# Fileset

[Jasiński_2024_2D_Mater._11_025007.pdf](https://mdr.nims.go.jp/filesets/80a57aa7-a9c6-4b88-8ae7-633551c9a93c/download)

## Creator

Jakub Jasiński, Joshua J P Thompson, Swaroop Palai, Maciej Śmiertka, Mateusz Dyksik, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Michał Baranowski, Duncan K Maude, Alessandro Surrente, Ermin Malic, Paulina Płochocka

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Control of the valley polarization of monolayer WSe<sub>2</sub> by Dexter-like coupling](https://mdr.nims.go.jp/datasets/ffc6c123-22f8-4355-b705-44f52f87e60f)

## Fulltext

Control of the valley polarization of monolayer WSe2 by Dexter-like coupling2D MaterialsPAPER • OPEN ACCESSControl of the valley polarization of monolayerWSe2 by Dexter-like couplingTo cite this article: Jakub Jasiński et al 2024 2D Mater. 11 025007 View the article online for updates and enhancements.You may also likeAnalysis of the impact of motor vehicles onthe air quality on the example of LegionowSquare in WroclawM Skrtowicz and A Galas-Szpak-Experimental verification of the method forproducing a three-dimensional cross-pairsmetamaterial structure based on adielectric AlN cubeP E Kozio, P A Górski, A Byndas et al.-pH-dependent fluorescence of thiol-coatedCdSe/CdS quantum dots in an aqueousphaseAnna Lesiak, Mateusz Banski, KingaHalicka et al.-This content was downloaded from IP address 144.213.253.16 on 19/01/2024 at 00:08https://doi.org/10.1088/2053-1583/ad1ae8/article/10.1088/1757-899X/421/4/042072/article/10.1088/1757-899X/421/4/042072/article/10.1088/1757-899X/421/4/042072/article/10.1088/0022-3727/49/6/065104/article/10.1088/0022-3727/49/6/065104/article/10.1088/0022-3727/49/6/065104/article/10.1088/0022-3727/49/6/065104/article/10.1088/1361-6528/abc4a0/article/10.1088/1361-6528/abc4a0/article/10.1088/1361-6528/abc4a02D Mater. 11 (2024) 025007 https://doi.org/10.1088/2053-1583/ad1ae8OPEN ACCESSRECEIVED29 August 2023REVISED7 December 2023ACCEPTED FOR PUBLICATION3 January 2024PUBLISHED17 January 2024Original Content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERControl of the valley polarization of monolayer WSe2 by Dexter-likecouplingJakub Jasiński1,2, Joshua J P Thompson3, Swaroop Palai2, Maciej Śmiertka1, Mateusz Dyksik1,Takashi Taniguchi4, Kenji Watanabe5, Michał Baranowski1, Duncan KMaude2, Alessandro Surrente1,Ermin Malic3 and Paulina Płochocka1,2,∗1 Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology,50-370 Wroclaw, Poland2 Laboratoire National des Champs Magnétiques Intenses, EMFL, CNRS UPR 3228, Université Grenoble Alpes, Université Toulouse,Université Toulouse 3, INSA-T, Grenoble and Toulouse, France3 Department of Physics, Philipps-Universität Marburg, Renthof 7 35032 Marburg, Germany4 International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan5 Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan∗ Author to whom any correspondence should be addressed.E-mail: paulina.plochocka@lncmi.cnrs.frKeywords: transition metal dichalcogenides, excitons, Dexter coupling, valleytronics, valley polarizationSupplementary material for this article is available onlineAbstractIntervalley scattering mechanisms strongly affect the dynamics of excitonic complexes in transitionmetal dichalcogenide monolayers. Here, we investigate the excitation energy dependence of thevalley polarization of excitons in a WSe2 monolayer. We observe that the valley polarizationdrastically decreases when the excitation is resonant with the B1s resonance. This behavior can beexplained by a Dexter-like coupling in the momentum space between exciton states residing inopposite valleys but with the same spin configuration. This induces a net transfer of the excitonpopulation from the optically driven valley towards the opposite, undriven valley. We observe thelong-term fingerprints of this population transfer as a vanishing valley polarization for the neutralexciton, and a negative valley polarization for biexcitonic complexes, in qualitative agreement withtheoretical predictions based on a fully microscopic many-particle approach. This, together with adecrease of the PL energy when the excitation is resonant with the B1s state, points to the prominentrole of the Dexter-like coupling in the exciton dynamics of atomically