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Yunus Waheed, Sumitra Shit, Jithin T. Surendran, Indrajeet D. Prasad, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Santosh Kumar

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[Large trion binding energy in monolayer WS2 via strain-enhanced electron–phonon coupling](https://mdr.nims.go.jp/datasets/8bc223ed-cc7c-4079-adef-f600a0016072)

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Large trion binding energy in monolayer WS2 via strain-enhanced electron–phonon couplingcommunicationsmaterials ArticleA Nature Portfolio journalhttps://doi.org/10.1038/s43246-025-00809-zLarge trion binding energy in monolayerWS2via strain-enhancedelectron–phononcouplingCheck for updatesYunus Waheed1,4, Sumitra Shit1,4, Jithin T. Surendran1, Indrajeet D. Prasad 1, Kenji Watanabe 2,Takashi Taniguchi 3 & Santosh Kumar 1Transition metal dichalcogenides and related layered materials in their monolayer and a few layersthicknesses regime provide a promising optoelectronic platform for exploring the excitonic- andmany-body physics. Here,we have investigated the effects of nanoparticle-induced local strain on theoptical properties of exciton, X0, and trion, X−, in monolayer WS2. Biaxial tensile strain up to 2.0%wasquantifiedand verifiedbymonitoring thechanges in threeprominentRamanmodesofWS2: E12g(Γ), A1g,and 2LA(M). We obtained an increase of 34meV in X− binding energy with an average tuning rate of17.5 ± 2.5 meV/% strain across all the samples irrespective of the surrounding dielectric environmentof monolayer WS2 and the sample preparation conditions. Strain-induced linewidth broadening anddeformation potentials of both X0 and X− emission elucidate that X− binding energy increases due tostrain-enhanced electron–phonon coupling. This work holds relevance for future X−-based nano-opto-electro-mechanical systems and devices.Transitionmetal dichalcogenides (TMDs) are gaining significant interest inthe scientific community due to possession of their unique optical andoptoelectronic properties1–3. The properties on account of which TMDsstand out from other 2D material platforms are: indirect to direct bandgapconversion when they are thinned down to monolayer (ML) thicknesses4–6,leading to stronger photoluminescence (PL) emission in visible and near-infrared spectral ranges1,7, reduced dielectric screening resulting inenhanced Coulombic interactions in the ML regime gives rise to higherexciton binding energies, Eb;X0 (in the range of 0.2–1.0 eV)8,9 and stronglight–matter interactions10. TMDs have proven to be an ideal candidate forthe next generation digital electronics due to their considerable bandgap2.Owing to their tunable bandgap, TMDs offer a platform for various elec-tronic and opto-electronic applications11. To date, different methods, suchas temperature, electric field, magnetic field, doping, and strain have beenemployed to effectively tune the electronic and optoelectronic properties ofTMDs12–14.MLs of widely investigated TMDs, such as MoS2, WS2, MoSe2, andWSe2, show prominent emission peaks in their PL spectra that are red-shifted by 15–41meV9,15,16 from the ground-state (1s) neutral–excitonic,X0,emission peaks. The formation of a singly-negative-charged trion,X− due tointrinsic or substrate-related n-doping of the ML is the cause of such red-shifted peaks. The quasiparticle X− presents a few observable advantagesover X0, such as its prolonged lifetime (by a factor of 5.0)17, a higher degree(by a factor of 1.5) of valley polarization18, and coupling to an additionalelectron. Upon dissociation ofX−, this systemmay allow us to control thesefundamental charges’ electronic spin, and valley properties. It is wellestablished in the literature19 that valley polarization plays a crucial role invalleytronic-based digital technology. The trion formation also enables theelectrical control of exciton transport in TMDheterostructures, broadeningtheir potential in various optoelectronic applications20. The energetic dif-ference, Eb;X� ¼ EX0 � EX� , where EX� EX0� �is the emission energy ofX� X0� �transition, is referred to the X− binding energy (BE)3,21,22 or dis-sociation energy23. The values of Eb;X� in ML-WS2 falls in the range of20–41meV3,15,23–25 owing to the nature of different dielectric environments.A lower Eb;X� leads to thermal quenching due to lower thermal stability,resulting in the shortening of X− lifetimes26,27. Thus, a requirement ofincreasing the Eb;X� arise for efficiently controlling the X−.It has been demonstrated that the ramping up of excitation laser powerresults in an increase in Eb;;X� by a maximum of 5meV22,23,28. Additionally,the use of laser light with high-order orbital angular momentum and at ahigher excitation power has shown a substantial decrease of Eb;X� by amaximum of 9meV22. A limitation of this method is that the excitationpowerabove a certain limitwould lead to a local heating effect; hence, tuningover a wider range is not possible. Strain-tuning has emerged as a powerful1School of Physical Sciences, Indian Institute of Technology Goa, Ponda, Goa, India. 