytronics and twistronics1–3.However, most studies focus on pure exciton physics and do notaddress the questions, if and how valley-polarized excitons in suchheterobilayers can transfer their valley polarization to free chargecarriers in either their conduction or valence bands, and if such atransfer mechanism can be controlled by parameters like thetwist-angle or the position of the Fermi level. Answers to thesequestions are crucial for the realization of opto-valleytronicdevices, in which the optically excited valley polarization may beextracted and measured by electrical means.In this article, we report on an optical excitation mechanism thattransfers the valley polarization from excitons in WSe2 to freecharge carriers in MoSe2 via an interlayer charge transfer intwisted WSe2/MoSe2-heterobilayers. We show that this transfer ofvalley polarization significantly depends on both the twist angleand the position of the Fermi level. In devices with large twistangles (LTAs), the interlayer valley transfer becomes most efficientwhen crossing the band edges of both the MoSe2 valence andconduction 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 photoemis-sion spectroscopy (ARPES). To measure both the valley polariza-tion and the respective valley lifetimes, we employ an all-optical,time-resolved Kerr rotation (TRKR) measurement technique thathas proven to be a powerful tool to investigate the valleydynamics25–35. In TRKR, circularly polarized laser pump pulses aretypically used to resonantly excite valley-polarized excitons, whiletheir temporal dynamics is being probed by linearly polarizedlaser probe pulses measuring the Kerr rotation angle. If the energyof the probe pulse is tuned to the trion (charged exciton) energyof the TMD material, TRKR is able to detect a valley polarization offree charge carriers in the corresponding TMD layer, as demon-strated in ref. 36 and discussed in the Supplementary Note 2.Therefore, for all measurements in this study, the pump and probeenergies are the trion energies of the specified TMD unless statedotherwise.We investigate five WSe2/MoSe2-heterobilayer devices (seeschematic device layout in Fig. 1a and details on the devicefabrication in the Method section) with varying twist angles, whichwere determined by polarization-dependent measurements of thesecond harmonic generation (see Supplementary Note 1 and 37).The devices can be divided into two subgroups, which, as we willshow, have substantially different valley dynamics: The firstsubgroup has a small twist angle (STA) towards a well-defined12nd Institute of Physics and JARA-FIT, RWTH Aachen University, 52074 Aachen, Germany. 2AMO GmbH, Advanced Microelectronic Center Aachen (AMICA), 52074 Aachen,Germany. 3Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany. 4Department of Applied Physics, Stanford University, 348 Via Pueblo Mall,Stanford, CA 94305, USA. 5Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich GmbH, 52428 Jülich, Germany. 6Fakultät für Physik and Center for NanointegrationDuisburg-Essen (CENIDE), Universität Duisburg-Essen, D-47048 Duisburg, Germany. 7Research Center for Functional Materials, National Institute for Materials Science, Tsukuba305-0044, Japan. 8International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan. 9Peter Grünberg Institute (PGI-9),Forschungszentrum Jülich, 52425 Jülich, Germany. 10JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen,Germany. ✉email: volmer@physik.rwth-aachen.dewww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00420-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00420-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00420-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00420-1&domain=pdfhttp://orcid.org/0000-0003-3526-2687http://orcid.org/0000-0003-3526-2687http://orcid.org/0000-0003-3526-2687http://orcid.org/0000-0003-3526-2687http://orcid.org/0000-0003-3526-2687http://orcid.org/0000-0002-0898-3860http://orcid.org/0000-0002-0898-3860http://orcid.org/0000-0002-0898-3860http://orcid.org/0000-0002-0898-3860http://orcid.org/0000-0002-0898-3860http://orcid.org/0000-0002-6408-3541http://orcid.org/0000-0002-6408-3541http://orcid.org/0000-0002-6408-3541http://orcid.org/0000-0002-6408-3541http://orcid.org/0000-0002-6408-3541http://orcid.org/0000-0002-7104-5420http://orcid.org/0000-0002-7104-5420http://orcid.org/0000-0002-7104-5420http://orcid.org/0000-0002-7104-5420http://orcid.org/0000-0002-7104-5420http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-4958-7362http://orcid.org/0000-0002-4958-7362http://orcid.org/0000-0002-4958-7362http://orcid.org/0000-0002-4958-7362http://orcid.org/0000-0002-4958-7362http://orcid.org/0000-0003-2359-2718http://orcid.org/0000-0003-2359-2718http://orcid.org/0000-0003-2359-2718http://orcid.org/0000-0003-2359-2718http://orcid.org/0000-0003-2359-2718https://doi.org/10.1038/s41699-023-00420-1mailto:volmer@physik.rwth-aachen.dewww.nature.com/npj2dmaterialscrystallographic stacking order (an R-type stacking order for atwist angle of zero, an H-type stacking order for a twist angle of60°18,24,38,39), while the second subgroup has a LTA with respect tothese stacking orders.RESULTSHeterobilayers with small twist anglesWe start our discussion with a WSe2/MoSe2 heterobilayer thathas a STA of 7 ± 3° towards an R-type stacking order (STA device#1). A photoluminescence (PL) measurement as a function of thegate voltage Vgate is shown in Fig. 1b, whereas Fig. 1d depicts aline-cut along the black dashed line of Fig. 1b. The two featureswith the highest PL intensities are the intralayer neutral exciton(X0) and trion (X−) emission of MoSe2. One observation that willget relevant as soon as we compare this device to ones thathave larger twist angles is the absence of any intralayer PLemission from WSe2. We note that even the PL emission fromMoSe2 is significantly reduced compared to the monolayer case,which can be attributed to an ultrafast charge transfer fromintralayer into interlayer excitons15,40–42. In fact, a majority of thephoto-excited electron-hole pairs must have been scattered intothe interlayer exciton state (IX) to explain the appearance of itsemission in Fig. 1b despite its very small oscillator strength43,44.The interlayer exciton appears between 1.3 and 1.4 eV andshows the expected gate-dependent energy shift due to itsdipole moment7,20 (dashed white lines in Fig. 1b are guides tothe eye).6420-2Vgate (V)Vgate (V)1.71.61.51.41.3energy (eV)PL intensity (arb. units)bIXMoSe2  X-MoSe2  X0a cSi ++SiO2hBNgraphite gate(optional)WSe2/MoSe2heterobilayerVgateSTA device #1 (7±3° to R-stacking)g80400-40-801.71.61.51.41.3energy (eV)PL intensity (arb. units)IXMoSe2  X--MoSe2  X0STA device #2 (4±3° to H-stacking)0102030400 4 12pump WSe2,probe MoSe2pump MoSe2,probe WSe2WSe2 MoSe2K K’ KQ K’Γdelay (ns)8ePL intensity energy (eV)1.3 1.4PL intensity (arb. units)energy (eV)1.3 1.4 1.5 1.6 1.7X0X-XIXdhfSTA device #1 (7±3° to R-stacking) STA device #1 (7±3° to R-stacking)0delay (ns)050100150200 pump WSe2, probe MoSe2pump MoSe2, probe WSe2delay (ns)5 1002040pump WSe2,probe  1.38 eV0 4 128energy (eV)1.3 1.4 1.5 1.6 1.7PL intensity (arb. units)1.3 1.4PL intensity energy (eV)STA device #2 (4±3° to H-stacking) STA device #2 (4±3° to H-stacking)IX|ΘKerr| (μrad)|ΘKerr| (μrad)|ΘKerr| (μrad)energy (eV)-0.6-0.301.21.5Q K MΓWSe2MoSe2Fig. 1 Photoluminescence and time-resolved Kerr rotation measurements on WSe2/MoSe2 heterobilayers with small twist angles towardsa crystallographic stacking order. a Schematic device structure of the heterobilayer devices. Only STA device #1 and LTA devices #1 and #3have 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 hybridizationand a