thin semiconductors.The spin-valley locking, characteristic of transitionmetal dichalcogenide (TMD) monolayers, [1–6]endows them with a binary degree of freedom,referred to as valley pseudospin. This can be ini-tialized and read out using circularly polarized light,which addresses separately the K+ and K− valleys,thus creating an imbalance in the exciton popula-tions, known as valley polarization [1–5]. Due to thelarge separation of the valleys in momentum space,it was thought that the polarization, once created,would prove to be very robust (long lived) in thesematerials. However, the polarization properties turnout to be more subtle than initially predicted. Severaldepolarization mechanisms have been invoked toexplain the decay of the valley polarization. They canbe classified based on whether they involve free car-riers or excitonic complexes. In the former case, theintervalley scattering entails a spin-flip and has to bemediated by interactions with localized impurities,short-wavelength phonons or by the spin precessiondue to spin–orbit coupling following these scatteringevents [7–13]. In the latter case, the electron–holeexchange-mediated intervalley scattering acting onexcitons with non-zero center of mass momentum[14] is considered to be the main source of valleydepolarization [2, 15–24]. The presence of a low-lying dark exciton state, acting as an exciton reservoir,has been identified as key mechanism [25, 26] for thepartial preservation of the valley polarization [15, 16,20, 27], even for excitation far from the A excitonresonance.Additionally, a Dexter-like mechanism, whichcouples the same-spin states of the A and B excitons(separated due to the large spin–orbit coupling in the© 2024 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/ad1ae8https://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/ad1ae8&domain=pdf&date_stamp=2024-1-17https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0003-0631-9461https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-5974-0850https://orcid.org/0000-0003-4078-4965https://orcid.org/0000-0002-4019-6138mailto:paulina.plochocka@lncmi.cnrs.frhttps://doi.org/10.1088/2053-1583/ad1ae82D Mater. 11 (2024) 025007 J Jasiński et alvalence band of TMDs [6]) between the valleys (i.e.A+ ↔ B− and B+ ↔ A−), as schematically presen-ted in figure 1(a), has been investigated by both the-oretical calculations and pump-probe measurementson WS2 monolayers [28]. This mechanism has beenshown to facilitate an efficient intervalley transferof coherent excitons and has been used to explainthe observed PL upconversion [29]. This intervalleytransfer results in an inversion of the optically excitedvalley polarization on a subpicosecond timescale.Here, we further explore the intricacies of the val-ley polarizationmechanisms via circular-polarizationresolved optical spectroscopy of monolayer WSe2combined with microscopic calculations. By invest-igating the excitation energy dependence of the val-ley polarization of different excitonic complexes, wereveal the prominent role played by Dexter-like coup-ling in determining the exciton valley polarization.We show that this mechanism enables us to con-trol the valley polarization of different excitonic com-plexes using resonant optical excitation of the Bexciton states. For the neutral exciton, the Dexter-likecoupling results in a vanishingly small valley polariz-ation of the neutral exciton, while for other excitoniccomplexes we achieve a negative valley polarization.Our results demonstrate that tuning the excitationenergy represents an additional handle to control thevalley polarization in monolayer WSe2, even allow-ing a reversal of the optically induced polarization.Moreover, the observed effect of band gap renormal-ization, which occurs for excitation resonant with B1sstate, can also be explained in the framework of theDexter-like coupling between the optically driven Bexciton and the A exciton in the opposite valley.We start our characterization of the hBN-encapsulated WSe2 flake (micrograph of the sampledisplayed in supplementary figure S1) by measuringlow-temperature photoluminescence (PL), PL excita-tion (PLE) and differential reflectivity spectra, shownin figures 1(b) and 2. Additional measurements andanalysis allowed