# Fileset

[s41467-025-65725-9.pdf](https://mdr.nims.go.jp/filesets/ac5b8d0f-23c8-4131-ab6a-1d9737b4d5ba/download)

## Creator

Minjeong Kim, Taeho Kim, Anna Galler, Dasol Kim, Alexis Chacon, Xiangxin Gong, Yuhui Yang, Rouli Fang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), B. J. Kim, Sang Hoon Chae, Moon-Ho Jo, Angel Rubio, Ofer Neufeld, Jonghwan Kim

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Quantum interference and occupation control in high harmonic generation from monolayer WS2](https://mdr.nims.go.jp/datasets/1621cd7f-654a-4948-970e-3a32754bebae)

## Fulltext

Quantum interference and occupation control in high harmonic generation from monolayer WS2Article https://doi.org/10.1038/s41467-025-65725-9Quantum interference and occupationcontrol in high harmonic generation frommonolayer WS2Minjeong Kim1,2,13, Taeho Kim1,2,13, Anna Galler 3,4,13, Dasol Kim1,Alexis Chacon 1,5,6,7, Xiangxin Gong8, Yuhui Yang8, Rouli Fang 8,Kenji Watanabe 9, Takashi Taniguchi 10, B. J. Kim11, Sang Hoon Chae 8,Moon-Ho Jo 1,2,11, Angel Rubio 4 , Ofer Neufeld 12 &Jonghwan Kim 1,2,11Two-dimensional hexagonal materials such as transition metal dichalcogen-ides exhibit valley degrees of freedom, offering fascinating potential for valley-based quantum computing and optoelectronics. In nonlinear optics, the K andK’ valleys provide excitation resonances that can be used for ultrafast controlof excitons, Bloch oscillations, and Floquet physics. Under intense laser fields,however, the role of coherent carrier dynamics away from the K/K’ valleys islargely unexplored. In this study, we observe quantum interferences in highharmonic generation frommonolayer WS2 as laser fields drive electrons fromthe valleys across the full Brillouin zone. In the perturbative regime, interbandresonances at the valleys enhance high harmonic generation through multi-photon excitations. In the strong-field regime, the high harmonic generation issensitively controlled by quantum interferences of laser-field-driven electronsoccupying various points in the Brillouin zone, including regions far from theK/K’ valleys. Our experimental observations are in strong agreement withquantum simulations, validating their interpretation. This work proposes newroutes for harnessing laser-driven quantum interference in two-dimensionalhexagonal systems and all-optical techniques to occupy and read-out elec-tronic structures in the full Brillouin zone via strong-field nonlinear optics,advancing quantum technologies.Under intense laser fields solids exhibit extreme nonlinear opticalresponses, such as high-harmonic generation (HHG)1,2. Recently, HHGhas been demonstrated in diverse material systems—superconductors3, Mott insulators4,5, topological solids6–9—and hasgarnered substantial interest as a powerful tool for exploring non-equilibrium quantum phenomena in condensed matter, includingBloch oscillations10,11, charge coherence12,13, and phonon dynamics14–16.The initial step in HHG is the coherent excitation of electrons from thevalence to the conduction bands, forming an electron-hole wavepacket10,11,17–19. Subsequently, two primary mechanisms contribute toHHG: (1) interband transitions, which induce nonlinear optical polar-izations via electron-hole recombination, and (2) intraband transitions,which generate laser-driven anharmonic currents. Two-dimensional(2D) hexagonal materials such as transition metal dichalcogenidesprovide a fascinating platform for investigating strong-field physics insolids. Due to the degenerate band gaps at the K and K’ valleys—wherenonzero Berry curvature arises—HHG is intimately connected to valley-specific excitations and all-optical readout20–24. Interband excitationand recombination can be resonantly enhanced at the band edges bystrong Coulomb interactions in atomically thin 2D structures20,25–27.Received: 30 March 2025Accepted: 21 October 2025Check for updatesA full list of affiliations appears at the end of the paper. e-mail: angel.rubio@mpsd.mpg.de; ofern@technion.ac.il; jonghwankim@postech.ac.krNature Communications |         (2025) 16:9825 11234567890():,;1234567890():,;http://orcid.org/0000-0002-8596-7784http://orcid.org/0000-0002-8596-7784http://orcid.org/0000-0002-8596-7784http://orcid.org/0000-0002-8596-7784http://orcid.org/0000-0002-8596-7784http://orcid.org/0000-0002-9279-4463http://orcid.org/0000-0002-9279-4463http://orcid.org/0000-0002-9279-4463http://orcid.org/0000-0002-9279-4463http://orcid.org/0000-0002-9279-4463http://orcid.org/0000-0003-3800-0180http://orcid.org/0000-0003-3800-0180http://orcid.org/0000-0003-3800-0180http://orcid.org/0000-0003-3800-0180http://orcid.org/0000-0003-3800-0180http://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/0000-0002-9612-5371http://orcid.org/0000-0002-9612-5371http://orcid.org/0000-0002-9612-5371http://orcid.org/0000-0002-9612-5371http://orcid.org/0000-0002-9612-5371http://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0002-5477-2108http://orcid.org/0000-0002-5477-2108http://orcid.org/0000-0002-5477-2108http://orcid.org/0000-0002-5477-2108http://orcid.org/0000-0002-5477-2108http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65725-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65725-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65725-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65725-9&domain=pdfmailto:angel.rubio@mpsd.mpg.demailto:ofern@technion.ac.ilmailto:jonghwankim@postech.ac.krwww.nature.com/naturecommunicationsIntraband carrier dynamics also generate nonlinear anomalous andregular currents28,29, enabling the reconstruction of the Berrycurvature28 and energy dispersions30–32 across the Brillouin zone (BZ).While bulk materials have shown that strong-field-driven quantuminterference between interband and intraband excitation pathwayscan manipulate HHG11,33,34, the corresponding effects in 2D hexagonalmaterials remain largely unexplored.In the perturbative laser-field regime, local excitation near the Kand K’ valleys dominates the optical response, offering fundamentalphysical principles for valleytronic applications that utilize coherentvalley-selective