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Kai-Qiang Lin, Jonas D. Ziegler, Marina A. Semina, Javid V. Mamedov, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Sebastian Bange, Alexey Chernikov, Mikhail M. Glazov, John M. Lupton

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[High-lying valley-polarized trions in 2D semiconductors](https://mdr.nims.go.jp/datasets/da01e073-4f56-43a4-8913-ef65618d8aeb)

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High-lying valley-polarized trions in 2D semiconductorsArticle https://doi.org/10.1038/s41467-022-33939-wHigh-lying valley-polarized trions in 2DsemiconductorsKai-Qiang Lin 1 , Jonas D. Ziegler2, Marina A. Semina3, Javid V. Mamedov 4,Kenji Watanabe 5, Takashi Taniguchi 6, Sebastian Bange 1,Alexey Chernikov2, Mikhail M. Glazov 3,4 & John M. Lupton 1Optoelectronic functionalities of monolayer transition-metal dichalcogenide(TMDC) semiconductors are characterized by the emergence of externallytunable, correlated many-body complexes arising from strong Coulombinteractions. However, the vast majority of such states susceptible to manip-ulation has been limited to the region in energy around the fundamentalbandgap. We report the observation of tightly bound, valley-polarized, UV-emissive trions inmonolayer TMDC transistors: quasiparticles composed of anelectron from a high-lying conduction band with negative effective mass, ahole from the first valence band, and an additional charge from a band-edgestate. These high-lying trions have markedly different optical selection rulescompared to band-edge trions and show helicity opposite to that of theexcitation. An electrical gate controls both the oscillator strength and thedetuning of the excitonic transitions, and therefore the Rabi frequency of thestrongly driven three-level system, enabling excitonic quantum interference tobe switched on and off in a deterministic fashion.Transition-metal dichalcogenide (TMDC) monolayers are known tohost tightly bound band-edge excitons1–3, as well as a variety of moreelaborate many-body species such as exciton complexes in the pre-sence of the Fermi sea of free carriers (known as trions and Fermipolarons)4–6 and excitonic molecules7–15. More recently, bound high-lying excitons (HXs), involving electrons from the upper conductionband (in particular, CB+2) and holes from the top-most valence band,have been observed16. Even though these high-lying excitons appearat almost twice the energy of the band-edge exciton (X), they exhibita particularly narrow linewidth that is comparable to that of band-edge excitons. Intriguingly, GW-BSE calculations show that the HXconsists of an electronoriginating predominantly fromadownwards-curved conduction band, i.e. a negative effective mass electron16.Although trion formation is well-known for the band-edge excitons intwo-dimensional semiconductors, it has so far remained unclearwhether such states can also form from these more exotic excitonicspecies.Coincidentally, in monolayer WSe2, these high-lying excitonsappear at around twice the band-edge exciton transition energy,giving rise to a degenerate atom-like three-level system that allowsfor a pronounced quantum interference phenomenon to occur inoptical second-harmonic generation (SHG)16–19. Combining suchquantum interference, which generally occurs in discrete multilevelsystems such as atomic vapors, crystal defects, or ions, with elec-tronic device functionality has been a long-standing goal. Anexciton-based three-level system promises the advantage of facileintegration into electronic devices and potentially offers uniquecontrol over quantum interference through electrical gate signals.However, such control remains a major conceptual challenge andhas not been developed yet.Received: 29 April 2022Accepted: 7 October 2022Check for updates1Department of Physics, University of Regensburg, 93053Regensburg, Germany. 2Dresden Integrated Center for Applied Physics and PhotonicMaterials andWürzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany. 3Ioffe Institute, 194021 St. Petersburg, Russia.4National Research University, Higher School of Economics, 190121 St. Petersburg, Russia. 5Center for Functional Materials, National Institute for MaterialsScience, Tsukuba, Ibaraki 305-004, Japan. 