us to assign spectral resonances todifferent excitonic transitions (see supplementaryfigures S2, S3 and supplementary table 1). We invest-igate the valley properties of our sample bymeasuringthe PL spectrum resolved in the circular polarizationbasis. As we show in the top panel of figure 1(b), thePL spectrum is strongly co-polarized with respect tothe laser when the excitation is performed in reson-ance with the A2s state. However, when we tune theexcitation energy close to the resonance with the B1s,the PL spectrum exhibits a zero or even slightly neg-ative degree of circular polarization, as can be seen inthe bottom panel of figure 1(b).To study more systematically the influence ofthe pump energy on the valley polarization, we per-formed circular polarization resolved PLE measure-ments. We then calculated the degree of circularpolarization, defined as Pc = (Ico − Icr)/(Ico + Icr),Figure 1. (a) Schematic of bright A and B exciton Rydbergstates (Ans and Bns, respectively). Arrows denote therelevant interaction of Dexter-like intervalley couplingupon excitation of the K+ valley resonantly with the B1sstate, which leads to a transfer of the bright excitonpopulation into the opposite K− valley. (b) PL spectra withdetection of the light co-polarized (co) and cross-polarized(cross) with the circularly polarized excitation. Theexcitation laser was tuned in resonance with the A2stransition (top panel) and at the energy corresponding tothe minimum of the degree of circular polarization Pc(bottom panel) near the B1s resonance. The scales in the topand bottom panels are the same for co and cross curves.where Ico/cr denotes the intensity of the co-polarized/cross-polarized emission, respectively. Dueto spin-valley locking, this quantity enables us todirectly quantify the valley polarization.Focusing on the A1s transition (see figure 2(a)),when we excite far from resonance, the Pc showsa low, positive value, which tends to increase fordecreasing excitation energy. This dependence ofthe valley polarization on the excess energy of theexcitation laser can be explained by noting that theelectron–hole exchange interaction behaves effect-ively like an in-plane momentum-dependent mag-netic field. The optically oriented valley pseudospinprecesses at a frequency which depends on the valueof this in-plane magnetic field, and thus depends onthe excess energy of the laser [18]. This precession22D Mater. 11 (2024) 025007 J Jasiński et alFigure 2. Excitation energy dependence of the intensity of the co- and cross-polarized emission (blue and red points, respectively)and the degree of circular polarization (Pc) (black points) for (a) A1s, (b) XX and (c) XX− excitonic transitions. Overlaiddifferential reflectivity spectra (green curves) allow to pinpoint the excitonic resonances. Horizontal dashed lines indicate the Pclevels of 0% and 30%.leads to a depolarization of the exciton population.This process is less efficient for decreasing excita-tion energy [25]. When the pump energy is in res-onance with either the B1s or the B2s state, the gen-erally positive Pc decreases strongly. This decrease isespecially pronounced at the B1s resonance, where Pcvanishes, consistent with a strong Dexter-like coup-ling. Finally, when we reduce even further the excit-ation energy, the valley polarization exhibited by thesystem tends again to increase with decreasing excit-ation energy. This confirms that the main depol-arization mechanism, which governs the intervalleydynamics far from resonance with B exciton states, isthe intervalley scattering via electron–hole exchangeinteraction [18, 25].By performing a similar analysis on otherexcitonic complexes, such as the biexciton (XX) andcharged biexciton (XX−), we notice that their polar-ization properties aremore strongly influenced by theDexter-induced intervalley coupling than the neutralA1s, as demonstrated by the excitation energy depend-ence of the valley polarization plotted in figures 2(b)and (c). At an excitation resonant with the B1s state,the valley polarization of the A1s state reaches its low-est value of Pc of near 0%, while XX and XX− exhibiteven a negative Pc of around −7%. This suggeststhat the biexcitonic complexes are less prone than theneutral A1s exciton to subsequent intervalley