excitations as effective two-level systems35. Althoughtheoretical models often match experimental data under these con-ditions, they typically focus only on the valleys and ignore the moreintricate band structure away from these high-symmetry points35. Onthe other hand, when the laser field is sufficiently strong, excited car-riers in the valleys can travel across the entire BZ, including to non-high-symmetry k-points with local energy minima or saddle points.While these alternative k-points do not benefit from valley-specificselection rules or minimal bandgap resonances, their coherent exci-tation under strong-field conditions can manipulate electrons fornonlinear optical applications similar to those in valleytronics, effec-tively forming a 2-level-like quantum system that can be controlledusing light. Fully capturing these dynamics requires capabilities thatdrive excitation beyond the K/K′ valleys and identify the uniquespectral signatures associated with such extended electron–hole wavepackets.In this study, we investigate how HHG evolves in monolayer WS2as photo-excited carriers localized within valleys expand throughoutthe BZ. By irradiating WS2 with mid-infrared pulses at 0.28 eV—reso-nant with a seven-photon transition to the optical gap—we initiateultrafast carrier dynamics in the edges of the valence and conductionbands. Systematically increasing the laser intensity causes a transitionto the non-perturbative regime,markedbynontrivial spectral features:(1) a pronounced kink in the harmonic yield’s intensity dependence,and (2) a distinct spectral evolution that exhibits peak splitting andsubsequent merging. Using ab-initio and model quantum mechanicalsimulations, we attribute these phenomena to quantum interferencearising from laser-field-driven carriermotion transitioning from valley-localized states to highly delocalized states across the BZ, includingthe Γ andMpoints, aswell as from interferencebetween interband andintraband pathways. These findings provide a new mechanism tocoherently populate and read out diverse electron–hole super-positions, expanding our ability tomanipulate and probe the full BZ of2Dhexagonal solids.Our study thus provides insight that canpave newavenues in ultrafast valleytronics, ultrafast quantum information, andrelated fields.Results and discussionTransition from perturbative to strong-field driven HHG inmonolayer WS2Figure 1a schematically illustrates the electronic processes in mono-layer WS2 initiated under intense laser driving. In the perturbativeregime, nonlinear optical processes primarily arise from excitonicmultiphoton transitions at the band gaps located at the K and K′ val-leys. Under intense laser fields, excitons become substantially delo-calized through hybridization with higher excitonic bound states andcontinuum states36. Eventually, ionized electrons and holes are drivenfar beyond the K andK′ valleys over wide regions ofmomentum space,which opens additional pathways for higher-order nonlinear opticalprocesses via intraband and interband transitions.We fabricate large-area, high-quality, WS2 monolayers using agold-assisted exfoliationmethod37. To further reduce external defects,the exfoliated monolayer WS2 is encapsulated with hexagonal boronnitride on sapphire substrates via a dry transfer process38. Ourhome-built femtosecond laser system provides linearly-polarized,mid-infrared pulses with ~ 120 fs duration at 100 kHz repetition rate.We intentionally set the photon energy at ~ 0.28 eV (4500nm) tomatch the 7-photon resonant exciton transition at the band edge. Thelaser power and polarization are precisely controlled and analyzedusing polarization optics. HHG spectra are recorded with an electron-multiplying charge-coupled device to achieve a high signal-to-noiseratio. Owing to the combined advantages of high sample quality andhigh repetition rate, we can sensitively observe the quantum inter-ference features from the perturbative to the non-perturbativeregimes, as will be shown below. Additional details on sample pre-paration, laser setup, and a comparison of HHG spectra with andwithout hBN encapsulation are provided in the Supplementary Infor-mation (SI).We now investigate HHG in monolayer WS2 as a function thedriving intensity. HHG signals are collected and integrated for bothparallel and cross-polarization components with respect to the drivinglaser fields. HHG spectra exhibitmarkedly different profiles dependingon the laser intensity (see Fig. 1b, c). At ~ 110GW/cm2 (red solid line inFig. 1c), strong 7th harmonic signals are observed at 1.93 eV, while allother harmonic orders—including lower harmonic orders—are nearlyabsent. This selective enhancement arises from excitonic resonancesat the K and K’ valleys. The reflection contrast spectrum (Fig. 1e) andHHG spectrum (Fig. 1d) show absorption and photoluminescencepeaks at 2 eV, respectively, originating from 1 s exciton resonances atthe optical gap. The 7th harmonic signal is located near 1 s excitonresonances with a small detuning of 70meV. Up to ~185 GW/cm2 laserdriving, the yield of 7th harmonic in Fig. 1f scale as ∝ I 7 with respectto laser peak intensity (I). A similar intensity dependence is observedfor photoluminescence under mid-infrared laser excitation (see SI),indicating that all optical processes observed in this regime are pri-marily mediated by the 7-photon transitions to the resonant exci-tonic state. Such excitonic enhancement has been experimentallyreported for second harmonic generation in TMD monolayers andheterostructures39,40. Recent theoretical studies predict that exci-tonic resonances can also strongly enhance high-order harmonicgeneration26,36,41,42, in agreement with our experimental observations.At higher driving intensity ( >185 GW/cm2), an HHG plateau spanning5–11th harmonics emerges (Fig. 1b, c). Under these conditions, theHHG yield becomes non-perturbative, including for the 7th harmonic—the main observable analyzed in this study. Notably, Fig. 1f reveals apronounced kink at ~200GW/cm2, which is not expected from theperturbative response, and which we will analyze with theorylater