6International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki305-004, Japan. e-mail: kaiqiang.lin@ur.de; glazov@coherent.ioffe.ruNature Communications |         (2022) 13:6980 11234567890():,;1234567890():,;http://orcid.org/0000-0001-9609-749Xhttp://orcid.org/0000-0001-9609-749Xhttp://orcid.org/0000-0001-9609-749Xhttp://orcid.org/0000-0001-9609-749Xhttp://orcid.org/0000-0001-9609-749Xhttp://orcid.org/0000-0001-8263-3191http://orcid.org/0000-0001-8263-3191http://orcid.org/0000-0001-8263-3191http://orcid.org/0000-0001-8263-3191http://orcid.org/0000-0001-8263-3191http://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/0000-0002-5850-264Xhttp://orcid.org/0000-0002-5850-264Xhttp://orcid.org/0000-0002-5850-264Xhttp://orcid.org/0000-0002-5850-264Xhttp://orcid.org/0000-0002-5850-264Xhttp://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0003-4462-0749http://orcid.org/0000-0002-7899-7598http://orcid.org/0000-0002-7899-7598http://orcid.org/0000-0002-7899-7598http://orcid.org/0000-0002-7899-7598http://orcid.org/0000-0002-7899-7598http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33939-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33939-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33939-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33939-w&domain=pdfmailto:kaiqiang.lin@ur.demailto:glazov@coherent.ioffe.ruHere, we demonstrate experimentally and theoretically that suchhigh-lying trions with negative-mass electrons can indeed form. Weprobe these charged HXs in a monolayer WSe2 transistor, where thecharge carrier density can be continuously controlled via the gatevoltage. We generalize these observations by demonstrating thatsimilar features exist in a monolayer MoSe2 transistor. In contrast tothe neutral HX, high-lying trions show pronounced helicity following avalley polarization selection rule that is distinct from those of theband-edge transitions. In addition to the bright HX trion, adark charged p-like HX is identified by the signature of excitonicquantum interference in SHG. Finally, we demonstrate robust controlof excitonic quantum interference by the gate voltage.ResultsElectrical tuning of high-lying trions in monolayer WSe2Figure 1a illustrates twoconceivable configurations of high-lying trionsin the vicinity of the K-points in momentum space: the photoexcitedelectron in the high-energy CB+2 band, and the photoexcited hole inthe top valence band (VB) forming a negative (positive) trion with anadditional resident electron (hole) at the band edge. To probe thesetrions, a gate-tunable device is needed to control the charge carrierdensity, i.e., the doping, in the monolayer. Figure 1b illustrates themonolayer WSe2 transistor device, a microscope photograph ofwhich is shown in Fig. 1c. The gate-voltage dependence of photo-luminescence (PL) from band-edge excitons is first measured tocharacterize the control of doping in monolayer WSe2. Figure 1dreproduces the characteristic features of the well-documented band-edge excitonic species, such as the negatively charged A excitonsinglet (X�S ) and triplet (X�T ), the positively charged A exciton (X+), thebiexciton (XXD), the intervalley dark exciton (XD), and the chargeddark excitons (X+D and X�D)20–22. With a thin graphite flake (few-layergraphene) as the top gate, such gate-voltage dependent measure-ments are completely reversible without noticeable hysteresis, asdiscussed in Supplementary Note 1 and Supplementary Fig. 1. From theappearance of the neutral exciton species such as the neutral darkexciton and biexciton in Fig. 1d, we can identify the charge neutralitypoint centered around −0.15 V.Resonant pumping of the A exciton followed by Auger-like exci-ton-exciton annihilation selectively promotes electrons to the high-lying conduction band near the ±K-points in momentum space,forming a high-lying exciton HX16,23,24. Supplementary Fig. 2 shows apump power dependence of UPL supporting the Auger-like process.Figure 1e shows the gate-voltage dependence of upconverted PL (UPL)in the energy range of 3.2 to 3.5 eV under continuous-wave (CW)excitation at 1.724 eV, i.e., at about twice the excitation energy.Figure 1f shows example UPL spectra at gate voltages of +0.2 V(negatively charged), −0.15 V (neutral), and −0.5 V (positively charged).In the neutral regime, the UPL spectrum of the HX (black line) shows acharacteristic phonon progression, as reported previously16, alongwith a sharp spectral feature at 3.448 eV, which arises due to the CWSHG of the incident laser25. The zero-phonon line of the HX is markedas HX0. Strikingly, newpeaks emerge under both positive and negativedoping (Fig. 1e). In the electron-doping regime, a new peak appears43meV below the HX0. In the hole-doping regime, a peak emerges35meV below the HX0. These two peaks have narrow linewidthsresembling those of the HX and are therefore assigned to the nega-tively (HX−) and positively (HX+) charged HX. As shown in Fig. 1e andSupplementary Fig. 1, gate voltages of +0.2 V and −0.5 V correspond toa lowdoping regimewhere