type-II band alignment. The bands at the Q- and Γ-valleys are strongly hybridized and, depending on parameters like stacking order ortwist angle, shift in energy with respect to the band maxima at the K-point (see Supplementary Note 4). b, g Photoluminescence (PL) spectraas a function of gate voltage Vgate for two different devices plotted with a logarithmic color scale and (d, f) respective line-cuts plotted on alinear scale along the black dashed lines in (b) and (g) (white dashed lines are guides to the eye). The features with the highest PL intensitiesare the intralayer neutral exciton (X0) and the trion (X−) emission of MoSe2. For STA device #1, the interlayer exciton (IX) emission consists ofseveral 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 inSTA 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-valleysdecreasing phonon-assisted scattering between the valleys (see schematic in the inset of e). This assumption is consistent to the TRKR datashown in (e, h). For STA device #1, we observe surprisingly short lifetimes of around 200 ps and extremely small amplitudes. Instead, Kerrrotation lifetimes and amplitudes of STA device #2 are one order of magnitude larger. All measurements were conducted at 10 K, pump andprobe energies are the trion energies of the specified TMD unless stated otherwise.F. Volmer et al.2npj 2D Materials and Applications (2023)    58 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;In this device, the interlayer exciton emission consists of severalsub-peaks (see fits in the inset of Fig. 1d) which exact origins arestill a debated topic45. Some studies argue that these sub-featurescan be related to transitions involving Q- and Γ-val-leys12,18,19,44,46,47. If this is the case, the appearance of thesesub-features would imply a strong hybridization between the twoTMD layers. To address this, we refer to band structure calculationsthat predict that the bands at the K-point of the heterobilayer onlyshow negligible signs of hybridization, i.e., that the conductionband minimum at the K-point of the heterobilayer mainly consistsof MoSe2 states, whereas the valence band maximum at theK-point mainly consists of WSe2 states, leading to a type-II bandalignment44,46–48 (see Fig. 1c for the calculated band structure incase of the RhX-stacking). On the other hand, the bands at boththe Q- and Γ-valleys are strongly hybridized and, depending onparameters like stacking order and twist angle, may shift in energytowards the band maxima at the K-point (see Supplementary Note4 for more calculations). Interestingly, different studies signifi-cantly differ in the prediction of these energy shifts. Some of themclaim a transition to an indirect semiconductor as either theQ-valley shifts below the K-point’s conduction band minimum, orthe Γ-valley shifts above the K-point’s valence band max-imum44,46–49. As we observe the sub-features in the interlayerexciton emission, we assume that both the Q- and Γ-valleys areenergetically close enough to the K-valleys that phonon-assistedscattering can take place between these valleys (see schematic inthe inset of Fig. 1e).This finding is important for the interpretation of the TRKR datashown in Fig. 1e, where we plot the Kerr rotation amplitude ΘKerrvs the time delay between pump (circularly polarized) and probe(linearly polarized) pulses. Regardless where we set the pump andprobe energies or which gate voltage we apply, we observesurprisingly short lifetimes of around 200 ps and small amplitudesof ΘKerr < 40 μrad. The only Kerr rotation signal with a goodenough signal-to-noise ratio to be analyzed was obtained bytuning the pump and probe energies to the trion energies of WSe2and MoSe2 (see Fig. 1e). Instead, no signal was detected at theinterlayer exciton energies (not shown). This is highly surprising intwo ways: On the one hand, these values fall significantly shortcompared to lifetimes of up to nanoseconds and amplitudes of upto several hundreds of μrad that are typically observed in TRKRmeasurements on monolayer TMDs25–34,36. On the other hand,and even more surprising, is the fact that the lowest valleylifetimes of interlayer excitons measured by time- and helicity-resolved PL measurements in WSe2/MoSe2-heterobilayers are alsoin the nanosecond range10–14. Although we observe interlayerexcitons in PL (see Fig. 1b), we conclude that TRKR is in alllikelihood unable to directly detect the interlayer exciton valleypolarization (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 carriersrelaxes quite fast in this heterobilayer. We attribute this to theaforementioned presence of the Γ- and Q-valleys, which provideadditional scattering channels for a valley polarization as soon asthese valleys are energetically in the phonon-assisted scatteringrange (see inset in Fig. 1e). This indicates the importance of thesevalleys in the understanding of the overall spin and valleydynamics of free charge carriers in heterobilayers that have STAsnear to a crystallographic stacking order, which is in accordancewith previous theoretical and experimental studies based onoptical measurement techniques other than TRKR4,40.To support this notion, we studied another WSe2/MoSe2heterobilayer (STA device #2) with a twist angle of 56 ± 3°, whichis a STA of 4 ± 3° to an H-type stacking order. This device alsoshows 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 mayimply that the Q- and Γ-valleys are energetically further separatedfrom the K-valleys and therefore no longer play a key role in theinterlayer exciton emission. The less pronounced hybridizationcompared to STA device #1 might be due to the different stackingorder (see also our calculations in Supplementary Note 4), anincreased separation between the layers, or strain50,51. If weassume a larger energy separation between the K-valleys and theQ- or Γ-valleys, we expect a less pronounced scattering ratebetween these valleys. This is in complete accordance to theresults of the TRKR measurements on this device, which yield Kerrrotation lifetimes and amplitudes which are one order ofmagnitude larger than the ones of STA device #1 (compare Fig.1e, h). Setting the energies of the pump and probe laser pulses tothe trion energies of the respective TMD layers, we now observe afast decaying Kerr rotation signal of several hundreds ofpicoseconds and a second smaller signal with a decay in thenanosecond range. Interestingly, we even observe a small Kerrrotation signal when the probe pulse is set to the interlayerexciton energy (see the inset of Fig. 1h). However, it must be thetopic of further studies to clarify, if this signal really originates fromthe interlayer exciton or is rather caused by a low-energy tail of abright, intralayer exciton resonance (see, e.g., the discussions toFig. 