scatter-ing processes, which lead to equalization of popula-tions between the valleys [30]. A possible mechanismwhich leads to a larger negative polarization of thebiexciton population relies on the Dexter-mediatedtransfer of the exciton population to the indirectlydriven valley. There, following the relaxation pro-cesses, a population of dark excitons is established.These, together with bright excitons, form biexcitoniccomplexes [31, 32]. These quasiparticles undergo aslower intervalley scattering, due to the larger num-ber of component particles [33], which allows us toobserve the stronger negative valley polarization.The drastic decrease of the valley polarization forexcitation energies resonant with B exciton states canbe explained by turning to the Dexter-like coupling ofthe same spin states in opposite valleys in the recip-rocal space [28]. This Coulomb-driven interactiontransfers a coherent population of excitons from thedirectly driven valley into the opposite valley, wherethey couple to photons with the opposite helicity.When the excitation is performed resonantly with theBns states, the Dexter-like coupling leads to a transferof exciton population to the Ans states of the oppos-ite valley, which have the same spin. Therefore, thesestates will be preferentially populated and thus exhibita negative valley polarization at short delays withrespect to the excitation laser, as demonstrated by theresults of theoretical simulation shown in figure S4in the supplementary information. The valley polar-ization observed in time-integrated spectra dependsthen on the efficiency of different processes, suchas intravalley relaxation preserving the induced val-ley polarization, intervalley Dexter transfer invert-ing the valley polarization as well as additional inter-valley scattering and exchange processes, which tryto equalize the valley polarization. Similar datasetsconsisting of excitation energy dependent degree ofcircular polarization of the A1s exciton have alreadybeen presented [27], although the origin of the com-plex valley polarization dependence on the excitationenergy was not discussed.We compare now the experimental data withmicroscopic calculations, which model the excitationenergy dependent time evolution of the valley32D Mater. 11 (2024) 025007 J Jasiński et alpolarization of the A1s exciton following a singleexcitation pulse. In the simulation, a circularly polar-ized laser pulse centered at 400 fs (full width at halfmaximum, FWHM, of 400 fs) is used to create acoherent exciton population in one of the valleys.The model tracks the time evolution of the PL fromthe two valleys and accounts for both intervalleyDexter-like coupling and scattering mediated via theelectron–hole exchange interaction, in addition toother phonon-driven decay processes (see Methodsand supplementary section for more details). Webegin by showing in figure 3(a) the simulated excit-ation energy dependence of the valley polarization,calculated by monitoring the population of the A1sstate 40 fs after the onset of the laser pulse. For allexcitation energies non-resonant with Bns excitonstates, the intensity of the PL emitted from the optic-ally pumped valley is considerably larger than thatfrom the valley not addressed optically. For excita-tion energies corresponding to resonances with Bnsstates, conversely, the simulated valley polarization isstrongly negative. This is a consequence of the effi-cient Dexter-like coupling between the states directlydriven by the excitation laser and the A states of theopposite valley. The large negative valley polarizationresults from a highly efficient Dexter-like couplingdue to the combination of an excitation resonantwith Bns states and a high coherence of the excitonpopulation at very short delays with respect to theexcitation laser [34]. In figure 3(b), we show a sim-ilar simulated excitation energy dependence of thevalley polarization captured at a 4 ps delay after theonset of the excitation pulse. At this delay, the pulseis mostly over and the exciton population has lostits coherence, which greatly reduces the efficiency ofthe Dexter-like coupling. This, together with inter-valley exchange processes, reduces the value of thenegative polarization. This decrease of the negativevalley