on.The crystal orientation dependence of the 7th harmonic yield alsoindicates the transition from the perturbative to the non-perturbativeregime. Figure 2b–f present the integrated yield as a function of theangle between the laser field and the WS2 zigzag direction (see theillustration in Fig. 2a). The crystal axis of WS2 is determined frompolarization analysis on even order harmonics (see SI). Polarizationanalysis confirms that the 7th harmonic is absent for the polarizationcomponent perpendicular to the driving laser field, as expected fromHHG dynamical mirror-symmetry selection rules20,43 (see SI). At a laserintensity of ~ 125GW/cm², dominated by the perturbative responsefrom excitonic resonances, no apparent dependence on crystalorientation is observed (i.e., an isotropic response). However, in thenon-perturbative regime, harmonic signals exhibit strong 60° periodicmodulation, which becomes increasingly pronounced as the laserintensity rises from ~ 235 to 380GW/cm², accompanied by significantchanges in modulation depth and phase (with 60o periodicity, asexpected from crystal symmetry44) – Initially, polar plots show stron-ger harmonic yields along the armchair direction, but as the laserintensity increases the polar plot rotates by 30°, revealing strongeryields along the zigzag direction. Figure 2f is consistent with previousworks20,21 in extreme laser intensities (>1 TW/cm2). The systematicmodification of polar plots is indicative of a change in laser excitationArticle https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 2www.nature.com/naturecommunicationsregime, and potentially also the physical mechanisms dominatingHHG, as will be discussed below.Laser intensity-dependent quantum interference in the 7thharmonic spectraFigure 3c presents a 2D color map of high-spectral-resolution 7thharmonic spectra from monolayer WS2 driven in the zig-zag direc-tion as a function of laser intensity (nearly identical spectra areobserved along the armchair direction, see SI). There are three keysurprising results here, which form themain findings of this letter: (i)At ~ 150 GW/cm² where non-perturbative responses emerge from thelaser-field-driven carriers, a very significant peak broadening arises.(ii) At slightly higher powers ( ~200GW/cm2) multiple distinct peaksemerge from the sharp peak that is characteristic of lower intensitydriving. At yet higher intensities, ~250GW/cm², these split peaksconverge, resulting in a broader recombined spectral profile. (iii)This evolution is accompanied by a notable kink in the integratedyield of the 7th harmonic (see Fig. 1f and Fig. 3a) over the same laserintensity range, whereby the yield does not increase with increasingdriving intensity.In the perturbative regime, harmonic spectral profiles are pri-marily dictated by the driving pulse shape, typically exhibitingGaussian-like profiles43. Beyond the perturbative regime, however, thespectral profile can also be affected by interference between multiplequantum pathways of charge carriers that emerge on sub-laser-cycletimescales. Specifically, interference between distinct quantumFig. 1 | Non-perturbative response of lightwave-driven electron-hole pairs inmonolayer WS₂. a Illustration of the electronic processes under strong laserexcitation: Intense laser driving excites carriers throughout the BZ, and drives themin the respective bands. Interband recombination and intraband currents (red andgray arrows, respectively) emit HHG from various points in the BZ, includingbeyond K/K’ valleys. In inset is an illustration of an electrons and holes driven bylaser fields. b Experimentally measured HHG spectra as a function of laser intensityfrom 80 to 350GW/cm². Note that harmonic yield in (b) is plotted in a logarithmicscale. The spectra display markedly different profiles in the perturbative and non-perturbative regimes, showing onset of HHG plateau at higher driving, and theresonant 7th harmonic appearing in much lower intensities. c Line-cuts of HHGspectra from (b). d Photoluminescence spectra showing clear excitonic signatureswith 1 s exciton resonance at 2 eV. e Reflection contrast spectrum indicatingabsorption near 2 eV, associated with the 1 s exciton resonance. f Measured inte-grated 7th harmonic yield as a function of laser intensity (obtained from (b)),showing a kink feature arising for both zigzag and armchair orientations. Note that(f) is plotted in a logarithmic scale.Article https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 3www.nature.com/naturecommunicationspathways can produce spectral fringes, including peak splitting, thatreflect the complex dynamics of charge carriers (as has been observeddue to othermechanisms in bulk systems10,45–47). Thus, we hypothesizethat these phenomena all arise from multiple quantum path inter-ferences. The main question is then which paths dominate theresponse of WS2 in this regime?To address this question, we perform exhaustive theoreticalcalculations based on several levels of theory. First, ab-initio time-dependent density functional theory (TDDFT) simulations are per-formed and compared with the experiment. Unfortunately, due tothe very long-wavelength driving TDDFT fails to reproduce thedominant experimental features. This arises primarily becauseTDDFT does not include sufficient dephasing channels, which arehighly relevant and can significantly alter the HHG spectra in ourconditions48 (because a single driving field period is ~ 15 fs, meaningdephasing occurs already within a single laser cycle, with recentdephasing times expected to be ~ fs on average49). Nonetheless, theTDDFT simulations allow us to conclude that in our conditionscontributions from electronic correlations and higher- or lower-order conduction and valence bands are expected to be minor in theoverall response (see SI). Consequently, we develop a simple two-band model based on a tight-binding (TB) Hamiltonian (with anapproach similar to that in refs. 50,51 see SI), which we employ insemiconductor Bloch equations (SBE) in the length gauge in a densitymatrix formalism52,53 (given in a.u):∂∂tρvvðk, tÞ= iEðtÞ � dcv kð