the Fermi level is close to the band edges towithin 1meV26. The offsets of the trion transitions observed withrespect to HX0 are therefore attributed to their binding energies. Aslisted in Table S1, these binding energies are, on average, 1.4 times aslarge as those of band-edge (A exciton) trions, in line with the fact thatthe HX binding energies, calculated from ab initio GW-BSE theory, areabout 1.3 times as large as the A-exciton binding energy16. The nega-tively charged HX has larger binding energy than the positivelya cbd e f42.6 meV35.2 meVHX-n-dopedp-dopedHX-X-TX-SXXXX+ -0.5 V-0.15 Vneutraln-dopedp-doped0.2 VCW SHGMomentumEnergy20 µmGraphitetop gateWSe2Graphite contactsHX0Phonon replicas HX+HX+MomentumEnergy+K -KSi/SiO2hBNhBNGraphiteGrGrVgateWSe2X+DXD DX-DSHG+K -KFig. 1 | High-lying trions in monolayer WSe2. a Illustration of negatively andpositively charged high-lying excitons (HX), composed of an electron from a high-lying conduction band with negative effective mass, a hole from the first valenceband, and an additional charge from a band-edge state. The semi-transparentelectron and curved lines on the left illustrate an alternative structure of thenegatively chargedHX, where the electrons are in different valleys.b, c Schematicsand microscope photograph of the transistor device. The WSe2 monolayer isencapsulated between thin hBN layers and connected to pre-pattern goldelectrodes via graphite flakes. The uppermost graphite flake covering monolayerWSe2 serves as the topgate.dPhotoluminescence (PL)of band-edge excitons (X) at488 nmexcitation,measured as a function of gate voltage. eUpconverted PL (UPL)of the HX at 719.2 nm (1.724 eV) excitation,measured as a function of gate voltage.The features attributed to the negatively charged HX and to the positively chargedHX aremarked as HX− and HX+, respectively. f Sample UPL spectra at gate voltagesof 0.2 V (electron doping), −0.15 V (neutral), and −0.5 V (hole doping). All mea-surements were performed at 5 K.Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 2charged one, analogous to the situation for the band-edge trions(Fig. 1d)27. However, we are not able to resolve singlet and triplet HX−species. These speciesmay bemasked by the phonon progressions, orare limited in population due to the formation process of the high-lying trions. As we discuss below, the high-lying trions can formthrough the capture of the resident charge carrier by the HX, which inturn was created in the course of either an Auger-like annihilation oftwo excitons in the ground state, or via an Auger-like annihilationprocess between a band-edge trion and a band-edge exciton. It isconceivable that the latter case shows a preference for certain internalstructures of negative high-lying trions, as explained in SupplementaryNote 2 and Supplementary Figs. 5–7.The neutral HX PL spectrum is characterized by a distinct phononprogression, as seen in Fig. 1f at a gate voltage of −0.15 V, since theelectron in the high-lying conduction band near the ±K-points couplesstrongly to zone-edge longitudinal acoustic (LA) phonons16. The peakintensities of the phonon replicas alternate with peak order number,indicating a transformation between momentum-direct, i.e., opticallyactive, and momentum-indirect, i.e., optically inactive, states28. Thespacing of 31meV between two bright peaks corresponds to theenergy of two LAphonons, scattering the electron between valleys andback again16. The same spacing is resolved in the trion UPL spectra asmarked by the curved black arrows in Fig. 1e. As shown in Supple-mentary Fig. 3, this phonon progression appears more pronouncedafter subtracting the UPL spectrum at charge neutrality (−0.15 V),confirming the excitonic origin of these peaks. Nevertheless, the zero-phonon lines for the charged HXs appear much stronger than that forthe neutral HX, indicating a weaker electron-phonon coupling for thecharged HXs.Valley polarization of high-lying trionsNext, we explore the valley polarization characteristics29 of thesechargedHXby examining thedegreeof circular polarization (CP) in theUPL. Figure 2a, b shows the circular dichroism of the UPL as a functionof gate voltage, with the corresponding helicity of the UPL plotted inpanel C. The helicity is calculated by ðIσ + =σ + � Iσ + =σ� Þ=ðIσ + =σ + + Iσ + =σ� Þ,where Iσ + =σ + (Iσ + =σ� ) is the intensity of the co-polarized (cross-polar-ized) UPL. Figure 2d–f plots representative CP-resolved UPL spectra ina cbd e fg h iHX-SHGSHGSHGSHGSHGHX-HX-HX-HX+HX+HX+HX+�+ �-�+HX0Vgate = 0.2 V Vgate = -0.15 Vneutraln-doped p-dopedVgate = -0.5 V+K -K +K -K +K -KCB+2±CB±VB±Fig. 2 | Valley polarization and helicity of the