polarization is reflected in the time-integratedsimulated valley polarization, shown in figure 3(c),whose minimum is strongly reduced with respectto the corresponding value extracted from a coher-ent exciton population. Finally, we compare theseresults with our time-integrated experimental data,shown in figure 3(d). The strong decrease of the valleypolarization when we excite resonantly with B1s statecan be considered a ‘long-term’ fingerprint of theDexter-like coupling, whereby the initial strong neg-ative polarization is reduced by intervalley scatteringevents to a near zero value.While the excitation energy dependence of thesimulated and experimental valley polarization showa good qualitative agreement, the simulated val-ley polarization features appear over a wider spec-tral range than in the experimentally determinedcurves. Thismight be related either to the discrepancybetween the real and simulated parameters of theFigure 3. Calculated circular polarization resolved PLEintensity and degree of circular polarization (Pc) at timedelay (a) t= 40 fs and (b) t= 4 ps after the onset of theexcitation pulse, respectively. (c) PLE and Pc of thesimulation time-integrated within the range of thesimulation time interval (0−20 ps). (d) Experimental,time-integrated PLE intensity and Pc.structure, which could not have been experimentallyobtained e.g. the rates of the coherent/incoherentexciton transfer or other effects beyond the scope ofthis work.Next, we show in figure 4(a) direct comparison ofthe excitation energy dependence of the valley polar-ization of the neutral exciton, biexciton and of thecharged biexciton with the calculated valley polariz-ation of the neutral exciton. In addition to the obser-vation of more negative polarization preserved by thebiexcitonic complexes (as compared to the neutralexciton)whichwe discussed above, theminimumval-ley polarization for all three complexes we find inour measurements is red shifted by approximately 20meV with respect to the PLE resonance of the B1sexciton, which is consistent with prior reports [27].Both in the simulated and experimental curve thevalley polarization begins to decrease at an energyconsiderably lower than the simulated B1s resonance,42D Mater. 11 (2024) 025007 J Jasiński et alFigure 4. Comparison of simulated (for the A1s exciton)and experimental (for A1s, XX and XX− excitons) Pc curvesas a function of excitation energy (top) and correspondingnormalized PLE intensity (bottom). The energy scale oftheoretical curves is shifted by 18 meV to match the energyposition of the B1s exciton resonance between theexperiment and simulation.which is a consequence of the broadening of itsresonance following its Dexter-mediated coupling tothe A1s state of the optically undriven valley.The simulated valley polarization remains flatacross the broadenings of the Bns states. This leads toan overlap of the Dexter-like coupling effect betweenthe B1s and B2s states, where the simulated valleypolarization reaches its minimum value. Conversely,the experimentally determined valley polarizationincreases rapidly between the B1s and B2s states. Thiseffect gradually counters the effect of the Dexter-likecoupling, thereby increasing the valley polarizationobserved experimentally. The combination of the lowenergy onset of the negative polarization related to thebroadening and the increase of the valley polarizationdue to the exciton population with a finite in-planemomentum leads to a ∼20 meV shift between theminimum of the valley polarization and the excitonresonance.Finally, theory predicts that another manifest-ation of the Dexter induced coupling between twostates in different valleys is an increase of theirenergy separation and a broadening of the excitonicresonances [35]. To investigate the former effect, wecompare the differential reflectivity spectrum shownin figure 5(a) with the dependence on the excita-tion energy of the PL peak energy of the A1s exciton,shown in figure 5(b), and of the neutral and chargedbiexciton, summarized in figures 5(c) and (d). Forall the three complexes, we observe a clear red shiftof the emission when the excitation laser is resonantwith the B1s transition. Regarding the latter effect,we have analyzed the energy dependent broadening(FWHM) of