Þρ*cv k, tð Þ � d*cv ρcvðk, tÞh i∂∂tρcv k, tð Þ= � iðεCB k tð Þð Þ � εVB k tð Þð Þ � iT2Þρcv k, tð Þ+E tð Þ � dcc kð Þ � dvv kð Þ� �ρcv k, tð Þ+dcv kð Þ 2ρvv k, tð Þ � 1� � !26643775ð1ÞwherekðtÞ=k0 +1cAðtÞ, withk0 the crystalmomentumat t = 0, and EðtÞthe electric field vector (in the dipole approximation), which is con-nected to the vector potential via:�∂tAðtÞ= cEðtÞ, and c is the speed oflight. In Eq. (1),ρij is the densitymatrix, εCB=VB is the band eigen-energy,dij are transition dipole matrix elements, and T2 is the phenomen-ological dephasing time (taken as 5 fs49). From the density matrix weobtain the time-dependent current, J tð Þ= Jintra tð Þ+ JinterðtÞ (separatedto inter- intra-band contributions):JintraðtÞ= �Xk2BZ½ρvvðk, tÞpvvðkðtÞÞ+ρccðk, tÞpccðkðtÞÞ�JinterðtÞ= �Xk2BZ2Re½ρcvðk, tÞpvcðkðtÞÞ�ð2Þwhere pij are the momentum matrix elements. All momentum anddipolematrix elements, as well as band energies, are obtained through0500010000150000306090120150180210240270300330X1.305000100000306090120150180210240270300330X20100020000306090120150180210240270300330X10= / = 235 /= 305 / = 350 /050001000015000200000306090120150180210240270300330= 380 /a b cd e fArmchairZigzagWS0501000306090120150180210240270300330X200Fig. 2 | Crystal orientation dependence of the 7th harmonic generation yield.a Schematic of themonolayerWS₂ crystal structure and laser polarization axis (redarrow). The x(y)-axis corresponds to the zigzag (armchair) directions, respectively.The angle θ represents the counterclockwise rotation of the excitation laserpolarization relative to the zigzag axis. b–f Crystal orientation dependence ofseventh harmonics at increasing laser peak intensities: b 125 GW/cm², c 235 GW/cm², d 305GW/cm², e 350GW/cm², and f 380GW/cm². For low driving power theharmonic response is isotropic and perturbative. At higher intensity in the transi-tion to non-perturbative HHG, a distinct six-fold pattern emerges with emissionalong the armchair direction. At yet higher intensity the six-fold pattern is slightlyless pronounced and rotated by 30°, exhibiting stronger harmonic intensity alongthe zigzag direction. The harmonic signals in (b), (c), (d), and (e) are magnified byfactors of 200, 10, 2, and 1.3, respectively, to clearly visualize the pattern evolutionat lower laser intensities.Article https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 4www.nature.com/naturecommunicationsanalytical expressions from the TB Hamiltonian, which is optimallyfitted to DFT bands throughout across entire BZ with an accurate 14th-order nearest-neighbor Hamiltonian (where spin is neglected and withthe gap at K/K’ offset to match experimental values, as it is oftenunderestimated in DFT). From J tð Þ we compute the HHG spectrum asIHHG Ωð Þ= R dtf tð Þ∂t J tð Þe�iΩt�� ��2, with f tð Þ being a super-gaussianwindowfunction. For all additional technical details of the propagation andnumerical procedures see the SI.Figure 3b, d, f present numerical results employing the SBE-TBformalism, showing strong agreement with the experiment. The simu-lations correctly predict the kink in the 7th harmonic yield vs. peakintensity (Fig. 3d). A pulse duration of ~ 200 fs is employed to resolve thepeak splitting in Fig. 3d. In the inset of Fig. 3d, we confirm that nearly thesamebehavior is observed for a pulse duration of ~120 fs, correspondingto the actual experimental value. The total current (red line) can bedecomposed into intraband (green line) and interband (blue line)components, elucidating that this effect originates from quantuminterference between interband and intraband emission channels—afeature absent in either channel alone and requiring their complete orpartial destructive interference. This is the first observation to ourknowledge of such clear interferences in 2D systems. We note that theonset intensity of this effect is overall higher in the theory, likely due toFig. 3 | Quantum interference in harmonic generation. a The 7th harmonic yieldvs. peak intensity in the zigzag direction (same as Fig. 1(f)). b Theoretical calculation ofthe 7th harmonic yield vs. peak intensity under laser excitation along the zigzagdirection. We use a pulse duration of ~200 fs to resolve the peak splitting in (f). Weconfirm that nearly the same behavior is observed for a pulse duration of ~120 fs,corresponding to the actual experimental value (inset). The total current (red line) canbe decomposed into intraband (green line) and interband (blue line) components,demonstrating that the kink arises from quantum interference between interband andintraband transitions. c Experimental and d theoretical 2D color map of the 7th har-monic spectra as a function of peak intensity under excitation along the zigzagdirection, respectively. The color is plotted on a logarithmic scale. e Normalized 7thharmonic spectra at specific laser peak intensity corresponding to 145, 195, 210, and255GW/cm², which are linecuts of (c). At low laser field strength, a single peak isobserved, but as the field strength increases, this single peak begins to broaden andsplit into multiple peaks, indicating the emergence of an interference between differ-ent electron pathways or transitions. As the field strength further increases to 255GW/cm² and beyond, the formation of shoulder peaks becomes more pronouncedpotentially due to more complex quantum pathways or transitions. f Theoretical cal-culation of normalized 7th harmonic spectra at the specific laser peak intensity cor-responding to 100, 375, 600 and 900GW/cm², which is the linecut of (d). Thecalculated spectra exhibit interference patterns that closely resemble the experimentalobservations, particularly in the peak broadening and the emergence ofmultiple peaksat higher field strengths. All calculations were performed using the Tight Bindingmodel, which was employed for solving the Semiconductor Bloch Equations.Article https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 5www.nature.com/naturecommunicationsexcitonic effects not captured in our simulations. Excitonic resonancescan enhance carrier excitation even at lower laser intensities. StrongCoulomb