high-lying trion in UPL frommonolayer WSe2. a, b Gate-voltage dependence of co-polarized (a) and cross-polarized (b) UPL under left-hand circularly polarized excitation. c Helicity of theUPL as a function of gate voltage. d–f Polarization resolved UPL spectra at gatevoltagesof 0.2 V (d),−0.15 V (e), and−0.5 V (f).g Illustration of resonantpumpingofthe A exciton in the +K valley with a σ+ circularly polarized CW laser. This excitationselectively polarizes resident spin-down electrons in the conduction band, CB. Theinset illustrates the Auger-like exciton-exciton annihilation process that promotesthe electron to high-lying conduction bands. h Schematic of negatively chargedhigh-lying trion in the −Kvalleywithσ+ polarized emission and a resident spin-downelectron in the −K valley. i Schematic of the positively charged high-lying trion inthe +K valley with σ− polarized emission.Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 3the electron-doping, neutral, and hole-doping regimes. The highest-energy peak in the spectra again arises from the CW SHG, which, inaccordance with the selection rules intrinsic to the C3 symmetry30,31,always retains a CP opposite to that of the incident laser and thereforeserves as a reference. Remarkably, the UPL from both HX trions iscircularly polarized by up to 50%, whereas the UPL of the neutral HXappears unpolarized. This stark difference in the valley polarization ofneutral and charged HXs could be due to the efficient electron-holeexchange interaction32–34, the underlying formation mechanism asillustrated in Supplementary Fig. 5, or differences in their lifetime.Given that spin-valley locking is only effective in a limited region ofmomentum space around the K-points for the high-lying conductionband16, the observed valley polarization of high-lying trions also cor-roborates our earlier finding that stable high-lying excitons must ori-ginate from the ±K-points16.Surprisingly, HX− and HX+ exhibit opposite valley polarizations,and the CP UPL hence shows opposite helicity, in stark contrast to theband-edge trions, which generally exhibit the same helicity1,27,29.Helicity-resolved two-photon PL of the neutral and charged HX dis-plays identical behavior as shown in Supplementary Fig. 4. The HX+shows CP opposite to that of the excitation (Fig. 2g, i). This inversionagreeswith the significant difference in selection rules for VB↔CB andVB↔CB+2 transitions in the same ±K valley35,36, as summarized inTable 1. In contrast, the HX− state is co-polarized with the laser, whichindicates a localization at the −K valley according to the selection ruleas sketched in Fig. 2h. We note that such an opposite helicity of posi-tive and negative trions has recently been observed for band-edgeexcitons inmonolayerWSe2 under CW excitation and was rationalizedby the resident-carrier polarization effect37, i.e., the creation of a largepolarization of resident electrons at the valley opposite to that ofexcitation. As illustrated in Fig. 2h and elaborated on in SupplementaryFig. 6, we therefore conclude that the most probable configuration oftheHX− is intravalley in nature. Becauseof the large spin–orbit splittingin the top valence band, this polarization process is not expected to beapplicable to resident holes.High-lying excitons and trions in monolayer MoSe2Since the resident-carrier polarization effect relies on a fast intervalleyscattering of the excited electron from the upper spin-split CB to thelower spin-split CB, it is not expected to arise in MoSe2 monolayers,where photoexcited electrons reside in the lower spin-split CB. Wewould therefore expect positively and negatively charged high-lyingtrions inMoSe2 to both have the same helicity, opposite to the helicityof the band-edge excitation. To test this hypothesis, we investigate thehigh-lying exciton and trions in a monolayer MoSe2 transistor device.Figure 3a presents the PL of band-edge excitons from monolayerMoSe2 as a function of the gate voltage.Weprobe theHXby resonantlypumping the A exciton and measuring the high-energy UPL. Figure 3bshows the UPL and CW SHG of monolayer MoSe2 as a function of thegate voltage. In stark contrast to the broad linewidth of thewell-knownC exciton38,39, a narrow-band high-energy emission feature indeedappears right below the CW SHG, reminiscent of the HX in monolayerWSe2. Figure 3c shows a rescaled plot, where the gate voltage depen-dence of this feature is clearly resolved and closely correlates with thegate voltage dependence of the band-edge excitons in Fig. 3a. Weassign this feature to the HX of monolayer MoSe2 and the associatedtrions. Following our initial report of the HX in monolayer