2b, c later on).Heterobilayers with large twist anglesAn even smaller impact of the Q- and Γ-valleys due to a largerenergy separation to the K-valleys is expected for twist angles thatare far away from a crystallographic stacking order (seecalculations in Supplementary Note 4). Therefore, we now focuson 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 asignificantly different coupling between the two TMD layers. Thisis evident not only in the absence of an interlayer excitonemission18, but also in the appearance of the intralayer exciton(X0) and trion peaks (X− and X 0�) of WSe252–54, which werecompletely quenched in the previous two devices (compare Fig.2a to Fig. 1b, g). It is important to note that many studies aboutWSe2/MoSe2-heterobilayers that are showing interlayer excitonemission show a much stronger quenching of WSe2 intralayerexcitons compared to the quenching of MoSe2 intralayerexcitons7,11,13,17,23,47. This implies the existence of fast,hybridization-induced scattering channels for photo-excitedelectron-hole pairs away from the K-valleys of WSe2 in hetero-bilayers with STA (see Supplementary Note 4 for a more detaileddiscussion). Conversely, the appearance of the WSe2 intralayeremission in LTA device #1 implies the suppression of thesescattering channels for larger twist angles and therefore asignificant decrease in the coupling strength between the TMDlayers.The conclusion of a decreased coupling is further supported bythe TRKR measurements on LTA device #1 (Fig. 2b) that exhibitlifetimes and amplitudes that are much higher than those of theSTA devices (compare Fig. 2b to Fig. 1e, h). In fact, amplitudes ofhundreds of μrad and lifetimes in the nanosecond range arereminiscent to values measured on monolayer TMDs25–34,36. Theenergy scan in Fig. 2c, in which the pump pulse energy was fixedat the trion energy of WSe2 and the probe pulse was tuned overthe whole energy range of the PL measurements, only showsresonances at the bright intralayer exciton and trion energies. Asmall Kerr rotation signal at the interlayer exciton energy(between 1.3 and 1.4 eV in case of the STA devices), which isscaled-up by a factor of 100 in Fig. 2b for better visibility, is onlydue to the long tail of the bright exciton resonances in Fig. 2c.Interestingly, two distinctly different TRKR signals can berevealed in the heterobilayer by tuning the Fermi level via a gatevoltage and by varying the energies of both pump and probepulses (see Fig. 2d–f for the respective amplitudes ΘKerr of theTRKR signals and the Supporting Information of ref. 36 for the usedF. Volmer et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    58 fitting procedure). The occurrence of these two signals dependson whether the Fermi level is tuned either in the band gap of theprobed TMD layer (reddish colors in Fig. 2d–f) or in the valence orconduction band (blueish colors). For example, if we set theenergies of both the pump and probe pulses to the trion energyof WSe2 (Fig. 2d), a Kerr rotation signal with a lifetime between 4and 10 ns (Fig. 2g) appears as soon as the trion emission of WSe2in Fig. 2a vanishes for gate voltages smaller than 0 V, i.e., as soonas we leave the conduction band and enter the band gap of WSe2.If the probe pulse energy is instead tuned to the trion energy ofMoSe2 (see Fig. 2e, f, where we used different pump energies), aTRKR signal with similarly long lifetimes appears in the gatevoltage range that also shows the appearance of the neutralexciton (X0) emission of MoSe2 in Fig. 2a, which in turn marks thegate range of the band gap in MoSe2. Similar long-lived stateswithin the gate voltage range, in which emission of neutralexcitons predominates, have been reported previously in bothWSe2/MoSe2 heterobilayers55 and WSe2 monolayer devices36,56.The corresponding amplitude of this long-lived signal ismaximal within the band gap region and falls as soon as theFermi level enters either the conduction band (VB) or valenceband (VB) of MoSe2, where the band edges are determined by thecb0|ΘKerr| (μrad)1000500pump WSe2probe WSe2probe at 1.38 eV(x100) probe MoSe20 4 12delay (ns)8a86420-2-4-61.71.61.51.41.3energy (eV)MoSe2 X0MoSe2 X -MoSe2 X+WSe2 X -PL intensity (arb. units)WSe2 X0no IXVgate (V)WSe2 X -́probe energy (eV)0ΘKerr (μrad)pump WSe21.4 1.5 1.6 1.7750500250-250g h id e f630-3-6Vgate (V) Vgate (V) Vgate (V)630-3-6 630-3-60306090120ΘKerr (μrad)0306090120ΘKerr (μrad)050100150200ΘKerr (μrad)pump WSe2probe WSe2pump WSe2probe MoSe2VBbandgap bandgapCBVB CBVB CBVB CBpump MoSe2probe MoSe2pump WSe2probe WSe2pump WSe2probe MoSe2pump MoSe2probe MoSe2630-3-6Vgate (V) Vgate (V) Vgate (V)630-3-6 630-3-60.00.51.01.52.02.5039612lifetime (ns)lifetime (ns)0.00.51.01.52.02.5lifetime (ns)6-8 ns6-8 nsFig. 2 Photoluminescence and time-resolved Kerr rotation measurements on a WSe2/MoSe2 heterobilayer with a large twist angle of23 ± 3° (LTA device #1). 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 0�) 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 #1implies the suppression of these scattering channels, resulting in TRKR lifetimes and amplitudes that are much larger than the ones of theprevious 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, onlyshows resonances at the bright intralayer exciton and trion energies. A Kerr rotation signal at the interlayer exciton energy, which is scaled-upby 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 amplitudesand (g–i) lifetimes for different combinations of pump and probe energies, which reveal two different types of signals. The first signal (reddishcolors) 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. Thesecond 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 inthe text). All measurements were conducted at 10 K, pump and probe energies are the trion energies of the specified TMD unless statedotherwise.F. Volmer et al.4npj 2D Materials and Applications (2023)    58 Published in partnership with FCT NOVA with the support of E-MRSappearance of the negatively or positively charged trion emissionin Fig. 2a, respectively. Small shifts in the gate-dependentpositions of the features in Fig. 2a compared to Fig. 2d–f areexpected due to photo-induced gate screening effects thatdepend on both the energy and intensity of the used lasersystems, which are different for TRKR and PL measurements (seeref. 57 and the Supporting Information of ref. 36). As we discussfurther below in more detail, the band gap related TRKR signalresults from defect-bound exciton states within the band gap.Accordingly, the corresponding TRKR signal has a lifetime similarto the recombination time of these bound exciton states, whichspans the nanosecond to microsecond range at cryogenictemperatures58–60.A distinctly different TRKR signal in the WSe2/MoSe2 hetero-bilayer appears when the Fermi level gets tuned into either thevalence or the conduction band of MoSe2 and when the probeenergy is tuned to MoSe2 (see blueish colors in Fig. 2e, f). Theinitial increase of the Kerr rotation amplitude indicates that thissignal is linked to a valley-polarization of free charge carriers.Interestingly, such a gate-dependent TRKR signal is completelymissing if both the pump and probe energies are set to the WSe2energy (Fig. 2d). Remarkably, this result is exactly opposite to whatwas found in the respective monolayer cases, as some of usdemonstrated in ref. 36. There, a valley polarization of free chargecarriers could only be achieved in WSe2, where the polarizationmechanism was explained by an intervalley scattering channel viadark trion states, which are not available in MoSe2 monolayers52.Comparing Fig. 2d, e instead reveals the existence of a mechanismthat transfers the valley polarization from excitons in WSe2 to freecharge carriers in MoSe2 via an interlayer charge transfer.Deviation from the expected type-II band alignmentTo explain this intriguing charge transfer process, we first discussthe PL data in Fig. 2a in more detail to determine the bandstructure of LTA device #1 and the gate-dependent position of theFermi level. There is a striking gate-tunability of the WSe2 trionemission, which shows a pronounced red-shift and a transitionfrom the X− to the X 0� trions, which is normally seen in monolayersof WSe261,62, but to our knowledge has not yet been reported insuch clarity in WSe2/MoSe2-heterobilayers. The exact origin of theX 0�-feature is still under debate: Whereas in earlier publications itwas attributed to the filling of the energetically higher, spin-splitconduction band of WSe2, more recent publications explain thisfeature with a coupling between plasmons and excitons or thecreation of many-body exciton states63–66. Whatever its exactorigin is, the appearance of this feature is only expected if theconduction band of WSe2 at the K-point gets filled with electrons.However, this is unexpected in case of a type-II WSe2 to MoSe2band alignment with well-separated conduction band minima ofWSe2 and MoSe2 (see Fig. 1c)44,46–48,67. It was proposed that largedisplacement fields or high gate-induced charge carrier densitiescan reduce the energy separation between the conduction bandminima of WSe2 and MoSe2 at the K-point, which eventually mayeven lead to a transition from a type-II to a type-I bandalignment9,68,69. However, this explanation cannot be applied toLTA device #1 as the trion emission of both MoSe2 and WSe2 inFig. 