interactions also give rise to tightly bound excitons in realspace, which in turn promote greater momentum-space delocalizationof excited photo-carriers, even without laser-field-driven intrabandexcitations. According to recent studies54, exciton–phonon andexciton–plasmon scattering processes can provide finite momentum tothe carriers. Furthermore, strong-laser-field-driven exciton ionizationprocesses36 can open additional HHG pathways that are not captured bythe current theory. To accurately address the issues above, time-resolved photoemission spectroscopy or time-resolved absorptionspectroscopy under identical mid-infrared excitation can provide directaccess to the probe excitonic states and carrier scattering dynamics inthe time domain. However, such an investigation goes beyond the scopeof the present study.Theoretical analysis of HHG in monolayer WS2At the next stage, our theory reproduces the peak broadening andsplitting dynamics vs. laser intensity (see Fig. 3a–d)). Note that hereweemployedmuch longer driving laser pulses in order to obtain sufficientspectral resolution (~200 fs FWHM), but otherwise employed the sameconditions as in the experiment. In the simulations, such long time-scale dynamics are necessary to be able to resolve peak splitting on anenergy scale of ~0.02 eV. Our theoretical analysis reveals that thesplitting and converging dynamics do not arise solely due to inter-ference of interband and intraband channels, as the effect appears ineach channel separately (see SI for 7th harmonic spectrum frominterband and intraband channels). Togain further insight, weperforma comprehensive k-resolved analysis of the HHG yield, and uncoverthat at the onset of the peak splitting, a substantial portion of the BZ isexcited (comparing occupations in Fig. 4a, b, middle panel). Indeed, athigh laser powers, electrons occupy not only regions near K/K’ valleys,but also towards Γ andMpoints. TheHHGemission from these regionsis comparable to that from the K/K′ valleys and, under certain condi-tions, can be even stronger. Mathematically, this is clear due to therelatively low optical gap throughout the BZ (e.g., the gap at Γ is ~ 3 eV,only ~1 eV higher than the gap at K/K’). The detailed spectral profilesare determined by the magnitudes and phases of the HHG emission,which depend on specific laser excitation conditions including finitebeam size, temporal and spectral pulse profiles45,55. Nevertheless, thisresult clearly indicates that the peak splitting originates fromquantuminterference of laser-field-driven carriers occupying multiple k-pointsincluding regions near Γ and M points.This conclusion is further validated by performing additionalsimulations where the TB Hamiltonian is modified to reproduce thecorrect electronic structure only near K/K’ valleys, while the gap isartificially increased towards Γ and M to suppress their contribution(see right panels in Fig. 4b, c). Indeed, in these conditions, the peaksplitting phenomena are completely suppressed at identical laserpower, corroborating that interference of emission between differentpoints in the BZ accounts for the physical mechanism of peak splitting(and that specifically the K/K’ valleys, including their Berry curvature,cannot alone account for the effect). The peak closing dynamics at yethigher driving is seen to arise due to increased dominance of theintraband emission channel where the split peak converges.DiscussionIn conclusion, we studied HHG in WS2 monolayers with tunable long-wavelength laser driving. We identified a transition from perturbativeHHG—dominated by bound excitons and valley-confined carriers withnear-isotropic orientation dependence—to a strong-field regime char-acterized by delocalized carrier dynamics across the BZ and pro-nounced anisotropic orientation dependence. In the perturbativeregime, exciton resonances strongly enhance the 7th harmonic nearthe 1 s exciton resonance. As the laser intensity grows, ionized carrierstake over, producing nontrivial spectral features such as splitting andmultiple kinks in the HHG yield. These experimentally observed, andtheoretically validated, phenomena, signify the activation of newquantum pathways in intense fields. Our quantum simulations,including k-resolved analysis, reveal that these effects result fromquantum interference between interband and intraband transitions, aswell as quantum interference of laser-field-driven carriers occupyingmultiple points in the BZ along the laser driving axis. These findingsexpandour understanding of ultrafast carrier dynamics in valley-based2D materials and demonstrate the power of HHG for probinglight–matter interactions in 2D hexagonal systems.Especially, we note that these are the first signatures of suchinterference phenomena in 2D systems, offering a direct all-opticalpathway to not only to selectively excite electrons in various high/low-symmetry points of the hexagonal BZ (beyond K/K’, also Γ andM), butalso read them out as clear spectral interference signatures in HHG.Thus, this work paves the way for the next generation of optoelec-tronic and quantum devices capable of operating at petahertz fre-quencies, and utilizing multiple k-points beyond valleytronics formimicking 2-level quantum systems.MethodsSample fabricationA high-qualitymonolayerWS2 sample was prepared by the gold-assistedexfoliation method. A 150nm thickness gold layer was deposited on aflat silicon substrate with a 90nm thick oxide layer. A poly-vinylpyrrolidone (PVP) solution (Sigma Aldrich, mw 40000, 10% wt inethanol/acetonitrile wt 1/1) was spin-coated on the top of the Au film andcured at 150 °C for 5min. This PVP layer served as a sacrificial layer toprevent contamination from tape residue. The prepared PVP/Au waspicked up with thermal release tape (TRT), revealing an ultra-flat, clean,and fresh gold surface-referred to as the gold tape. The gold tape ispressed onto a freshly cleaved bulk WS2 crystal (HQ graphene). As thetape is lifted off the surface, it carries the PVP/Au layer with amonolayerWS2 crystal attached to the Au surface. And then it is further transferredonto a silicon