WSe216, thisobservation constitutes the first experimental confirmation of thehigh-energy and narrow-linewidth state in another type of TMDCmonolayer. The fact that HX+ andHX− have the same binding energy inthis case, in contrast to the case ofWSe2, matches well with the findingthat positively and negatively charged A excitons have the samebinding energy as seen in Fig. 3a and previously reported in ref. 5. Thisobservation has been supported by the fact that the band-edge elec-trons and holes having the same effective mass5. We further char-acterize the helicities in the n-doped, neutral, and p-doped regimes. Asshown in Fig. 3d–f, HX− and HX+ have the same helicity, opposite tothat of the excitation laser, which matches well with what is expectedfrom the selection rules in Table 1 when there is no resident-carrierpolarization effect. Supplementary Fig. 8 shows the SHG on thefull scale.Theoretical considerations of high-lying trionsNext, we consider the high-lying trions with negative-mass electronsfrom a theoretical perspective. We first analyze the HX binding ener-gies in the parabolic approximation for the bands. We introduce thehole effective mass,mh>0, the CB electron effective mass,m1>0, andthe effective mass of the high-lying electron from the CB+2 band,m2<0. Corresponding electron-hole reduced masses are denoted asμ1 =m1mh=ðm1 +mhÞ and μ2 =m2mh=ðm2 +mhÞ. Accordingly, μ2>0because ∣m2∣>mh16. In the case of HX+, the calculation of the trionbinding energy can be performed following ref. 40 (see also refs.41,42). This calculation yields the binding energy of the HX+ ofapproximately 10% of the HX binding energy, depending on thescreening parameters and the effective masses, in reasonable agree-ment with experimental observations for monolayer WSe2 summar-ized in Table 2 and Supplementary Table 1.The situation with the HX− is more involved. Due to the fact thatthe trion envelope function should be symmetric with respect to thepermutation of identical charge carriers, while the antisymmetry of thetotal wavefunction results from the Bloch amplitudes, the problem forthe HX− is mapped, in the parabolic approximation, to the problem ofthe trion with an effectively reduced mass �μ�1 = ðμ�11 +μ�12 Þ=2 and aneffective-mass ratio σ =2m1m2= mh m1 +m2� �� �. As detailed in Supple-mentary Note 3, the calculations show that, neglecting the non-localdielectric screening effects, the trion binding energy can be recast asEb,HX� =2μ2e4_2k2�μμ21 + χð Þ � 1� �:Here, χ � χ σð Þ≈0:1 ~ 0:5 is the ratio of the trion to exciton bindingenergies in the case of equal effective masses of identical electrons.The analysis shows that for the bound trion to exist, Eb,HX�>0, theeffective masses need to satisfy stringent conditions, mh<2χm1 andm2 <m1mh 1 + 2χð Þ=ðmh � 2χm1Þ, which are not necessarily given forrealistic band-structure parameters (see Supplementary Note 3 for adetailed discussion). Atomistic calculations show, however, that thedispersion of the high-lying CB+2 band is strongly non-parabolic.We analyze the role of quartic terms in the CB+2 dispersion taken inthe simplest form ECB+ 2 = _2k2=2m2 +Bk4, with B > 0. Variationalcalculations presented in Supplementary Note 3 demonstrate thatform2 <0 and a not too small B>0, bound HX− states can exist withbinding energies in the range of 0.1–1 of the exciton binding energy.We also confirm these variational calculations with the model ofcontact interaction of the exciton and free electron, accounting fornon-parabolic terms in the dispersion. Consideration of dielectricscreening by the Rytova-Keldysh potential43 does not qualitativelychange the results. However, a detailed comparison between theTable 1 | The selection rules of the group C3h at +K and −Kvalleys for circularly polarized PLTransition +K valley −K valleyIrrep Helicity Irrep HelicityVB↔CB+2 A0 ↔ E02 σ� A0 ↔ E01 σ +VB↔CB A0 ↔ E01 σ + A0 ↔ E02 σ�Irrep irreducible representation.Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 4experiment and theory, and fitting of the binding energies, requiresaccounting for the dielectric screening and the full dispersion of CB+2, including its anisotropy, and goes beyond the current work.Electrical control of excitonic quantum interferenceHaving presented experimental evidence and a theoretical rationali-zation of high-lying trions, we now turn to the influence of the elec-trical tunability of these species on excitonic quantum interference.Optical re-excitation of one and the same electron by a femtosecondlaser pulse can drive direct transitions between the band edge and thehigh-lying conduction band, providing an optical couplingmechanismthat interconverts the band-edge