2Research Center for Electronic and Optical Materials, National Institute forMaterials Science, Tsukuba, Japan. 3Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 4These authorscontributed equally: Yunus Waheed, Sumitra Shit. e-mail: skumar@iitgoa.ac.inCommunications Materials |            (2025) 6:86 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00809-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00809-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00809-z&domain=pdfhttp://orcid.org/0009-0001-6822-9384http://orcid.org/0009-0001-6822-9384http://orcid.org/0009-0001-6822-9384http://orcid.org/0009-0001-6822-9384http://orcid.org/0009-0001-6822-9384http://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/0000-0001-7070-057Xhttp://orcid.org/0000-0001-7070-057Xhttp://orcid.org/0000-0001-7070-057Xhttp://orcid.org/0000-0001-7070-057Xhttp://orcid.org/0000-0001-7070-057Xmailto:skumar@iitgoa.ac.inwww.nature.com/commsmattechnique to tune the electronic properties and latticedynamics ofMLand afew-layer TMDs. An introduction of strain into the TMDs layers modifiesthe bandgaps and alters the effective masses and mobilities of chargecarriers29, leading to increased device performances. Uniaxial strain upto≈2.2%30 and biaxial strain up to ≈2.5%31 have been introduced in 2Dmaterials by bending the flexible substrates containing the flakes of 2Dmaterials25,30,32–36, by nano-indentation of 2Dmaterials using sharp-tips likeAFM-tip37 and tapered fiber-tip38, by pressurizing the cylindrical-cavitycovered with the flakes31, and by creating a thermal expansion coefficientmismatch between two materials39,40. Very recently, Henríquez-Guerra etal.21, demonstrated the effects of biaxial strain on the Eb;X� inML-WS2 andhave shown an increase in Eb;X� by ≈3meV under the introduction of a1.5% compressive strain.Here, we have investigated the effects of local biaxial tensile-strain onPL emission properties of X0 and X− in ML-WS2, and have demonstrated asignificant increase in Eb;X� by 34meV and a five-fold enhancement in theemission intensity of X−. We correlated the strain-induced broadening ofboth X0 and X− emission linewidths with their deformation potentials toconclude that the change in X− BE is mainly governed by electron–phononcoupling mechanism. In this regard, we used a simple and cost-effectiveapproach of imparting local strain on ML-WS2 using spherical and shape-modified (see “Methods”) dielectric (SiO2) nanoparticles (NPs) as localstressors. The size distribution of NPs, together with the different levels ofconformality of the flake at NP locations allowed us to explore strain in therange 0.1–2.0%.Weperformedmicro-PL (μ-PL) spectroscopy to investigateexcitonic emissions and micro-Raman (μ-Raman) spectroscopy for quan-tifying and verifying strain of strained ML-WS2.ResultsNanoparticle-induced local-strain effects on X0 and X− emissionenergiesWe started our investigation with μ-PL measurements on Sample 1a.Figure 1a shows the PL peak intensity map of Sample 1a, displaying a stronglight emission at all NP locations in the ML region of the flake due to astrain-induced funneling effect41,42. A one-to-one correlation of the stronglight emission spots in the PLmap with the dark contrast spots in the opticalimage can be seen in Supplementary Fig. S1. The deposition of a flake on topof the NPs-coated substrate has resulted in formations of different levels ofconformalities: from a full conformality (see an SEM image in the left-inset ofFig. 