substrate with a 90nm thick oxide layer. The TRT isremoved by heating at 135 °C. The PVP layer is removed by dissolving indeionized (DI) water for 2 h. Finally, the sample on the substrate, cov-ered by Au layer, was rinsed with acetone and cleaned by O2 plasma for4min to remove any remaining PVP polymer residues.We note thatWS2monolayers are not directly exposed to the O2 plasma during this stepbecause theWS2monolayers are protectedby theAufilm. Finally, theAulayer is dissolved in a KI/I2 gold etchant solution and then themonolayerTMD is rinsed with DI water and isopropanol.The van der Waals heterostructure of WS2 monolayer and hBNwas prepared by the dry transfer technique38. The thickness of WS2monolayer was first identified by the optical contrast of a microscopeimage, followed by the detailed spectroscopic characterization.Approximately 20 nm-thick hBN flakes were exfoliated onto a siliconsubstrate with 90nm oxide layer. To fabricate the encapsulated WS2monolayer, we used the thermoplastic methacrylate copolymer(Elvacite 2552C, Lucite International) stamp to pick up the hBN flakesand WS2 monolayer in sequence with accurate alignment based on anoptical microscope. The Elvacite stamp with the heterostructure wasthen stamped onto a sapphire substrate. The polymer and sampleswere heated up at 70 °C for the pick-up and 200 °C for the stampprocess, respectively. Finally, we dissolved the Elavcite in acetone for3min at 100 °C.HHG measurementsMid-infrared pulses were generated from a femtosecond laser system(Light Conversion PHAROS) using an optical parametric amplifier(ORPHEUS) and a difference frequency generator (LYRA). The outputserved wavelength-tunable multi-cycle pulses with a repetition rate of100 kHz. The fundamental laser wavelength is set at 4.5 µm, that canArticle https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 6www.nature.com/naturecommunicationsavoid strong CO2 absorption bands. The spectral linewidth of thepulse is estimated to be 15.4meV in full width at half maximum(FWHM), and the pulsedurationwas estimated to be 120 fs, assuming aFourier-transform-limited pulse. Laser intensity was precisely con-trolled by a pair of linear polarizers inserted into the beam path. Half-wave plates were also inserted into the beam path to control thepolarization of the excitation laser. The mid-infrared pulses were thenfocused near the center of the monolayer WS₂ sample using ZnSefocusingobjectives, producing a spot size of approximately 30–80 µm.The emitted HHG was collected by a 50× objective lens in a transmis-sion geometry, and its polarization was analyzed by a half-wave platemounted on a motorized stage and a fixed Glan-Taylor polarizer. TheHHG spectra were recorded by an electron-multiplying charge-cou-pled device detector (ProEM, Princeton Instruments) and a gratingspectrometer (SP-2300, Princeton Instruments) atMaterials Imaging &Analysis Center of POSTECH.Data availabilityAll of thedata that support thefindings of this study are available in themain text or Supplementary Information. Source data are availablefrom the corresponding authors on request.Code availabilityTDDFT simulations were performed on Octopus code, which is freelyavailable and is open access. Additional information can be obtainedfrom the corresponding authors upon request.References1. Ghimire, S. et al. Observation of high-order harmonic generation ina bulk crystal. Nat. Phys. 7, 138–141 (2011).2. Ghimire, S. & Reis, D. A. High-harmonic generation from solids.Nat.Phys. 15, 10–16 (2019).3. Alcalà, J. et al. High-harmonic spectroscopy of quantum phasetransitions in a high-Tc superconductor. Proc. Natl Acad. Sci. USA119, e2207766119 (2022).4. Orthodoxou, C., Zaïr, A. & Booth, G. H. High harmonic generation intwo-dimensional Mott insulators. npj Quantum Mater. 6, 76 (2021).5. Murakami, Y., Eckstein,M.&Werner, P.High-harmonicgeneration inmott insulators. Phys. Rev. Lett. 121, 057405 (2018).6. Bai, Y. et al. High-harmonic generation from topological surfacestates. Nat. Phys. 17, 311–315 (2021).7. Heide, C. et al. Probing topological phase transitions using high-harmonic generation. Nat. Photon. 16, 620–624 (2022).-1 -0.5 0 0.5 1x u-1-0.500.51 (a.u.)6.8 7.0 7.202468)stinu .bra(  dlei y GHHHarmonic orderWS2 (modifield large Γ    gap)6.8 7.0 7.202468)stinu .bra( dlei y GHHHarmonic orderWS26.8 7.0 7.201)stinu .bra( dleiy GHHHarmonic orderWS2abcky0.080.070.060.050.040.030.020.01-1 -0.5 0 0.5 1-1-0.500.51 3.532.521.510.50-1 -0.5 0 0.5 1kx (a.u.)-1-0.500.51.50.450.40.350.30.250.20.150.10.050.5-1 -0.5 0 0.5 1 -1-0.500.51 22.533.5-1 -0.5 0 0.5 1 -1-0.500.51 22.533.5-1 -0.5 0 0.5 1kx (a.u.)-1-0.500.51 234567 =10/ =3.75×10/ =3.75×10/ (a. u.)ky (a. u.)kyFig. 4 | Theory of peak splitting in HHG fromWS2. a SBE simulated 7th harmonicspectrum (left), showing no onset of peak splitting at lower power (100GW/cm2).Middle panel shows the k-resolved contributions to this peak, indicating mostlylocalized charge carrier excitation and emission from the K/K’ valleys. Right panelshows the optical gap throughout the BZ in this system. The color is plotted on alinear scale for both middle and right panel. b Same as (a) for higher driving power(375GW/cm2)where there is peak-splitting occurring.Here, emission is contributedform delocalized regions in the BZ, including from Γ and M. The evenly spacedinterference pattern in k-space presumably indicates regions with constructive/destructive interference due to the phase of the harmonic emission. c Same as (b)but with themodified TBmodel (see text) that reproduced the electronic structurein WS2 only near the K/K’ valleys (see right panel), where peak splitting does notoccur. The white hexagon shows the outline of the first Brillouin zone edge.Article https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 7www.nature.com/naturecommunications8. Schmid, C. P. et al. Tunable non-integer high-harmonic generationin a topological insulator. Nature 593, 385–390 (2021).9. Neufeld, O., Tancogne-Dejean, N., Hübener, H., De Giovannini, U. &Rubio, A. Are there universal signatures of topological phases inhigh-harmonic generation? Probably not. Phys. Rev. X 13, 031011(2023).10. Reislöhner, J., Kim, D., Babushkin, I. & Pfeiffer, A. N. Onset of Blochoscillations in the almost-strong-field regime. Nat. Commun. 