all three complexes (see supplementaryFigure 5. (a) Differential reflectivity with marked A2s, B1sand B2s resonances (green curve). (b)–(d) Excitation energydependence of the shift of the emission energy∆E for theco- and cross-polarized emission (blue and red points,respectively), for (b) A1s, (c) XX and (d) XX−. Here∆Ecorresponds to the shift in peak energy of a given excitoniccomplex with respect to its average peak energy of co andcross polarized emission at the highest excitation energy.figure S6). There, similarly to the aforementionedenergy redshift, we observed the increase in broad-ening of the emission for all three complexes(approximately∼3 meV) for excitation energy res-onant with the B1s transition. This effect is greaterthan previously reported in WS2 [35], where thebroadening of the A1s state remained approximatelyunchanged.In conclusion, we have demonstrated the long-term effects of the excitation-drivenDexter-like coup-ling mechanism on the valley polarization proper-ties of a monolayer WSe2. We have shown that, dueto this mechanism, a valley-selective excitation res-onant with the B exciton states strongly decreasesthe valley polarization to a near zero value for theneutral exciton (A1s) or inverts the valley polariz-ation (∼−7%) of other excitonic complexes suchas XX and XX−. This, together with the decreaseof the PL peak energy of these excitonic com-plexes when the excitation energy is tuned in res-onance with the B1s exciton, is in qualitative agree-ment with theoretical simulations of the excitondynamics which account for the Dexter coupling.This property could prove to be a useful tool invalleytronic devices, e.g. for optical polarizationswitching.52D Mater. 11 (2024) 025007 J Jasiński et al1. MethodsThe sample was fabricated using flakes mechanicallyexfoliated on PDMS and then assembled on the sil-icon substrate flake by flake via dry transfer method[36]. All the experimental results have been obtainedat cryogenic temperatures of ∼4 K, by cooling downthe sample mounted on the cold finger of a He flowcryostat. A pulsed Ti-sapphire laser (80 MHz repeti-tion rate, 150 fs pulse width) was used to pump anoptical parametric oscillator (generated pulse width∼300–400 fs), whichwas used as the excitation sourcein PLEmeasurements, in order to achieve wavelengthtuning in a wide range. For excitation power depend-ent PL measurements, a 405 nm laser was used ineither CWor pulsedmode. A 50×microscope object-ive with numerical aperture 0.55was used to focus theexcitation laser on the sample and collect the signalwith a spatial resolution of∼1 µm. Themeasurementspot of the experiments was always chosen on the flatarea of the sample to avoid the impact of the strainedareas such as bubbles and wrinkles that tend to formon mechanically exfoliated structures. The signal wasdirected to a spectrometer equipped with a liquid-nitrogen-cooled CCD camera. For reflectivity meas-urements, a white light source was used instead of thelaser.In order to microscopically determine theexcitonic landscape in WSe2, we use the Wannierequation [34] to derive the excitonic energy levels,ϵiη , and wavefunctions, φη,ik , for both the A and Bexcitons(h̄2k22µir+ EiGap)φη,ik +∑k ′Vkk ′Kel φη,ik ′ = ϵiηφη,ik (1)where µr is the reduced mass of the exciton, k is therelative momentum and EiGap is the electronic bandgap. Here, i denotes the compound index determin-ing both the valley (K , K′) and spin (↑↑,↓↓) of theexciton. The Coulomb interaction is described by thegeneralized 2D Keldysh potential, Vkk ′Kel , which takesinto account the reduced screening in 2D systems[28]. The parameterization of this Hamiltonianand other quantities are outlined in previousstudies [22, 28, 34, 35, 37].The evolution of the valley polarization in aTMD system can be captured within the dens-ity matrix formalism. Using Heisenberg’s equationof motion ih̄∂t⟨Ô⟩= [Ô,Ĥ], we derive a series ofsemiconductor Bloch equations [38], to track theevolution of the excitonic states. In particular, wecapture the evolution of both coherent, P̂ηi , andincoherent N̂ηij exciton densities [37]. More detailscan be found in the supplementary information.Solving this series of differential equations allows usto track the time-evolution of the excitonic states