1a to a tent-like structure (see an SEM image in the right-inset of Fig. 1a).The magnitude of local strain in the ML-WS2 strongly depends on its extentof bending/conformality to the NPs and their size distribution, leading to avariation of local strain. This explicitly explains the different brightness ofthose NP-associated PL hotspots in Fig. 1a. Other features of the PL signalhave also been affected greatly by this variation in the local strain.In the next, we examine the effects of variation in local strain on emissionenergies of two important quasiparticles,X0 andX−, by acquiringPL spectra onall theNP locations aswell as theunstrained regions inML-WS2.The statisticalinvestigation of EX0 , EX� , and Eb;X� for both the strained and unstrainedML-WS2 is presented in Fig. 1c in the formof Box-charts. Figure 1b compares a PLspectrum (open circles) taken at the NP16 location from theML-WS2 region,representing one of the highly strained conditions with another PL spectrum(closed circles) from the unstrainedML-WS2.We employed a two-peak fittingfunction (solid lines), a Gaussian function for high-energy X0 emission peak(dotted lines) and a Lorentzian function for low-energy X− emission peak(dashed lines) for extracting the X0 and X− emission energies. On theunstrained region, we obtained an Eb;X� of 32.3meV which is well within therange (20–41meV) of values reported in literature3,15,23–25. Narrower distribu-tionsofEX0 andEX� , shownby solidboxes in theBox-charts are forunstrainedML-WS2 and they indicate homogeneity of flake throughout the substrate.However, we observe wider distributions of EX0 and EX� due to variation ofstrainatNP locations.OnNP16,weobserveda significant redshift of 36.8meVin the EX0 and a relatively large red-shift of 48.8meV in EX� resulting asubstantial increase in anEb;X� of 15.5meV as shown in Fig. 1b.We obtain anaverage PL emission energy value of 2.008 eV (1.976 eV) (represented by smallsquares in solid Box-charts) corresponding to EX0 EX�� �for the unstrainedregions. As per literature, for unstrained ML-WS2, the PL peak emissionenergiesofX0 andX− at roomtemperature are 2.018and1.975 eV43. ThevaluesofX0 andX− emission energies in the unstrained region of Sample 1a are 2.009and 1.976 eV. Due to the deposition of 75 nm-thick SiO2 film with a lowerdielectric constant than the272 nm-thick thermally-grownSiO2 layerontheSi-substrate, we observed a lower EX0 in the unstrained region of ML-WS244. Onthe NP locations, an average emission energy value of 1.979 eV (1.935 eV)(representedby small squares in openBox-charts) corresponding toEX0 EX�� �is observed. Analogous to the results on NP16, the average Eb;X� for theunstrained flake comes out to be 32.5meV while the average Eb;X� from allmeasuredNP locations is 44.3meV,which is giving an average increasedEb;X�of 11.8meV as shown in the Fig. 1c. The red-shifts of EX0 and EX� indicatetoward the significant amount of local tensile strain created at theNP locationsdue to the bending of the flake45.Quantification of NP-induced local strainFor a quantitative understanding of local strain, we performed μ-Ramanspectroscopy, in back-reflection geometry, on all investigated NP locationsof ML-WS2. Figure 2a shows a comparison of Raman spectra of ML-WS2taken on the NP16 location (open circles) with the Raman spectra taken atunstrained region (closed circles) in Sample 1a. We employed the Lor-entzian peak fitting function to identify and extract the frequencies of all sixdifferent Raman modes in the Raman spectra of ML-WS2 taken in theunstrained region and at the NP locations (see Supplementary Fig. S3). Inaccordancewith our expectations,we observed differentRaman shifts for allthe sixRamanmodesofML-WS2 as shownbydottedvertical lines in Fig. 2a.Fig. 1 | μ-PL and SEM characterization of Sample 1a. a Combined image of color-coded PL peak intensity maps of Sample 1a showing emission in the wavelengthrange of 535–880 nm. Inset: SEM images of two NPs with different flake con-formalities: Conformality offlake according to theNP surface (left) and formation oftent-like structure on NP location. b Comparison of μ-PL spectra taken on-the-NPlocation (open circles, top) and unstrained region (closed circles, bottom) in ML-WS2. Solid thick lines are the fits for the spectrum on-the-NP and unstrainedlocations. c Box-chart showing the X0 and X− emission energies distribution forunstrained and strained locations in the sample. Dotted gray lines show the dis-tribution average for both strained and unstrained locations.https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 2www.nature.com/commsmatWe utilized three dominant and extensively studied Raman peaks: A1g,E12g(Γ) and 2LA(M) in the Raman spectra of ML-WS2 as three differentprobes to calculate strain created in theML-WS2 due to