A exciton and an HX state16,17. Such ahigh-energy state is clearly identified in the two-photon excitationspectrumbut not in the luminescence16, and is therefore attributed to adark p-like HX. Because of the lack of an inversion center inmonolayerWSe2, both the s-like and p-like excitons at the band edge are mixedand can be simultaneously one- and two-photon active44. However, thep-states are expected to dominate the two-photon absorption44. Thesame should be true for the trions. Together with the ground state ofthe system, i.e. the state where no exciton is present, an excitonicthree-level system is formed. Interactions with the light field can thenbe treated in analogy to the familiar case of atomicmulti-level systemsin quantum optics17,45. As illustrated in the left panel of Fig. 4b, laser-driven transitions between states can undergo Rabi oscillations.The associated quantum interference between |1> → |2> and |1>→|2> → |3> → |2> transition pathways is then observed in the SHG spec-trum generated by a femtosecond laser pulse17. These interferencesappear as dips in the SHG spectrumalongwith a characteristic spectralanti-crossing feature in the excitation-energy dependence of the SHGspectra, shown in the left panels of Fig. 4a.In analogy to the neutral excitonic three-level system reportedpreviously16,17, it is conceivable that a band-edge trion and a p-like HXtrion can also form a three-level system, which should give rise to ana cbd feHX-HX- HX+X-XMonolayer MoSe2X+ HX+HX-HX+SHGHX0HX021 meVHX0C-excitonVgate = 2 Vn-dopedVgate = 0 VneutralVgate = -2 Vp-dopedg h iHX- HX+�-+K -K +K -K +K -K�-CB+2±CB±VB±�+Fig. 3 | High-lying excitons and trions in monolayer MoSe2. a Dopingdependence of band-edge excitons (X) from monolayer MoSe2, measured bythe PL as a function of the gate voltage applied to a top graphite electrode.b UPL as a function of gate voltage. The excitation is at 1.654 eV in resonancewith X. The features attributed to the neutral HX, and the negatively andpositively charged HX are marked as HX0, HX−, and HX+, respectively. c Arescaled plot of panel B highlighting the HX emission. d–f Polarization resolvedUPL spectra at gate voltages of 2 V (d), 0 V (e), and −2 V (f). g Illustration ofresonant pumping scheme of the A exciton in the +K valley with a σ+ circularlypolarized CW laser. The inset illustrates the Auger-like exciton-excitonannihilation process. h Schematic of the dominant negatively charged high-lying trion at the +K valley, with σ− polarized emission. i Schematic ofthe dominant positively charged high-lying trion at the +K valley, withσ− polarized emission.Table 2 | Experimental binding energies of the high-lyingtrions and band-edge trions in hBN encapsulated monolayerWSe2 and MoSe2High-lying trions WSe2 MoSe2HX− HX+ HX− HX+Binding energy (meV) 43 35 21 21Band-edge trions X�S X�T X+ X− X+Binding energy (meV) 36 29 21 26 26Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 5additional quantum-interference feature in the resonant SHG of thecoherently driven system. We note that the stability of excited trionstates is a separate theoretical problem, see refs. 26,40,46 for details,and thus refrain here froma precise assignment of the excited chargedHX state involved in the quantum interference process. We use theterm “charged p-like HX” here for brevity.Figure 4a shows the gate-voltage dependence of SHG excitationspectra frommonolayer WSe2. Themeasurement was carried out witha wavelength-tunable laser with 80 fs pulse duration. With increasinggate voltage and thus electron-doping density, the A exciton energyand the corresponding anti-crossing feature in the spectrum shift tohigher energies. Remarkably, an additional anti-crossing feature (grayarrow in the second panel from the right) appears at a gate voltage of1.5 V, 42meV below the main transparency dip. For ladder-type three-level systems, the position of this dip translates directly to the energyof the associated high-lying state17,47, which in this case can tentativelybe assigned to the p-like HX− trion. Interestingly, upon further increaseof the gate voltage, this additional anti-crossing feature shifts to thered, opposite to the shift direction of the main anti-crossing feature.This opposite doping dependencematches well with the expectationsfor a charged and a neutral exciton, as outlined in SupplementaryFig. 