andhence determine the time-resolved PLE spectra. Inparticular, the PLE spectra are determined by theElliot-formula [28, 39] at fixed resonance, h̄ωprobe,with varying excitation energy, ω, leading to theformIσσ ′,ωprobePLE (t,ω) =∑ξ,i,η[|⟨P̂ηξi (t,ω,σ)⟩|2 + ⟨N̂ηξij (t,ω,σ)⟩]×ℑ(|φη,i (r= 0) |2|Miξ · êσ ′ |2ϵiη − h̄ωprobe + iγ)whereσ (σ ′) describes the polarization of the exciting(measured) light. The magnitude of each excitonicsignature depends on the optical matrix element andthe polarization vector of the emitted light êσ ′ , aswell as |φη,i(r= 0)|, which describes the probabilityof finding the electron and hole at the same posi-tion, for a given excitonic state. The broadening ofthe PLE is determined by γ, which we calculatemicroscopically [34].Data availability statementAll data that support the findings of this study areincluded within the article (and any supplementaryfiles).AcknowledgmentsThe Marburg group has received funding fromDeutsche Forschungsgemeinschaft via CRC 1083.This study has been partially supported throughthe EUR Grant NanoX n◦ ANR-17-EURE-0009 in the framework of the’Programme desInvestissements d‘Avenir’. K W and T T acknow-ledge support from JSPS KAKENH I (GrantNumbers 19H05790, 20H00354 and 21H05233).M B acknowledges funding from the National ScienceCentre Poland within the SONATA BIS program(Grant No. 2020/38/E/ST3/00194) and OPUS LAP(2021/43/I/ST3/01357). J J acknowledges fundingfrom the National Science Centre Poland within thePreludium Bis 1 (2019/35/O/ST3/02162) program.ORCID iDsJakub Jasiński https://orcid.org/0000-0003-0631-9461Kenji Watanabe https://orcid.org/0000-0003-3701-8119Michał Baranowski https://orcid.org/0000-0002-5974-0850Alessandro Surrente https://orcid.org/0000-0003-4078-4965Paulina Płochocka https://orcid.org/0000-0002-4019-6138References[1] Yao W, Xiao D and Niu Q 2008 Phys. Rev. B 77 235406[2] Xiao D, Liu G-B, Feng W, Xu X and Yao W 2012 Phys. Rev.Lett. 108 1968026https://orcid.org/0000-0003-0631-9461https://orcid.org/0000-0003-0631-9461https://orcid.org/0000-0003-0631-9461https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-5974-0850https://orcid.org/0000-0002-5974-0850https://orcid.org/0000-0002-5974-0850https://orcid.org/0000-0003-4078-4965https://orcid.org/0000-0003-4078-4965https://orcid.org/0000-0003-4078-4965https://orcid.org/0000-0002-4019-6138https://orcid.org/0000-0002-4019-6138https://orcid.org/0000-0002-4019-6138https://doi.org/10.1103/PhysRevB.77.235406https://doi.org/10.1103/PhysRevB.77.235406https://doi.org/10.1103/PhysRevLett.108.196802https://doi.org/10.1103/PhysRevLett.108.1968022D Mater. 11 (2024) 025007 J Jasiński et al[3] Xu X, Yao W, Xiao D and Heinz T F 2014 Nat. Phys.10 343[4] Yu H, Cui X and Yao W 2015 Natl Sci. Rev. 2 57[5] Stier A V, McCreary K M, Jonker B T, Kono J andCrooker S A 2016 Nat. Commun. 7 10643[6] Zhu Z Y, Cheng Y C and Schwingenschlögl U 2011 Phys. Rev.B 84 153402[7] Schmidt H, Yudhistira I, Chu L, Neto A C, Özyilmaz B,Adam S and Eda G 2016 Phys. Rev. Lett. 116 046803[8] Wang L and WuM 2014 Phys. Rev. B 89 115302[9] Song Y and Dery H 2013 Phys. Rev. Lett. 111 026601[10] Ochoa H and Roldán R 2013 Phys. Rev. B 87 245421[11] Lu H-Z, Yao W, Xiao D and Shen S-Q 2013 Phys. Rev. Lett.110 016806[12] Dey P, Yang L, Robert C, Wang G, Urbaszek B, Marie X andCrooker S A 2017 Phys. Rev. Lett. 119 137401[13] Kim J et al 2017 Sci. Adv. 3 e1700518[14] Maialle M, Silva E d A and Sham L 1993 Phys. Rev. B47 15776[15] Zeng H, Dai J, Yao W, Xiao D and Cui X 2012 Nat.Nanotechnol. 7 490[16] Zhu C, Zhang K, Glazov M, Urbaszek B, Amand T,Ji Z, Liu B and Marie X 2014 Phys. Rev. B90 161302[17] Yu H, Liu G-B, Gong P, Xu X and Yao W 2014 Nat. Commun.5 3876[18] Yu T and WuM 2014 Phys. Rev. B 89 205303[19] Wang Y-T, Luo C-W, Yabushita A, Wu K-H, Kobayashi T,Chen C-H and Li L-J 2015 Sci. Rep. 5 8289[20] Plechinger G, Nagler P, Arora A, Schmidt R, Chernikov A,Del Águila A G, Christianen P C, Bratschitsch R, Schüller Cand Korn T 2016 Nat. Commun. 7 12715[21] Dery H 2016 Phys. Rev. B 94 075421[22] Schmidt R, Berghauser G, Schneider R, Selig M, Tonndorf P,Malic E, Knorr A, Michaelis de Vasconcellos S andBratschitsch R 2016 Nano Lett. 16 2945[23] Hao K et al 2017 Nat. Commun. 