underneathNPs.Asthese three different peaks correspond to different modes of atomic vibra-tions in the crystal lattice, they exhibit different peak shifts in response to theparticular magnitude of strain. We quantified the magnitude of local strainon multiple NP locations in Sample 1a, as shown in Fig. 2b using the shiftrate of −1.8, −5.7, and −6.3 cm−1/% strain and unstrained Raman shiftfrequencies of 419, 357, and 353 cm−1 for A1g, E12g(Γ) and 2LA(M)modes ofvibration25,46. As can be seen in Fig. 2b, the values of strain estimated using2LA(M) and E12g(Γ) modes are within the error bar of each other showingagreement in the estimated values of strains. The distribution of NP sizestogether with different levels of conformality of flake on the NP locations(see Supplementary Figs. S2 and S4) serve as local stress-inducing agents,enabling us to explore strain in the range of 0.1–1.0% in Sample 1a.We further cross-verified the quantified strain through the followingprocedures. Figure 2c show the Raman shifts of E12g(Γ) and A1g modes as afunction of strain quantified from 2LA(M) mode. Similarly, Fig. 2d showsthe Raman shifts of 2LA(M) and A1g as a function of strain quantified fromE12g(Γ) mode and Fig. 2e shows the Raman shifts of E12g(Γ) and 2LA(M) as afunction of strain quantified fromA1gmode; the solid lines are the linear fitsin all these three figures. It can be seen that the fitted values of Raman shiftsof unstrained ML-WS2 for all three Raman modes are in good agreementwith the values reported in the literature (see also Supplementary Table S1).Whenweuse 2LA(M) (E12g(Γ))mode to estimate the strain, then the verifiedshift-rates/% strain of the other two modes, E12g(Γ) and A1g (2LA(M) andA1g) are in agreement with the reference values that were utilized for strainestimation in the first hand. However, when the cross-verification of shiftrates was done using the strain estimated fromA1g, the obtained shift rates/% strain of the other two modes showed considerable variations, althoughwithin the error bar. Thus, we observed that the strain estimation using A1gmodeunderestimated the strain, and 2LA(M) andE12g(Γ)modes are the bestmethods for the strain estimation. The slight mismatch in the shift rate ofA1g peak from the reported shift rate can be attributed to the fact that A1g issensitive to doping concentration in the material14,47.Excitons’ (X0 andX−) energy gauge-factors andX− BE tuning ratePost acquiring the strain from Raman modes, we correlated the EX0 andEX� in PL spectra of ML-WS2 with the measured strain in Sample 1awhich is summarized in Fig. 3. The local strains plotted in Fig. 3a–c, havebeen quantified using A1g, 2LA(M) and E12g(Γ) Ramanmodes, respectively.Taking into consideration that a small range of strains is accessed in thisexperiment, we performed linear fittings of these energy variations15 andobtained values of E0X0 E0X�� �, emission energy of X0 X�ð Þ transition in anunstrained ML-WS2, that are plotted in Fig. 3d. From these fits (solid linesin Fig. 3), we also obtained ΔEX0=% ΔEX�=%� �strain, an energy-gauge-factor of X0 (X−) transition in strainedML-WS2, that are plotted in Fig. 3e.As can be seen in Fig. 3d, we obtained slightly different values of EX0 andFig. 2 | Strain quantification and its verification via different Raman modes inSample 1a. a μ-Raman spectra taken on-the-NP location (open circles, top) andunstrained region (closed circles, bottom) ofML-WS2. Solid thick lines are thefits forthe spectrumon-the-NP and unstrained locations. bPlot showing the distribution ofstrain on different NP locations. cRaman shift of E12g (Γ) and A1gmodes as a functionof strain quantified from 2LA(M)mode. dRaman shift of 2LA(M) andA1gmodes asa function of strain quantified from E12g (Γ) mode. e Raman shift of E12g(Γ) and2LA(M)modes as a function of strain quantified fromA1gmode. The gray solid linesrepresent the linear fits. The error bars represent one standard deviation, consideringmeasurement and fitting errors, and whichever is the higher.https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 3www.nature.com/commsmatEX� for unstrained ML-WS2 using different strain estimating Ramanmodes. The average (solid line) of these three EX0 (EX� ) values is 2.008(1.973) eV, which is similar to the value obtained in the statistical PLinvestigation of unstrained ML-WS2. Similarly, we obtained the averageΔEX0=% ΔEX�=%� �strain of −38 ± 3.0 (−51 ± 3.5) meV/% strain foremission energies of X0 (X−) transition, which are well within the range of−11 to −130meV/% strain, reported in the literature13,25. Both uniaxialand biaxial strains have been utilized to estimate the gauge factors of X0and X− in ML TMDs, as summarized in Supplementary Table S2. How-ever, the strain introduction methods primarily rely on the method ofsubstrate bending in a two-point (four-point) configuration, resulting inuniaxial (biaxial) strain throughout the flake. The use of NPs as stressinducers facilitates the introduction of localized strain right at the NP’slocation. This approach allows for the precise introduction of strain in theregion of interest, minimizing the need for global substrate deformation.As the emission of light due to X− happens at a lower energy than X0, thedifference in X0 and X− gauge factors lead to an increase in the BE of X−with a tuning rate, ΔEb;X� /%, of 13 ± 4.5meV/% strain for Sample 1a.We attribute this significant change in Eb;X� to the pronounced var-iation in the local strain that can be qualitatively understood in terms ofstrain-induced variations in the interaction energies between the constituentparticles of X0 and X− in ML-WS2. The quasiparticle X− consists of twoelectrons (e−) and one hole (h), and the interaction energies between theseconstituent particles play a significant role in contributing to the Eb;X� ofML-WS2. Biaxial strain induces changes in both electron-hole interactionenergy (Jeh) as well as electron–electron interaction energy (Jee). However,for a strongly 2D-confined system, under the assumption that strain inducesnegligible changes in the single-particle confinement energies, the rate ofchange of Eb;X� per unit strain is given by:ddϵkEb;X�� � � ddϵkJeh� �� ddϵkJee� �ð1ÞDing et al.48, have shown that with increasing biaxial tensile strain, thedecrease in the second term in Eq. (1) ismore significant as compared to thefirst term, therefore rendering a positive value of dEb;X� /dϵ∥. It clearlyindicates the increase in X− BE for ML-WS2 via the introduction of biaxialtensile strain.X− tuning-rates verification across various samplesTo authenticate this large tuning rate,ΔEb;X� /%, we investigated four moresamples with optically active material ML-WS2 and findings are summar-ized in Fig. 4. It is expected that strain will decrease as we move away fromthe center of NPs. Therefore, in Sample 3, a single and isolated NP locationwas investigated by performing a line-scan PL measurement. The opticalmicrograph of the Sample 3 showing the isolated NP location and changesin theX0 andX− energies are shown in the inset of Fig. 4.Weutilized a gaugefactor ΔEX0 /% biaxial strain,−38meV/% that is obtained in Sample 1a, toestimate strain in all the samples. Figure 4 shows the variation of Eb;X� as afunction of strain for all investigated samples where the pentagons, circles,hexagons, triangles and inverted triangles represent the measured datapoints for Samples 1a, 1b, 2, 3, and 4, respectively. ΔEb;X� /% biaxialstrain obtained from the linearfitting ofmeasured data fromallfive samplesare summarized in Table 1, and it shows thatΔEb;X� /% biaxial strain for allsamples are similar andwithin the error bars. Conclusively, we state that onaverage, we obtain the tuning rate of X− BE, ΔEb;X� /% biaxial strain of17.5 ± 2.5meV/%.Correlation of enhanced X− BE with electron–phonon couplingLooking at the fact that the local strainhas increased the energetic separationbetween X0 and X− transitions, it is expected to alter the transition prob-ability of both transitions. In the following, we inspect this aspect bymonitoring the emission intensity and linewidth of both the transitions, andthe outcome is summarized in Fig. 5. Figure 5a shows the IX� /IX0 ratios forFig. 3 | Binding-energy tuning-rate per % biaxial strain (gauge factor) of X−emission inML-WS2 in Sample 1a.X0 andX− emission energies as a function of strainquantified using (a) A1g, (b) 2LA(M) and (c) E12g (Γ) Raman modes, showing unequalenergy tuning rates leading to a change in the binding energy ofX−.dX0 andX− emissionenergies of unstrained ML-WS2 and e X0 and X− energy gauge factors of ML-WS2quantified using A1g, 2LA(M) and E12g (Γ) Ramanmodes. The diamonds and squares areforX0 andX−, respectively. The solid lines in (a–c) represent the linear fits and in (d) and(e) represent the averages. The error bars represent one standard deviation, consideringmeasurement and fitting errors, and whichever is the higher.Fig. 4 | Strain