1d for the band-edge A exciton and the corresponding trions. Wetherefore assign this additional spectral anti-crossing feature to thecharged p-like HX and obtain an energy difference of roughly 42meVbetween the charged and the neutral p-likeHX. This energy difference,measured by the resonant SHG, coincides perfectly with the 43meVenergy difference between the s-like HX− and the zero-phonon line ofthe s-like HX found in the UPL spectra in Fig. 1f.Signatures of quantum interference in the SHG spectrum alsoprovide insight into the coherence timeof the excitonic species, whichis a crucial parameter enabling the quantum-interference phenom-enon as shown by simulations in the density-matrix formalism17. Sincesimilar spectral features are observed in the neutral and chargedexcitonic three-level system, we conclude that the coherence times ofthe excitons and the trions must be comparable. This conclusion of asignificant coherence time of the trion is supported by the relativelyweak effect of the electron-trion scattering, consistent with previouswork on trions and the Fermi polaron description of the effect6,26,48,49.Finally, we evaluate the potential to control the excitonic quan-tum interference electrically. The electrical gate tunes the charge-carrier density in the monolayer and leads to a change in both theoscillator strength and the detuning of the excitonic transitions(Supplementary Fig. 1d). These changes are expected to alter the Rabifrequency. Figure 4c shows the voltage dependence of the SHGspectrum generated under 1.7 eV excitation, revealing a dramaticchange in the spectral structure. Figure 4d exhibits three examples ofSHG spectra at gate voltages of 2.4, 0, and −2.4 V. With simulations ofthe density-matrix dynamics it can be shown that each dip in the SHGspectrum corresponds to one full Rabi cycle of the strongly drivensystem17. At 2.4 V, the SHG spectrumdoes not showanyprominent dip:in this case, noRabifloppingoccurs.At−2.4 V, one cleardip emerges inthe spectrum, implying one Rabi cycle. At 0 V, two dips are identified,implying that thedriven systemmustundergo twoRabi cycles. Suchanevolution of the number of Rabi cycles with electrical gate voltagedemonstrates an unprecedented control over a quantum-opticalphenomenon in the form of excitonic quantum interference.DiscussionWe have demonstrated the existence of UV-emissive trions in bothWSe2 and MoSe2 monolayer transistor structures. These unusualexcitonic species exhibit a high degree of valley polarization, corro-borating our earlier conclusion that high-lying excitons originate fromthe ±K-points in momentum space and consist of an electron from ahigh-lying conduction band CB+216. We systematically studied thehigh-lying trions comprising negative-mass electrons in theory andhave uncovered a broad set of conditions under which such trions canbe stable. In addition to the bright high-lying trions, we identify a darkhigh-lying trion that couples with band-edge trions to form a chargedexcitonic three-level system, which enables laser-driven excitonicquantum interference. We show that excitonic quantum interferenceFig. 4 | Electrical control of excitonic quantum interference involving the p-like high-lying trion inmonolayerWSe2. a Excitation-energy dependence of SHGspectra at gate voltages of 0, 0.5, 1.5, and 2.5 V, measured under excitation by alaser of 80 fs pulse length.b Illustration of an excitonic three-level systembasedonneutral and charged species. The neutral three-level system is formed by the band-edgeA excitonand thep-likeHX. Anegatively charged three-level system is formedby the band-edge trion and the charged p-like HX. c Gate-voltage dependence ofthe SHG spectrummeasured at an excitation energy of 1.7 eV.d SHG spectra at gatevoltages of 2.4, 0, and −2.4 V. Black arrows mark the SHG dips. The gray linepresents the same spectrumat0 V (blue line)multipliedby 10 at the correspondingenergy range, showing the UPL of the s-like HX. All measurements were per-formed at 5 K.Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 6from both neutral and charged excitonic three-level systems can becontrolled by the gate voltage. The number of Rabi cycles under-gone during the laser pulse can be tuned via the gate voltage withoutchanging the laser power. Such electrical control of quantum inter-ference is not conceivable in conventional quantum-optical experi-ments on dilute atomic gases. Our findings therefore expand thespectral working range of future valleytronic devices to the UV, andopen up new possibilities for quantum nonlinear optoelectronics.MethodsDevice fabricationWe fabricate the monolayer WSe2 and MoSe2 transistors by a dry-transfer method50. Monolayer WSe2, monolayer MoSe2, few-layerhexagonal boron nitride, and few-layer graphite flakes are exfoliatedfrom bulk crystals (WSe2 and MoSe2, HQ Graphene; hBN, NIMS) ontoPDMS films (Gel-Pak, Gel-film X4) using Nitto tape. We stack theselayers onto a Si/SiO2 substratewith prepatterned