8 15552[24] Yan T, Qiao X, Tan P and Zhang X 2015 Sci. Rep. 5 15625[25] Baranowski M, Surrente A, Maude D K, Ballottin M,Mitioglu A, Christianen P, Kung Y, Dumcenco D, Kis A andPlochocka P 2017 2D Mater. 4 025016[26] Tornatzky H, Kaulitz A-M and Maultzsch J 2018 Phys. Rev.Lett. 121 167401[27] Wang G et al 2015b Nat. Commun. 6 10110[28] Berghäuser G, Bernal-Villamil I, Schmidt R, Schneider R,Niehues I, Erhart P, Michaelis de Vasconcellos S,Bratschitsch R, Knorr A and Malic E 2018 Nat. Commun.9 971[29] Manca M et al 2017 Nat. Commun. 8 14927[30] Li Z et al 2018 Nat. Commun. 9 3719[31] Nagler P et al 2018 Phys. Rev. Lett. 121 057402[32] Cunningham P D, Hanbicki A T, Reinecke T L,McCreary K M and Jonker B T 2019 Nat. Commun. 10 5539[33] Singh A et al 2016 Phys. Rev. Lett. 117 257402[34] Selig M, Berghäuser G, Raja A, Nagler P, Schüller C,Heinz T F, Korn T, Chernikov A, Malic E and Knorr A 2016Nat. Commun. 7 13279[35] Bernal-Villamil I et al 2018 2D Mater. 5 025011[36] Castellanos-Gomez A, Buscema M, Molenaar R, Singh V,Janssen L, Van Der Zant H S and Steele G A 2014 2D Mater.1 011002[37] Brem S, Selig M, Berghaeuser G and Malic E 2018 Sci. Rep.8 8238[38] Kira M and Koch S W 2006 Prog. Quantum Electron. 30 155[39] Koch S, Kira M, Khitrova G and Gibbs H 2006 Nat. Mater.5 5237https://doi.org/10.1038/nphys2942https://doi.org/10.1038/nphys2942https://doi.org/10.1093/nsr/nwu078https://doi.org/10.1093/nsr/nwu078https://doi.org/10.1038/ncomms10643https://doi.org/10.1038/ncomms10643https://doi.org/10.1103/PhysRevB.84.153402https://doi.org/10.1103/PhysRevB.84.153402https://doi.org/10.1103/PhysRevLett.116.046803https://doi.org/10.1103/PhysRevLett.116.046803https://doi.org/10.1103/PhysRevB.89.115302https://doi.org/10.1103/PhysRevB.89.115302https://doi.org/10.1103/PhysRevLett.111.026601https://doi.org/10.1103/PhysRevLett.111.026601https://doi.org/10.1103/PhysRevB.87.245421https://doi.org/10.1103/PhysRevB.87.245421https://doi.org/10.1103/PhysRevLett.110.016806https://doi.org/10.1103/PhysRevLett.110.016806https://doi.org/10.1103/PhysRevLett.119.137401https://doi.org/10.1103/PhysRevLett.119.137401https://doi.org/10.1126/sciadv.1700518https://doi.org/10.1126/sciadv.1700518https://doi.org/10.1103/PhysRevB.47.15776https://doi.org/10.1103/PhysRevB.47.15776https://doi.org/10.1038/nnano.2012.95https://doi.org/10.1038/nnano.2012.95https://doi.org/10.1103/PhysRevB.90.161302https://doi.org/10.1103/PhysRevB.90.161302https://doi.org/10.1038/ncomms4876https://doi.org/10.1038/ncomms4876https://doi.org/10.1103/PhysRevB.89.205303https://doi.org/10.1103/PhysRevB.89.205303https://doi.org/10.1038/srep08289https://doi.org/10.1038/srep08289https://doi.org/10.1038/ncomms12715https://doi.org/10.1038/ncomms12715https://doi.org/10.1103/PhysRevB.94.075421https://doi.org/10.1103/PhysRevB.94.075421https://doi.org/10.1021/acs.nanolett.5b04733https://doi.org/10.1021/acs.nanolett.5b04733https://doi.org/10.1038/ncomms15552https://doi.org/10.1038/ncomms15552https://doi.org/10.1038/srep15625https://doi.org/10.1038/srep15625https://doi.org/10.1088/2053-1583/aa58a0https://doi.org/10.1088/2053-1583/aa58a0https://doi.org/10.1103/PhysRevLett.121.167401https://doi.org/10.1103/PhysRevLett.121.167401https://doi.org/10.1038/ncomms10110https://doi.org/10.1038/ncomms10110https://doi.org/10.1038/s41467-018-03354-1https://doi.org/10.1038/s41467-018-03354-1https://doi.org/10.1038/ncomms14927https://doi.org/10.1038/ncomms14927https://doi.org/10.1038/s41467-018-05863-5https://doi.org/10.1038/s41467-018-05863-5https://doi.org/10.1103/PhysRevLett.121.057402https://doi.org/10.1103/PhysRevLett.121.057402https://doi.org/10.1038/s41467-019-13501-xhttps://doi.org/10.1038/s41467-019-13501-xhttps://doi.org/10.1103/PhysRevLett.117.257402https://doi.org/10.1103/PhysRevLett.117.257402https://doi.org/10.1038/ncomms13279https://doi.org/10.1038/ncomms13279https://doi.org/10.1088/2053-1583/aaaa8bhttps://doi.org/10.1088/2053-1583/aaaa8bhttps://doi.org/10.1088/2053-1583/1/1/011002https://doi.org/10.1088/2053-1583/1/1/011002https://doi.org/10.1038/s41598-018-25906-7https://doi.org/10.1038/s41598-018-25906-7https://doi.org/10.1016/j.pquantelec.2006.12.002https://doi.org/10.1016/j.pquantelec.2006.12.002https://doi.org/10.1038/nmat1658https://doi.org/10.1038/nmat1658 Control of the valley polarization of monolayer WSe2 by Dexter-like coupling References