tuning-rate of trion’s binding energy, ΔEb;X� /% across varioussamples. Strain-dependent trion’s binding energy, Eb;X� for Sample 1a (pentagons),Sample 1b (circles), Sample 2 (hexagons), Sample 3 (triangles) and Sample 4(inverted triangles), showing a very similar tuning-rates of trion binding energy per% of biaxial strain. Inset: The optical micrograph of Sample 3. A dotted line isrepresenting the PL linescan (top) and the change inX0 (diamonds) andX− (squares)PL peak energy positions as a function of distance across the NP location (bottom).The error bars represent one standard deviation, considering measurement andfitting errors, and whichever is the higher.https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 4www.nature.com/commsmatall the investigated samples,where IX0 (IX� ) is the intensity ofX0(X−) that areplotted as a functionof strain. In each investigated sample,wenoticed a clearincrease in the IX� /IX0 ratio with increasing strain. Along with the increasein the IX� /IX0 , we observed two different sets of data points. Although boththe data sets show a similar increase in the intensity ratio IX� /IX0 , theminimum intensity ratio of one data set is higher than the other because ofdifferent dielectric environment and sample preparation conditions.However, irrespective of the value of strain quantified for different samples,we observed up to ≈5 × enhancement in the IX� /IX0 ratio on the intro-duction of up to 2% tensile strain. This observation is in accordancewith themass action law exhibiting an increase in the IX� /IX0 with increasing Eb;X�that is increasing with strain16,22. Also, we monitored the strain-inducedbroadening (increase) in the full width at half maximum, linewidth, of X0andX− emission peaks for all investigated samples, which is summarized inFig. 5. As per literature, the broadening in the linewidth of excitonic emis-sion peak in the PL spectra as a function of strain has only been observed forMoS2 with a broadening rate of 10–15meV/%49,50 while MoSe2, WS2, andWSe2 showed narrowing (decrease) in linewidth as function of strain withrates 5, 8, and 20meV/%, respectively50. Our linewidth vs strain data forboth X0 and X− peaks of ML-WS2 plotted in Fig. 5b, c show a clearbroadening in the linewidth under tensile strain. The linear fits of themeasured data produced a linewidth shift rate of 42meV/% (71meV/%)biaxial strain for X0 X�ð Þ which shows that the phonon is interacting morestrongly withX− than X0. Shen et al.51 have shown that the valence bands ofWSe2 arenotmuchaffectedby strainup to2%.Thus,we further investigatedthese strain effects on excitons through the coupling strength ofelectron–phonon interaction that is given by:β / DP2Yð2Þwhere, DP is the gap deformation potential of the quasiparticle, and Y isYoung’s Modulus of elasticity. In this work, since we are monitoring theΔEX0ðX�Þ, we can calculate the DP of both the transitions given by52:DPX0ðX�Þ ¼ΔEX0ðX�Þð2� ρÞ � ϵkð3Þwhere, ρ (= 0.19) is the Poisson’s ratio of ML-WS2, ϵ∥ refers to localstrain, which we have also measured in this work. Since, ΔEX0ðX�Þ perunit strain can be obtained from Fig. 3, the calculated DPX0ðX�Þ is 2.10(2.82) eV, giving rise to coupling strengths ratio of electron–phononinteraction for X0 and X−, βX� /βX0 = 1.80 ± 0.27. It is striking to see thataforementioned ratio of coupling strengths of electron–phonon interac-tion for X0 and X−, which is obtained from the strain-induced energychanges in them, also agrees well with the ratio of linewidth shift rates ofX0 and X−, ΔωX� /ΔωX0 per percent strain, rendering a value of1.71 ± 0.14. From this, we conclude that the strain-induced changes inthe binding energies of X− can be explained by electron–phononinteractions. A further understanding of electron–phonon coupling at alength scale less than the optical diffraction limit can be developed byinvestigating the optical signals at a few nanometer length scales, e.g., byusing the scanning near-field optical microscopy technique.DiscussionIn this work, we report the large increase ofX−BE by 34meVdue to strain-enhanced electron–phonon coupling in ML-WS2. To demonstrate thisTable1 |X−BE tuning-rateper%biaxial strain (gauge factor) ofML-WS2 for all samplesSample Tuning-rate of trion’s BE, ΔEb;X� /%biaxial strainmeV/%Sample 1a 13.0 ± 4.5Sample 1b 20.0 ± 5.0Sample 2 21.5 ± 5.5Sample 3 14.5 ± 2.5Sample 4 17.5 ± 7.0Fig. 5 | Strain-dependent PL emission intensity and linewidth (FWHM) ofX0 andX− emission