2a appear almost simultaneously at gate voltages that areonly slightly larger than 0 V. Hence, it seems that the conductionband minima of MoSe2 and WSe2 are aligned close to each other,which allows the Fermi level EF to almost simultaneously enterboth conduction bands (see schematics in Fig. 3a, d, the blue linesin the figures represent spin-up and red lines represent spin-downbands, slightly opaque rectangles represent the filling of therespective bands with charge carriers). We propose that thisunexpected band alignment might be caused by a combination ofthe LTA together with a slight n-doping of both the WSe2 andMoSe2 (note that in all PL maps, i.e., Figs. 1b, g, 2a, and 4a, thestrongest emission of the neutral exciton is observed at gatevoltages Vgate < 0 V, especially in Figs. 1g and 4a it is clear that thenegatively charged trion emission prevails over the neutral excitonemission at Vgate= 0 V). The donor states may originate eitherfrom chalcogenide vacancies or substitutional dopants70,71. Beforestacking the TMD layers into a heterostructure, the respectiveFermi level in each TMD layer is therefore not in the middle of theband gap, but somewhere between the donor states and theconduction band minimum. Similar to conventional bulk semi-conductors, we expect that the band alignment in the TMDheterostructure will be determined in first order approximation(i.e., ignoring any charge transfer processes) by the alignment ofthese two Fermi levels. Assuming similar donor binding energies(black solid lines below the conduction bands in Fig. 3a, drepresent donor states) we therefore conclude that the conduc-tion band minima of both TMD layers must be close to each other.For the given band alignment we expect that for negative gatevoltages 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 becaused by photo-exited or gate-induced charge carriers9,72,73, thevalence band maximum of WSe2 in Fig. 3d cannot be reachedwithin a technically achievable gate voltage range. This is indeedin accordance to the PL data of Fig. 2a that shows the appearanceof the positively charged trion (X+) of MoSe2 for Vgate <− 1 V, butno clear tuning into the positively charged trion regime of WSe2(note that we have chosen a logarithmic color scale for all PLmaps, the very small emission in the trion energy range of WSe2for Vgate < 0 V can be readily attributed to strain-induced bandfluctuations at bubbles in the heterostructure74,75).Whereas the PL measurements in Fig. 2a provide informationabout the respective band alignment at the K-valleys, we employARPES measurements to get further information about the relativeposition of the Γ-valley with respect to the K-valleys. Dependingon stacking order, interlayer distance, or twist angle, theoreticalstudies come to different conclusions about whether the valenceband maximum lies either at the Γ- or the K-valley44,46–49.Interestingly, even experimental ARPES studies come to differentconclusions: Whereas one of the first reported measurementsclaims that the Γ-valley lies below the K-valley76, a more recentmeasurement claims the opposite77. As we cannot conduct ARPESmeasurements on the devices with a top hexagonal boron nitride(hBN) layer (see Fig. 1a), we fabricated another heterobilayer (LTAdevice #2) with a twist angle comparable to LTA device #1. Weused the same crystals and fabrication methods that were used forthe other devices and placed a MoSe2/WSe2/graphite-stackdirectly onto an n-doped silicon wafer (i.e., with MoSe2 on top,which therefore contributes most to the surface-sensitive ARPESmeasurements).The ARPES measurements are shown in Fig. 3b, e for both s-and p-polarized light with a photon energy of 50 eV. The answerto the question in which valley the valence band maximum lies ismade more difficult by the fact that the signal strength of anindividual 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). Onlyconsidering linecuts that are normalized and averaged over asmall wave-vector range at the K-, K’-, and Γ-points of the ARPESmeasurements with p-polarized light therefore may lead to theerroneous conclusion that the Γ-valley is slightly higher in energythan the K-valleys (see Fig. 3c). Instead, considering both the s-and p-polarized measurements and comparing linecuts that showthe highest intensity for each individual valley demonstrates thatthe valence band maximum is rather located at the K-valleys (seeFig. 3f). However, Γ- and K-valleys are energetically close enoughto each other that phonon-mediated scattering between thesevalleys is most likely more relevant than it already is in case ofmonolayer TMDs27,40,78–82.F. Volmer et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    58 Based on these ARPES results, we assume that in the other LTAdevices the Γ-valley is also energetically lower than the K-valleys ofMoSe2, however energetically close enough such that the Γ-valleylies in between the K-valleys of WSe2 and MoSe2 (see schematic inFig. 3g). It is also important that our DFT calculations show that theΓ-valley is spin-degenerate, whereas the Q-valley is showing asmall spin-splitting (see Fig. 1c and Supplementary Note 4), whichis consistent to previous studies44,46,47,83.Model of the interlayer transfer mechanismWith this knowledge, we now provide a model that explains theobserved dependence of the valley polarization (Kerr rotationamplitude) in Fig. 2d–f on both the pump/probe energy and thegate. Figure 3g–j show the underlying dynamics for the case thatthe energy of the pump laser is set to WSe2 and the Fermi levelenters the valence band of MoSe2, i.e., −6 V < Vgate <−1 V in Fig. 2.Under such conditions, the right circularly polarized pump pulsewill excite charge carriers from the upmost valence band of WSe2to its upper spin-split conduction band (see transition fromFig. 3g–h)52. It is likely that the predominant energy relaxationpath for the photo-excited electrons involves an interlayer transferfrom the upper spin-split conduction band of WSe2 to the lowerspin-split conduction band of MoSe2, with the same spin-orientation and the same K-valley (see upper black dashed linein Fig. 3h). In contrast, the photo-excited holes can experiencespin scattering caused by the spin-degenerate Γ-valley (seetransition from Fig. 3h–i) leading to a population of the K’-valley’svalence band with photo-exited holes.The different interlayer spin/valley-scattering paths and rates ofthe photo-excited electrons and holes lead to a situation whereeventually more photo-exited electrons than photo-excited holesare in the K-valley of MoSe2, whereas the situation is reversed inthe K’-valley (see Fig. 3i). During exciton recombination (seetransition from Fig. 3i–j), photo-excited electrons also recombinewith free holes in the K-valley, pushing the charge carrier densitybelow the Fermi level (continuous dashed black line through Fig.3g–j). As there are more photo-excited holes than electrons in the01LTA device #2 (24±3°) 234E F - E (eV)K K'Γ01LTA device #2 (24±3°) 234E F - E (eV)K K'Γbep-polarizations-polarizationWSe2 MoSe2EFn-dopingK K' K K'ap-dopingp-dopingEEFEnormalized counts K , p-pol.