13,7716 (2022).11. Schubert, O. et al. Sub-cycle control of terahertz high-harmonicgeneration by dynamical Bloch oscillations. Nat. Photon 8, 119–123(2014).12. Heide, C. et al. Probing electron-hole coherence in strongly driven2D materials using high-harmonic generation. Optica 9, 512–516(2022).13. Freudenstein, J. et al. Attosecond clocking of correlations betweenBloch electrons. Nature 610, 290–295 (2022).14. Neufeld, O., Zhang, J., De Giovannini, U., Hübener, H. & Rubio, A.Probing phonon dynamics with multidimensional high harmoniccarrier-envelope-phase spectroscopy. Proc. Natl Acad. Sci. 119,e2204219119 (2022).15. Zhang, J. et al. High-harmonic spectroscopy probes latticedynamics. Nat. Photon. 18, 792–798 (2024).16. Rana, N., Mrudul, M. S., Kartashov, D., Ivanov, M. & Dixit, G. High-harmonic spectroscopy of coherent lattice dynamics in graphene.Phys. Rev. B 106, 064303 (2022).17. Wu, M., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation fromBloch electrons in solids. Phys. Rev. A91,043839 (2015).18. Vampa, G. et al. Theoretical analysis of high-harmonic generation insolids. Phys. Rev. Lett. 113, 073901 (2014).19. Yue, L. & Gaarde, M. B. Introduction to theory of high-harmonicgeneration in solids: tutorial. J. Opt. Soc. Am. B 39, 535–555 (2022).20. Yoshikawa, N. et al. Interband resonant high-harmonic generationby valley polarized electron–hole pairs. Nat. Commun. 10, 3709(2019).21. Liu, H. et al. High-harmonic generation from an atomically thinsemiconductor. Nat. Phys. 13, 262–265 (2017).22. Jiménez-Galán, Á, Silva, R. E. F., Smirnova, O. & Ivanov, M. Sub-cycle valleytronics: control of valley polarization using few-cyclelinearly polarized pulses. Optica 8, 277–280 (2021).23. Mrudul,M. S., Jiménez-Galán, Á, Ivanov,M. &Dixit,G. Light-inducedvalleytronics in pristine graphene. Optica 8, 422 (2021).24. Neufeld, O., Hübener, H., Jotzu, G., De Giovannini, U. & Rubio, A.Band nonlinearity-enabled manipulation of Dirac nodes, Weylcones, and valleytronics with intense linearly polarized light. NanoLett. 23, 7568–7575 (2023).25. Hader, J., Neuhaus, J., Moloney, J. V. & Koch, S. W. Coulombenhancement of high harmonic generation in monolayer transitionmetal dichalcogenides. Opt. Lett. 48, 2094 (2023).26. Molinero, E. B. et al. Subcycle dynamics of excitons under stronglaser fields. Sci. Adv. 10, eadn6985 (2024).27. Chang Lee, V., Yue, L., Gaarde, M. B., Chan, Y. & Qiu, D. Y. Many-body enhancement of high-harmonic generation in monolayerMoS2. Nat. Commun. 15, 6228 (2024).28. Luu, T. T. & Wörner, H. J. Measurement of the Berry curvature ofsolids using high-harmonic spectroscopy. Nat. Commun. 9, 916(2018).29. Yue, L. & Gaarde, M. B. Characterizing anomalous high-harmonicgeneration in solids. Phys. Rev. Lett. 130, 166903 (2023).30. Vampa, G. et al. All-optical reconstruction of crystal band structure.Phys. Rev. Lett. 115, 193603 (2015).31. Borsch, M. et al. Super-resolution lightwave tomography of elec-tronic bands in quantummaterials. Science 370, 1204–1207 (2020).32. Lanin, A. A., Stepanov, E. A., Fedotov, A. B. & Zheltikov, A. M.Mapping the electron band structure by intraband high-harmonicgeneration in solids. Optica 4, 516 (2017).33. Hohenleutner, M. et al. Real-time observation of interferingcrystal electrons in high-harmonic generation. Nature 523,572–575 (2015).34. Tancogne-Dejean, N., Mücke, O. D., Kärtner, F. X. & Rubio, A. Ellip-ticity dependence of high-harmonic generation in solids originatingfrom coupled intraband and interband dynamics. Nat. Commun. 8,745 (2017).35. Schaibley, J. R. et al. Valleytronics in 2D materials. Nature Reviews.Materials 1, 16055 (2016).36. Kobayashi, Y. et al. Floquet engineering of strongly driven excitonsinmonolayer tungsten disulfide.Nat. Phys. https://doi.org/10.1038/s41567-022-01849-9 (2023).37. Liu, F. et al. Disassembling 2D van der Waals crystals into macro-scopicmonolayers and reassembling into artificial lattices. Science367, 903–906 (2020).38. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).39. Wang, G. et al. Giant enhancement of the optical second-harmonicemission of \mathrmwse_2 monolayers by laser excitation at exci-ton resonances. Phys. Rev. Lett. 114, 097403 (2015).40. Shree, S. et al. Interlayer exciton mediated second harmonic gen-eration in bilayer MoS2. Nature. Communications 12, 6894 (2021).41. Jensen, S. V. B., Madsen, L. B., Rubio, A. & Tancogne-Dejean, N.High-harmonic spectroscopy of strongly bound excitons in solids.Phys. Rev. A 109, 063104 (2024).42. Chang Lee, V., Yue, L., Gaarde, M. B., Chan, Y. & Qiu, D. Y. Many-body enhancement of high-harmonic generation in monolayerMoS2. Nature. Communications 15, 6228 (2024).43. Shen, Y. R. The Principles of Nonlinear Optics. (Wiley, 2003).44. Neufeld, O., Podolsky, D. & Cohen, O. Floquet group theory and itsapplication to selection rules in harmonic generation. Nat. Com-mun. 10, 405 (2019).45. Xia, P. et al. High-harmonic generation in GaAs beyond the pertur-bative regime. Phys. Rev. B 104, L121202 (2021).46. Sekiguchi, F. et al. Enhancing high harmonic generation in GaAs byelliptically polarized light excitation. Phys. Rev. B 108, 205201(2023).47. Kim, Y. W. et al. Spectral interference in high harmonic generationfrom solids. ACS Photonics 6, 851–857 (2019).48. Kim, Y. et al. Dephasing dynamics accessed by high harmonicgeneration: determination of electron–hole decoherence of Diracfermions. Nano Lett. 24, 1277–1283 (2024).49. Korolev, V. et al. Unveiling theRoleof Electron-PhononScattering inDephasing High-Order Harmonics in Solids. arXiv preprintarXiv:2401.12929 (2024).50. Wang, Y. et al. Tight-binding model for electronic structure ofhexagonal boron phosphide monolayer and bilayer. J. Phys.: Con-dens. Matter 31, 285501 (2019).51. Galler, A., Rubio, A. & Neufeld, O. Mapping light-dressed floquetbands by highly nonlinear optical excitations and valley polariza-tion. J. Phys. Chem. Lett. 14, 11298–11304 (2023).52. Yue, L. & Gaarde, M. B. Structure