gold electrodes usinga stamping method. A microscope image of a representative device isshown in Fig. 1c.Optical spectroscopyWe cool down the sample to 5 K in a helium-flow microscope cryostat(Janis, ST-500).We focus the laser onto the samplewith an objective of0.6 numerical aperture (Olympus, LUCPLFLN, 40×) and measurereflected signals. Tomeasure the PL,weuse anargon-ion laser (SpectraPhysics, 2045E) at 488 nm for excitation and a 488 nm long-pass edgefilter to remove the laser line. To measure the UPL, we use a tunablecontinuous-wave laser (Sirah, Matisse CR) for excitation and a 680nmshort-pass filter to remove the laser line. For the helicity-resolvedmeasurements, we use a Berek compensator (Newport) to generatethe circularly polarized excitation and determine the signal polariza-tion through a combination of a superachromatic quarter-wave plateand a polarizer. To measure SHG, we use a tunable pulsed Ti:sapphirelaser (Mai Tai XF, 80MHz repetition rate) for excitation and a 680nmshort-pass filter to remove the laser line. For both PL and UPL mea-surements, we use a grating of 600 grooves mm−1 to disperse thesignals and a CCD camera (Princeton Instruments, PIXIS 100) fordetection. For SHG, a grating of 1200 grooves mm−1 is used.Data availabilitySource data for figures are provided with the paper. Any additionaldata are available from the corresponding authors upon reasonablerequest.References1. Wang, G. et al. Colloquium: excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).2. Liu, G.-B. et al. Electronic structures and theoretical modelling oftwo-dimensional group-VIB transition metal dichalcogenides.Chem. Soc. Rev. 44, 2643–2663 (2015).3. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semi-conductor transition metal dichalcogenides. Nat. Photonics 10,216–226 (2016).4. Mak, K. F. et al. 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Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1,011002 (2014).AcknowledgementsThe authors thank Paulo Eduardo Faria Junior and Yaroslav Zhumagulovfrom thegroupof Jaroslav Fabian formanyhelpful discussions,ChristianBäuml and Nicola Paradiso from the group of Christoph Strunk for pre-paring substrates with prepatterned gold electrodes, and SebastianKrug for technical support. Financial support is gratefully acknowledgedfrom the Deutsche Forschungsgemeinschaft (DFG, German ResearchFoundation) through SFB 1277 (Project-ID: 314695032) projects B03,B05, and B11, SPP 2244 (Project-ID: LI 3725/1-1, 443378379), an Emmy-Noether Grant (Project-ID: CH 1672/1-1, 287022282), and the Würzburg-DresdenCluster of Excellence onComplexity and Topology inQuantumMatter ct.qmat (EXC2147, Project-ID: 390858490).Growthof hexagonalboron nitride crystals was supported by the Elemental Strategy Initiativeconducted by the MEXT, Japan (Grant Number JPMXP0112101001) andJSPS KAKENHI (Grant Numbers 19H05790 and JP20H00354). M.M.G. isgrateful to the Russian Science Foundation, Grant No. 19-12-00051(analytical theory); M.A.S. acknowledges support from RFBR Grant No.19-52-12038 (numerical computations).Author contributionsK.-Q.L. conceived theproject andcarriedout themeasurementswith thesupport of S.B.; J.D.Z. and A.C. fabricated the gate-tunable devices;M.M.G., M.A.S., and J.V.M. contributed the theoretical work; K.W. andT.T. provided hBN crystals. K.-Q.L., J.D.Z., M.A.S., J.V.M, S.B., A.C.,M.M.G., and J.M.L. discussed the results, analyzed the data, and con-tributed to the writing of the manuscript.FundingOpen Access funding enabled and organized by Projekt DEAL.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-33939-w.Correspondence and requests formaterials shouldbe addressed to Kai-Qiang Lin or Mikhail M. Glazov.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to the peer review of thiswork. Peer reviewer reports are available.Reprints and permission information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in 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 any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-33939-wNature Communications |         (2022) 13:6980 8https://doi.org/10.1038/s41467-022-33939-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ High-lying valley-polarized trions in 2D semiconductors Results Electrical tuning of high-lying trions in monolayer WSe2 Valley polarization of high-lying trions High-lying excitons and trions in monolayer MoSe2 Theoretical considerations of high-lying trions Electrical control of excitonic quantum interference Discussion Methods Device fabrication Optical spectroscopy Data availability References Acknowledgements Author contributions Funding Competing interests Additional information