Γ, p-pol.K', p-pol.LTA device #2 (24±3°) EF - E (eV)0 1 2 3 4chighlowcounts highlowcounts WSe2 MoSe2K K' K K'dnormalized counts K , s-pol.Γ, p-pol.K', s-pol.LTA device #2 (24±3°) EF - E (eV)0 1 2 3 4fWSe 2 MoSe2Kσ+QK' K K'ΓWSe2 MoSe2QK K' K K'ΓWSe2 MoSe2QK K' K K'ΓWSe2 MoSe2VBvalleyboundrecQK K' K K'Γτ τgE Fh i jEFig. 3 Band structure at the K-, Q- and Γ-valleys for LTA devices and the resulting transfer mechanism of a valley polarization fromexcitons to free charge carriers. a, d Band structure of LTA device #1 at the K-points derived from the gate-dependence of the bright excitonemission in Fig. 2a. Blue and red colors represent spin-up and spin-down states, respectively. Sightly opaque rectangles represent the filling ofthe bands with charge carriers. a The fact that the negatively charged trion features of WSe2 and MoSe2 appear almost at the same gatevoltage in Fig. 2a hints to an alignment of the respective conduction band minima to each other. This deviation from the expected type-IIband alignment may be caused by a combination of the large twist angle together with a slight n-doping of both TMD layers (black solid linesbelow the conduction bands in (a, d) represent donor states). d For negative gate voltages, the smaller band gap of MoSe2 prevents the Fermilevel to enter the valence band of WSe2 within the applicable gate voltage range, explaining the absence of the positively charged trionemission of WSe2. b, e ARPES measurements of LTA device #2 for both s- and p-polarized light and (c, f) linecuts that are normalized andaveraged 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 theK-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 gatedependence of the Kerr data in Fig. 2. See text for a detailed explanation.F. Volmer et al.6npj 2D Materials and Applications (2023)    58 Published in partnership with FCT NOVA with the support of E-MRSK’-valley, it now shows a surplus of holes after the recombinationprocess. Overall, this mechanism transfers the valley polarizationfrom excitons to free charge carriers by a valley selective interlayercharge transfer. The resulting valley polarization then relaxes backinto the equilibrium state with the genuine valley lifetime τVBvalley(see Fig. 3j).The same interlayer transfer mechanism can be readily appliedto the case in which the Fermi level is tuned into the conductionband of MoSe2, resulting in a net valley polarization of free chargecarriers in the conduction band. As the Q-valley plays a lesssignificant role in the scattering process than the Γ-valley, weexpect, however, that the respective valley lifetimes in theconduction band are longer than the ones in the valence band,which is indeed observed in our data (see Fig. 2h, i). Our modelcan also explain the great similarity between Fig. 2e, h on the onehand and Fig. 2f, i on the other hand, i.e., between setting thepump energy either to WSe2 or MoSe2. Creating electron-holepairs directly in the K-valley of MoSe2 would lead to the exactsame condition that is depicted in Fig. 3i, if we assume that thephoto-excited holes will be subjected to scattering via the Γ-valley.Despite the energy separation of the Γ-valley from the K-valleys ofMoSe2, this scattering is very likely to occur during the shorttimescale of the pump pulse because of photo-induced band gaprenormalization effects and the amount of available phonons thatare created by the scattering of photo-excited charge carriers intolower-energy states72,73,84,85.Finally, the long-lived Kerr rotation signal that is present whenthe Fermi level lies within the band gap of one of the two TMDlayers (reddish data points in Fig. 2d–f) can be explained by themechanism that was discussed in ref. 36 and can be easilyincorporated into our current model: A part of the photo-excitedelectron-hole pairs scatter into defect-bound exciton states (seeFig. 3h), which can have quite long recombination times τboundrecfrom the nanosecond up to the microsecond range58–60 and alsomay create a valley polarization of resident charge carriers duringtheir recombination process (Fig. 3j). As this polarization process isdirectly connected to the lifetime of the bound excitons, i.e., thepolarization occurs during the full exciton recombination time, itdoes not allow the direct probing of the respective valley lifetimes(see rate equation model in the Supplemental Material of ref. 36 fora more detailed discussion).We note that we simplified our model in Fig. 3g–j in the sensethat we did only consider the most important scattering andrecombination channels. However, the consideration of, e.g.,additional spin-flip scattering processes or non-radiative recombi-nation processes does not change the overall result, as long as thephoto-excited electrons and holes undergo differently strongvalley scattering processes. Here a simplified explanation for thisnecessary condition: If the photo-excited holes recombine withthe photo-excited electrons in the same valley (either the valley inwhich they were created or in which both were scattered into) thesystem will end up in its initial state, which means that no netvalley polarization of free charge carriers can be induced. Instead,with different scattering rates for electrons and holes, there will bean imbalance of photo-excited charge carriers in the conductionand valence bands of a specific valley and, therefore, theirrecombination necessitates the involvement of resident (free)charge carriers, which get polarized during the recombinationprocess.Counter-play of two different scattering channelsFinally, we explore another device with large twist angle (LTAdevice #3), which additionally allows for charge transport840-41.701.751.651.551.601.50energy (eV)PL intensity (arb. units)MoSe2 X-MoSe2 X0WSe2 X0WSe2 X -608040200current (nA)abWSe2 X-́Vgate (V)Vgate (V)ΘKerr (μrad)ΘKerr (μrad)05101520lifetime (ns)0100200300050100150200051015lifetime (ns)pump WSe2probe WSe2pump WSe2probe WSe2cd e-4 -2 0 2 4 6 8Vgate (V)-4 -2 0 2 4 6 8Vgate (V)-4 -2 0 2 4 6 8Vgate (V)-4 -2 0 2 4 6 8pump WSe2probe MoSe2pump MoSe2probe MoSe2pump WSe2probe MoSe2pump MoSe2probe MoSe2Fig. 4 Photoluminescence and time-resolved Kerr rotation measurements on a third WSe2/MoSe2 heterobilayer with large twist angle(LTA device #3). a The gate-dependent PL map of LTA device #3 that is plotted on a logarithmic color scale is also showing intralayer excitonemission of WSe2, comparable to LTA device #1 in Fig. 2a. Because LTA device #3 was built with several graphite contacts, electrical transportmeasurements could be conducted on this device. The white line depicts the current at a bias voltage of 2 V. b The bound-exciton related Kerrrotation signal has the highest amplitude at the gate voltage range at which the neutral exciton emission in (a) indicates the position of theband 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 torise 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.F. Volmer et al.7Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    58 measurements as it was built with multiple graphite contacts. Thegate-dependent PL map of this device (Fig. 4a) is quitecomparable to the one of LTA device #1 in Fig. 2a, especiallywith respect to the appearance of the exciton emission of WSe2.When tuning both pump and probe energies to WSe2 we againobserve the long-lived Kerr rotation signal (Fig. 4b, d) that isrelated to the bound exciton states and that has its largestamplitude at the gate voltage range where the neutral exciton ofWSe2 is most pronounced in Fig. 4a.The white solid line in Fig. 4a depicts the source-drain currentmeasured at a bias voltage of 2 V and shows that the current startsto rise at a gate voltage of around Vgate= 0 V. It is exactly at thisgate voltage at which the TRKR signal that can be attributed to thevalley polarization of free charge carriers appears when the probeenergy is tuned to MoSe2 (see Fig. 4c). Its amplitude first increasesalmost linearly with the gate voltage (the more free charge carriersare induced by the gate, the more can be polarized), before iteventually decreases again for larger gate voltages, i.e., largerelectron densities, which is in complete accordance to LTA device#1. The respective valley lifetimes are shown in Fig. 4e, whereasFig. 