gauges and laser gauges for thesemiconductor Bloch equations in high-order harmonic generationin solids. Phys. Rev. A 101, 053411 (2020).53. Mrudul, M. S. & Dixit, G. High-harmonic generation frommonolayerand bilayer graphene. Phys. Rev. B 103, 094308 (2021).54. Madéo, J. et al. Directly visualizing the momentum-forbidden darkexcitons and their dynamics in atomically thin semiconductors.Science 370, 1199–1204 (2020).55. Floss, I. et al. Ab initio multiscale simulation of high-order harmonicgeneration in solids. Phys. Rev. A 97, 011401 (2018).Article https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 8https://doi.org/10.1038/s41567-022-01849-9https://doi.org/10.1038/s41567-022-01849-9www.nature.com/naturecommunicationsAcknowledgementsWe acknowledge fruitful discussions with Prof. Dieter Bauer, Prof.Marcelo Ciappinna, Prof. Gopal Dixit, and Dr. Lun Yue. This work wassupported by the Institute for Basic Science (IBS), Korea under ProjectCode IBS-R014-A1. J.K. acknowledge the support from the NationalResearch Foundation of Korea grants (NRF-2023R1A2C2007998). Thisstudy was also supported by the MSIT(Ministry of Science and ICT),Korea, under the ITRC (Information Technology Research Center)support program (IITP-2023-RS-2022-00164799) supervised by theIITP(Institute for Information & Communications Technology Planning& Evaluation). This work was supported by the European ResearchCouncil (ERC-2015-AdG694097), the Cluster of Excellence ‘AdvancedImaging of Matter’ (AIM), Grupos Consolidados (IT1453-22), andDeutsche Forschungsgemeinschaft (DFG)-SFB-925-proj-ect170620586. The Flatiron Institute is a division of the Simons Founda-tion. We acknowledge support from the Max Planck-New York CityCenter for Non-Equilibrium Quantum Phenomena. A.C. acknowledgespartial support by the Sistema Nacional de Investigación de Panama.A.G. acknowledges support by the Austrian Science Fund (FWF) grant10.55776/V988. S.H.C. acknowledges funding from the A*STAR, Sin-gapore, Advanced Manufacturing and Engineering (AME) IndividualResearch Grant (IRG) under the Project M23M6c0109. This work issupported by the MOE AcRF Tier 3 grant (MOE-MOET32023-0003)“Quantum Geometric Advantage” and the Nanyang NanoFabricationCenter (N2FC). K.W. and T.T. acknowledge support from the JSPSKAKENHI (Grant Numbers 21H05233 and 23H02052), the CREST(JPMJCR24A5), JST and World Premier International Research CenterInitiative (WPI), MEXT, Japan.Author contributionsJ.K., O.N., and A.R. conceived the project. M.K. built the optical setupand, together with T.K., obtained the HHG spectra. T.K., X.G., Y.Y., andR.F. fabricated the monolayer WS₂ samples using Au-assisted exfolia-tion. K.W. and T.T. provided the hBN crystals used for encapsulation.O.N., A.G., and D.K. carried out theoretical calculations. M.K., T.K., A.G.,D.K., A.C., B.J.K., S.H.C., M.-H.J., A.R., O.N., and J.K. analyzed the HHGdata. All authors discussed the results and contributed to writing themanuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65725-9.Correspondence and requests for materials should be addressed toAngel Rubio, Ofer Neufeld or Jonghwan Kim.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. Apeer review file is available.Reprints and permissions 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-NonCommercial-NoDerivatives 4.0 International License,which permits any non-commercial use, sharing, distribution andreproduction in any medium or format, as long as you give appropriatecredit to the original author(s) and the source, provide a link to theCreative Commons licence, and indicate if you modified the licensedmaterial. Youdonot havepermissionunder this licence toshare adaptedmaterial derived from this article or parts of it. The images or other thirdparty material in this article are included in the article’s CreativeCommons licence, unless indicated otherwise in a credit line to thematerial. If material is not included in the article’s Creative Commonslicence and your intended use is not permitted by statutory regulation orexceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 20251Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea. 2Center for van der WaalsQuantum Solids, Institute for Basic Science (IBS), Pohang, Republic of Korea. 3Institute of Theoretical and Computational Physics, Graz University ofTechnology, Graz, Austria. 4Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany. 5Departamento de Física, Área de Física,Universidad de Panamá, Ciudad Universitaria 3366 Octavio Mendez Pereira, Panama City, Panama. 6Sistema Nacional de Investigación, ClaytonPanama, Panama. 7Parque Científico y Tecnológico, Universidad Autónoma de Chiriquí, Ciudad Universitaria, David, Panama. 8School of Electrical andElectronics Engineering, School of Materials Science and Engineering, Nanyang Technological University, Singapore, Singapore. 9Research Center forElectronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 10Research Center for Materials Nanoarchitectonics, NationalInstitute forMaterials Science, Tsukuba, Japan. 11Department of Physics, PohangUniversity of Science andTechnology, Pohang,Republicof Korea. 12TechnionIsrael Institute of Technology, Faculty of Chemistry, Haifa, Israel. 13These authors contributed equally: Minjeong Kim, Taeho Kim, Anna Galler.e-mail: angel.rubio@mpsd.mpg.de; ofern@technion.ac.il; jonghwankim@postech.ac.krArticle https://doi.org/10.1038/s41467-025-65725-9Nature Communications |         (2025) 16:9825 9https://doi.org/10.1038/s41467-025-65725-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/mailto:angel.rubio@mpsd.mpg.demailto:ofern@technion.ac.ilmailto:jonghwankim@postech.ac.krwww.nature.com/naturecommunications Quantum interference and occupation control in high harmonic generation from monolayer WS2 Results and discussion Transition from perturbative to strong-field driven HHG in monolayer WS2 Laser intensity-dependent quantum interference in the 7th harmonic spectra Theoretical analysis of HHG in monolayer WS2 Discussion Methods Sample fabrication HHG measurements Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information