4d shows the lifetime of the bound-exciton driven signal. As itwas the case for LTA device #1 (see Fig. 2h, i), the valley lifetime ofthe free charge carriers (Fig. 4e) first increases for small carrierdensities, then exhibit a maximum at intermediate densities,before it eventually decreases towards higher densities. Weattribute this overall trend to an interplay of two differentscattering channels that have opposite dependencies with respectto the Fermi level. Pushing the Fermi level further into theconduction 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 getstronger36,81,86,87.We note that when probing at the MoSe2 energy, LTA device #3does not exhibit any long-lived, bound-exciton related Kerrrotation signal when the Fermi level is tuned into the band gap.This indicates a low defect density in the MoSe2 layer. At the sametime, we observe much longer valley lifetimes of free chargecarriers 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 chargecarrier densities.DISCUSSIONIn summary, we have demonstrated that the twist angle has asignificant impact on the dynamics of valley-polarized free chargecarriers in WSe2/MoSe2 heterobilayers. For small twist angles neara crystallographic stacking order (an R-type stacking order for atwist angle of zero, an H-type stacking order for a twist angle of60∘), scattering via Q- and Γ-valleys highly diminishes the valleypolarization of free charge carriers, despite the simultaneousoccurrence of interlayer excitons with their presumably longrecombination and polarization times. For twist angles that liebetween these stacking orders, we observe a substantial increasein 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 devicesenable us to disentangle two different Kerr signals, one that isrelated to defect-bound states within the band gap region, andone that represents the actual valley-polarization of free chargecarriers within either valence or conduction band. Interestingly, forthese devices we also observe a deviation from the widelyassumed type-II band alignment that we contribute to analignment of the respective conduction bands by donor states.This observation could open the possibility of tailoring the bandalignment in these heterobilayer devices, and thus the valley andspin dynamics, by using differently doped TMD layers. Mostimportantly, the unexpected band structure alignment in thesedevices enables an interlayer transfer of photo-induced, valley-polarized excitons from the WSe2 layer into a pronounced valleypolarization of free charge carriers in the MoSe2 layer. This transferis most efficient at the onsets of either valence or conductionband, demonstrating the possibility of extracting and utilizing thisvalley polarization by electrical means.METHODSDevice fabricationThe WSe2/MoSe2-heterobilayer devices are fabricated fromexfoliated flakes with a dry-transfer method, protected by hBNfrom both sides and contacted via graphite electrodes (seeschematic in Fig. 1a; detailed information about device fabricationcan be found in refs. 36,88). For STA device #1 and LTA devices #1and #3 we furthermore incorporated a graphite gate, whereas forSTA device #2 we use the Si++/SiO2 (285 nm) wafer for gating. Anexception from this general fabrication procedure is LTA device #2that is used for the ARPES measurements and therefore cannot beprotected by hBN. For this device we directly placed a MoSe2/WSe2/graphite-stack onto an n-doped silicon wafer.MeasurementsDetailed technical information about the TRKR and PL measure-ment techniques and the used fitting procedures can be found inthe Supporting Information sections of refs. 27,34,36. We note that itis important to account for photo-induced screening effects of thegate electric field57 to unveil the true lifetimes and amplitudes ofthe Kerr signal that can be attributed to free charge carriers. In theSupporting Information of ref. 36 we show how the standardoptical measurement techniques can be modified to account forthe photo-induced gate screening and we demonstrate thatdisregarding this procedure can lead to erroneous conclusionsdrawn from gate-dependent measurements.Time-resolved Kerr rotationTwo mode-locked Ti:sapphire lasers are used to independentlytune the energies of both pump and probe pulses. An electronicdelay between both pulses covers the full laser repetition intervalof 12.5 ns. The pulse widths are on the order of 3 ps. The laserbeams are focused onto the device by a 15mm focal lengthaspheric lens (numerical aperture of 0.66 NA). Typical spotdiameters are 6−8 μm measured as a full width at half maximum(FWHM) value. The laser power was around 500 μW for both pumpand probe beams.PhotoluminescenceA microscope objective lens (numerical aperture of 0.5 NA) is usedfor the photoluminescence measurement. The resulting spot sizeis around 1–2 μm FWHM. A continuous wave laser with an energyof 2.33 eV and a power between 10 and 50 μW is used for thesemeasurements.Angle-resolved photoemission spectroscopyThe ARPES measurements have been performed at the NanoESCAbeamline of Elettra, the Italian synchrotron radiation facility, usinga FOCUS NanoESCA photoemission electron microscope (PEEM) inthe k-space mapping mode operation89. The PEEM is operating ata background pressure p < 5 × 10−11 mbar and the photoelectronsignal is collected from a spot size of about 5−10 μm. Before theexperiment the sample was outgassed in UHV at T= 180 °C for60min. The measurements were conducted with a photon energyof 50 eV and an overall energy resolution of 50 meV using p- ands-polarized synchrotron radiation, while keeping the sample at90 K.F. Volmer et al.8npj 2D Materials and Applications (2023)    58 Published in partnership with FCT NOVA with the support of E-MRSDATA AVAILABILITYAll data are available from the corresponding author on request.Received: 25 January 2023; Accepted: 10 August 2023;REFERENCES1. Ciarrocchi, A., Tagarelli, F., Avsar, A. & Kis, A. Excitonic devices with van der Waalsheterostructures: valleytronics meets twistronics. Nat. Rev. Mater. 7, 449–464 (2022).2. Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).3. Mueller, T. & Malic, E. Exciton physics and device application of two-dimensionaltransition metal dichalcogenide semiconductors. npj 2D Mater. Appl. 2, 29 (2018).4. Jiang, Y., Chen, S., Zheng, W., Zheng, B. & Pan, A. Interlayer exciton formation,relaxation, and transport in TMD van der Waals heterostructures. Light Sci. Appl.10, 72 (2021).5. Liu, Y. et al. Valleytronics in transition metal dichalcogenides materials. Nano Res.12, 2695–2711 (2019).6. Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomicallythin heterostructures. Science 366, 870–875 (2019).7. Ciarrocchi, A. et al. Polarization switching and electrical control of interlayerexcitons in two-dimensional van der Waals heterostructures. Nat. Photonics 13,131–136 (2019).8. Kiemle, J. et al. Control of the orbital character of indirect excitons in MoS2/WS2heterobilayers. Phys. Rev. B 101, 121404 (2020).9. Meng, Y. et al. Electrical switching between exciton dissociation to exciton fun-neling in MoSe2/WS2 heterostructure. Nat. Commun. 11, 2640 (2020).10. Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor het-erostructure. Science 351, 688–691 (2016).11. Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2-WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).12. Miller, B. et al. Long-lived direct and indirect interlayer Excitons in van der WaalsHeterostructures. Nano Lett. 17, 5229–5237 (2017).13. Jiang, C. et al. Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures. Nat. Commun. 9, 753 (2018).14. Nagler, P. et al. Giant magnetic splitting inducing near-unity valley polarization invan der Waals heterostructures. Nat. Commun. 8, 1551 (2017).15. Zimmermann, J. E. et al. Ultrafast charge-transfer dynamics in twisted MoS2/WSe2heterostructures. ACS Nano 15, 14725–14731 (2021).16. Yuan, L. et al. Twist-angle-dependent interlayer exciton diffusion in WS2-WSe2heterobilayers. Nat. Mater. 19, 617–623 (2020).17. Choi, J. et al. Twist angle-dependent interlayer Exciton lifetimes in van der WaalsHeterostructures. Phys. Rev. Lett. 126, 047401 (2021).18. Nayak, P. K. et al. Probing evolution of twist-angle-dependent interlayer Excitonsin MoSe2/WSe2 van der Waals Heterostructures. ACS Nano 11, 4041–4050 (2017).19. Sigl, L. et al. Signatures of a degenerate many-body state of interlayer excitons ina van der Waals heterostack. Phys. Rev. Res. 2, 042044 (2020).20. Li, W., Lu, X., Dubey, S., Devenica, L. & Srivastava, A. Dipolar interactions betweenlocalized interlayer excitons in van der Waals heterostructures. Nat. Mater. 19,624–629 (2020).21. Jin, C. et al. Identification of spin, valley and moiré quasi-angular momentum ofinterlayer excitons. Nat. Phys. 15, 1140–1144 (2019).22. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiréheterostructure. Nature 580, 472–477 (2020).23. Kremser, M. et al. Discrete interactions between a few interlayer excitons trappedat a MoSe2-WSe2 heterointerface. npj 2D Mater. Appl. 4, 8 (2020).24. Woźniak, T., Faria Junior, P. E., Seifert, G., Chaves, A. & Kunstmann, J. Exciton gfactors of van der Waals heterostructures from first-principles calculations. Phys.Rev. B 101, 235408 (2020).25. Kumar, A. et al. Spin/valley coupled dynamics of electrons and holes at the MoS2-MoSe2 interface. Nano Lett. 21, 7123–7130 (2021).26. Kravtsov, V. et al. Spin-valley dynamics in alloy-based transition metal dichalco-genide heterobilayers. 2D Mater. 8, 025011 (2021).27. Ersfeld, M. et al. Spin states protected from intrinsic electron-phonon couplingreaching 100 ns lifetime at room temperature in MoSe2. Nano Lett. 19, 4083–4090(2019).28. Song, X., Xie, S., Kang, K., Park, J. & Sih, V. Long-lived hole spin/valley polarizationprobed by Kerr Rotation in Monolayer WSe2. Nano Lett. 16, 5010–5014 (2016).29. Yang, L. et al. Long-lived nanosecond spin relaxation and spin coherence ofelectrons in monolayer MoS2 and WS2. Nat. Phys. 11, 830–834 (2015).30. Kempf, M., Schubert, A., Schwartz, R. & Korn, T. Two-color Kerr microscopy of two-dimensional materials with sub-picosecond time resolution. Rev. Sci. Instrum. 92,113904 (2021).31. McCormick, E. J. et al. Imaging spin dynamics in monolayer WS2 by time-resolvedKerr rotation microscopy. 2D Mater. 5, 011010 (2017).32. Zhu, C. R. et al. Exciton valley dynamics probed by Kerr rotation in WSe2monolayers. Phys. Rev. B 90, 161302 (2014).33. Plechinger, G. et al. Trion fine structure and coupled spin-valley dynamics inmonolayer tungsten disulfide. Nat. Commun. 7, 12715 (2016).34. Volmer, F. et al. Intervalley dark trion states with spin lifetimes of 150 ns in WSe2.Phys. Rev. B 95, 235408 (2017).35. Raiber, S. et al. Ultrafast pseudospin quantum beats in multilayer WSe2 andMoSe2. Nat. Commun. 13, 4997 (2022).36. Ersfeld, M. et al. Unveiling valley lifetimes of free charge carriers in monolayerWSe2. Nano Lett. 20, 3147–3154 (2020).37. Hsu, W. T. et al. Second harmonic generation from artificially stacked transitionmetal dichalcogenide twisted bilayers. ACS Nano 8, 2951–2958 (2014).38. Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and Moirépatterns in transition metal Dichalcogenide Heterostructures. ACS Nano 14,4550–4558 (2020).39. Faria Junior, P. E. & Fabian, J. Signatures of electric field and layer separationeffects on the spin-valley physics of MoSe2/WSe2 Heterobilayers: from energybands to dipolar Excitons. NanomaterIals 13, 1187 (2023).40. Jin, C. et al. Ultrafast dynamics in van der Waals heterostructures. Nat. Nano-technol. 13, 994–1003 (2018).41. Hong, X. et al. Ultrafast charge transfer in atomically thin MoS2/WS2 hetero-structures. Nat. Nanotechnol. 9, 682–686 (2014).42. Ji, Z. et al. Robust stacking-independent ultrafast charge transfer in MoS2/WS2bilayers. ACS Nano 11, 12020–12026 (2017).43. Ovesen, S. et al. Interlayer exciton dynamics in van der Waals heterostructures.Commun. Phys. 2, 23 (2019).44. Gillen, R. & Maultzsch, J. Interlayer excitons in MoSe2/WSe2 heterostructures fromfirst principles. Phys. Rev. B 97, 165306 (2018).45. Deilmann, T., Rohlfing, M. & Wurstbauer, U. Light-matter interaction in van derWaals hetero-structures. J. Phys. Condens. Matter 32, 333002 (2020).46. Okada, M. et al. Direct and indirect interlayer Excitons in a van der Waals het-erostructure of hBN/WS2/MoS2/hBN. ACS Nano 12, 2498–2505 (2018).47. Hanbicki, A. T. et al. Double indirect interlayer Exciton in a MoSe2/WSe2 van derWaals Heterostructure. ACS Nano 12, 4719–4726 (2018).48. Zheng, Q. et al. Phonon-coupled ultrafast interlayer charge oscillation at van derWaals heterostructure interfaces. Phys. Rev. B 97, 205417 (2018).49. Hagel, J., Brem, S., Linderälv, C., Erhart, P. & Malic, E. Exciton landscape in van derWaals heterostructures. Phys. Rev. Res. 3, 043217 (2021).50. Zollner, K., Faria Junior, P. E. & Fabian, J. Strain-tunable orbital, spin-orbit, andoptical properties of monolayer transition-metal dichalcogenides. Phys. Rev. B100, 195126 (2019).51. Kunstmann, J. et al. Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures. Nat. Phys. 14, 801–805(2018).52. Wang, G. et al. Colloquium: Excitons in atomically thin transition metal dichal-cogenides. Rev. Mod. Phys. 90, 021001 (2018).53. Ye, Z. et al. Efficient generation of neutral and charged biexcitons in encapsulatedWSe2 monolayers. Nat. Commun. 9, 3718 (2018).54. Borghardt, S. et al. Radially polarized light beams from spin-forbidden darkexcitons and trions in monolayer WSe2. Opt. Mater. Express 10, 1273–1285 (2020).55. Jin, C. et al. Imaging of pure spin-valley diffusion current in WS2-WSe2 hetero-structures. Science 360, 893–896 (2018).56. Li, J. et al. Valley relaxation of resident electrons and holes in a monolayersemiconductor: dependence on carrier density and the role of substrate-induceddisorder. Phys. Rev. Mater.5, 044001 (2021).57. Volmer, F. et al. How photoinduced gate screening and leakage currents dyna-mically change the fermi level in 2D mater. Phys. Status Solidi RRL 14, 2000298(2020).58. Goodman, A. J., Willard, A. P. & Tisdale, W. A. Exciton trapping is responsible forthe long apparent lifetime in acid-treated MoS2. Phys. Rev. B 96, 121404 (2017).59. Moody, G. et al. Microsecond valley lifetime of defect-bound Excitons in mono-layer WSe2. Phys. Rev. Lett. 121, 057403 (2018).60. Rivera, P. et al. Intrinsic donor-bound excitons in ultraclean monolayer semi-conductors. Nat. Commun. 12, 871 (2021).61. Jones, A. M. et al. Optical generation of excitonic valley coherence in monolayerWSe2. Nat. Nanotechnol. 8, 634–638 (2013).62. Wang, Z., Zhao, L., Mak, K. F. & Shan, J. Probing the spin-polarized electronic bandstructure in monolayer transition metal dichalcogenides by optical spectroscopy.Nano Lett. 17, 740–746 (2017).63. Wang, Z., Mak, K. F. & Shan, J. Strongly interaction-enhanced valley magneticresponse in monolayer WSe2. Phys. Rev. Lett. 120, 066402 (2018).64. Van Tuan, D., Scharf, B., Žutić, I. & Dery, H. Marrying Excitons and plasmons inmonolayer transition-metal dichalcogenides. Phys. Rev. X 7, 041040 (2017).F. Volmer et al.9Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    58 65. Van Tuan, D. et al. Probing many-body interactions in monolayer transition-metaldichalcogenides. Phys. Rev. B 99, 085301 (2019).66. Van Tuan, D., Shi, S.-F., Xu, X., Crooker, S. A. & Dery, H. Six-body and eight-bodyExciton states in monolayer WSe2. Phys. Rev. Lett. 129, 076801 (2022).67. Ponomarev, E., Ubrig, N., Gutiérrez-Lezama, I., Berger, H. & Morpurgo, A. F.Semiconducting van der Waals interfaces as artificial semiconductors. Nano Lett.18, 5146–5152 (2018).68. Zhang, F., Li, W. & Dai, X. Modulation of electronic structures of MoSe2/WSe2 vander Waals heterostructure by external electric field. Solid State Commun. 266,11–15 (2017).69. Huang, D. & Kaxiras, E. Electric field tuning of band offsets in transition metaldichalcogenides. Phys. Rev. B 94, 241303 (2016).70. Younas, R., Zhou, G. & Hinkle, C. L. A perspective on the doping of transition metaldichalcogenides for ultra-scaled transistors: challenges and opportunities. Appl.Phys. Lett. 122, 160504 (2023).71. Loh, L., Zhang, Z., Bosman, M. & Eda, G. Substitutional doping in 2D transitionmetal dichalcogenides. Nano Res. 14, 1668 (2021).72. Chernikov, A., Ruppert, C., Hill, H. M., Rigosi, A. F. & Heinz, T. F. Populationinversion and giant bandgap renormalization in atomically thin WS2 layers. Nat.Photonics 9, 466–470 (2015).73. Cunningham, P. D., Hanbicki, A. T., McCreary, K. M. & Jonker, B. T. PhotoinducedBandgap renormalization and Exciton binding energy reduction in WS2. ACSNano 11, 12601–12608 (2017).74. Shin, B. G. et al. Indirect Bandgap Puddles in Monolayer MoS2 by Substrate-Induced Local Strain. Adv. Mater. 28, 9378–9384 (2016).75. Peng, Z., Chen, X., Fan, Y., Srolovitz, D. J. & Lei, D. Strain engineering of 2Dsemiconductors and graphene: from strain fields to band-structure tuning andphotonic applications. Light Sci. Appl. 9, 190 (2020).76. Wilson, N. R. et al. Determination of band offsets, hybridization, and excitonbinding in 2D semiconductor heterostructures. Sci. Adv. 3, 1601832 (2017).77. Khalil, L. et al. Hybridization and localized flat band in the WSe2/MoSe2 hetero-bilayer. Nanotechnology 34, 045702 (2022).78. Christiansen, D. et al. Phonon sidebands in monolayer transition metal dichal-cogenides. Phys. Rev. Lett. 119, 187402 (2017).79. Raja, A. et al. Enhancement of Exciton-phonon scattering from monolayer tobilayer WS2. Nano Lett. 18, 6135–6143 (2018).80. Liu, F., Li, Q. & Zhu, X.-Y. Direct determination of momentum-resolved electrontransfer in the photoexcited van der Waals heterobilayer WS2/MoS2. Phys. Rev. B101, 201405 (2020).81. Molina-Sánchez, A., Sangalli, D., Wirtz, L. & Marini, A. Ab Initio calculations ofultrashort carrier dynamics in two-dimensional materials: valley depolarization insingle-layer WSe2. Nano Lett. 17, 4549 (2017).82. Wang, Z. et al. Phonon-mediated interlayer charge separation and recombinationin a MoSe2/WSe2 heterostructure. Nano Lett. 21, 2165–2173 (2021).83. Torun, E., Miranda, H. P. C., Molina-Sánchez, A. & Wirtz, L. Interlayer and intralayerexcitons in MoS2/WS2 and MoSe2/WSe2 heterobilayers. Phys. Rev. B 97, 245427(2018).84. Ruppert, C., Chernikov, A., Hill, H. M., Rigosi, A. F. & Heinz, T. F. The role ofelectronic and phononic excitation in the optical response of monolayer WS2after ultrafast excitation. Nano Lett. 17, 644–651 (2017).85. Katoch, J. et al. Giant spin-splitting and gap renormalization driven by trions insingle-layer WS2/h-BN heterostructures. Nat. Phys. 14, 355–359 (2018).86. Ochoa, H. & Roldán, R. Spin-orbit-mediated spin relaxation in monolayer MoS2.Phys. Rev. B 87, 245421 (2013).87. Gunst, T., Markussen, T., Stokbro, K. & Brandbyge, M. First-principles method forelectron-phonon coupling and electron mobility: applications to two-dimensional materials. Phys. Rev. B 93, 035414 (2016).88. Bisswanger, T. et al. CVD Bilayer Graphene Spin Valves with 26 μm Spin DiffusionLength at Room Temperature. Nano Lett. 22, 4949–4955 (2022).89. Schneider, C. M. et al. Expanding the view into complex material systems: frommicro-ARPES to nanoscale HAXPES. J. Electron Spectrosc. Relat. Phenom. 185,330–339 (2012).90. Albrecht, W., Moers, J. & Hermanns, B. HNF-Helmholtz Nano Facility. J. Large ScaleRes. Facil. 3, 112 (2017).ACKNOWLEDGEMENTSThe authors thank Riccardo Reho, Pedro Miguel MC de Melo, Zeila Zanolli, andMatthieu Verstraete for helpful discussions. This project has received funding fromthe European Union’s Horizon 2020 research and innovation program under grantagreement No 881603, by the Deutsche Forschungsgemeinschaft (DFG, GermanResearch Foundation) under Germany’s Excellence Strategy - Cluster of ExcellenceMatter and Light for Quantum Computing (ML4Q) EXC 2004/1 - 390534769, and bythe Helmholtz Nanoelectronic Facility (HNF) at the Forschungszentrum Jülich90.P.E.F.J. and J.F. acknowledge the financial support of the Deutsche Forschungsge-meinschaft (DFG, German Research Foundation) SFB 1277 (Project-ID 314695032,projects B07 and B11), SPP 2244 (Project No. 443416183), and of the European UnionHorizon 2020 Research and Innovation Program under Contract No. 881603(Graphene Flagship). L.W. acknowledges support by the Alexander von Humboldtfoundation. K.W. and T.T. acknowledge support from JSPS KAKENHI (Grant Numbers19H05790, 20H00354 and 21H05233).AUTHOR CONTRIBUTIONSB.B., C.S. and F.V. conceived and supervised the project. M.E. performed the TRKR, PL,and electrical measurements with the support of F.V., L.R. and S.D. M.E. and F.V.analyzed the data from the TRKR, PL, and electrical measurements. P.E.F.J. and J.F.performed the first-principles calculations. L.W. performed and analyzed the SHG.F.V., M.E. and B.B. derived the model of the interlayer transfer mechanism. L.R., S.D.and B.P. designed and fabricated the devices. B.P., L.P., I.C., V.F. and C.M.S. performed,analyzed, and supervised the ARPES measurements. K.W. and T.T. synthesized thehBN crystals. F.V. and B.B. wrote the paper with contributions from all authors.FUNDINGOpen Access funding enabled and organized by Projekt DEAL.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-023-00420-1.Correspondence and requests for materials should be addressed to Frank Volmer.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023F. Volmer et al.10npj 2D Materials and Applications (2023)    58 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-023-00420-1http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Twist angle dependent interlayer transfer of valley polarization from excitons to free charge carriers in WSe2/MoSe2 heterobilayers Introduction Results Heterobilayers with small twist angles Heterobilayers with large twist angles Deviation from the expected type-II band alignment Model of the interlayer transfer mechanism Counter-play of two different scattering channels Discussion Methods Device fabrication Measurements Time-resolved Kerr rotation Photoluminescence Angle-resolved photoemission spectroscopy DATA AVAILABILITY References Acknowledgements Author contributions Funding Competing interests ADDITIONAL INFORMATION