across different samples. a Strain-dependent ratio of the intensity ofX− emission peak (IX� ) to the intensity of X0 emission peak for Sample 1a (penta-gons), Sample 1b (circles), Sample 2 (hexagons) and Sample 3 (triangles). Strain-dependent linewidth of b X− and c X0 emission peaks, for all the investigatedsamples. Pentagons, circles, hexagons and triangles in (b) and (c) are for Samples 1a,1b, and 3, respectively. The error bars represent one standard deviation, consideringmeasurement and fitting errors, and whichever is the higher.https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 5www.nature.com/commsmatstrain-induced variation, we investigated the emission energies of X0 andX− by performing the μ-PLmeasurements on unstrained andNP locationsinML-WS2 across different samples. The strain inML-WS2was quantifiedby performing the Raman measurements as described in Fig. 2a, b. Threedominant and extensively studied Ramanmodes: A1g, E12g(Γ), and 2LA(M)modes were employed for this strain quantification. The cross-verificationof strain was done by plotting the Raman shift frequencies of two Ramanmodes against the strain quantified from the third Raman mode. Thisprocess was utilized for all three Raman modes as described in Fig. 2. Wefurther correlated the strain-induced variations in the peak emissionenergies of X0 and X− transitions of ML-WS2 with the quantified strain assummarized in Fig. 3 and obtained the energy gauge factor of X0 X�ð Þ,ΔEX0=% ΔEX�=%� �strain, of−38 ± 3.0 (−51 ± 3.5)meV/% biaxial strainleading toX− BE tuning rate,ΔEb;X� /% strain, of 13 ± 4.5 meV/% strain, asshown in Fig. 3e. To further verify this strain-induced large tuning rate, weinvestigated the PL spectra of strained ML-WS2 from four additionalsamples as shown in Fig. 4, where the strainwas quantified using the gaugefactor of −38meV/% biaxial strain obtained from Sample 1a. The dis-tribution in sizes of NPs and different levels of conformality of the flake onNP locations enabled us to explore strain in the range 0.1–2.0% across allsamples. Utilizing the excitonic gauge factor, where strain was quantifiedvia Raman spectroscopy of Sample 1a, we achieved similar X− BE tuningrates for other four samples, highlighting the consistency of this approach.Conclusively, we obtained an averageΔEb;X� /% strain of 17.5 ± 2.5 meV/%for all the investigated samples irrespective of the surrounding dielectricenvironment of ML-WS2 and the sample preparation conditions sum-marized in Table 1 and we have shown that this large change in BE can beunderstood in terms of the interaction energies between the constituentparticles in X0 and X− quasiparticles. Alongside the large variation in X−BE, we also investigated the strain-induced linewidth broadening shown inFig. 5b, c and the deformation potentials of both the X0 and X− transitionsand hence, elucidated the significant role of strain-enhancedelectron–phonon coupling in increasing the X− BE. We believe that thetechnique utilized in this work can be employed to enhanceelectron–phonon interactions via localized strain in other TMDs and theirexotic heterostructures53–55 to tune the optical properties of excitons andtrions at room temperature. This strain-induced increase in the Eb;X�followed by enhanced stability and efficient formation of X− holds rele-vance for future X− based nano-opto-electro-mechanical systems even atelevated temperatures.MethodsSample preparationThe studied samples consist of three different layered structures. Samples 1and 4 (Sample 2) consist of mechanically exfoliated ML-WS2 deposited onshape-modified (spherical) SiO2-NPs distributed over a SiO2 (272 nm)/Sisubstrate. Utilizing the spin-coating method, we obtained a random dis-tribution of individual NPs that are well isolated from each others on allsamples. The size of spherical NPs (Sigma-Aldrich) falls typically in therange of 125–175 nm. These NPs act as nano stressors, creating local strainin ML-WS2. NP concentration in ethanol was optimized to preventagglomeration. In Samples 1 and4, theprocess of shapemodificationofNPswas accomplished through deposition of 75 nm-thick SiO2 film onspherical-NPs distributed over a SiO2/Si substrate using an e-beamphysicalvapor deposition technique. The activematerial,ML-WS2, is thendepositedon top of shape-modified-NPs. In Sample 3, NPs were spin-coated onto thebottom-hBN deposited on SiO2/Si substrate, followed by transfer of ML-WS2, which is further encapsulated by a thin-hBN flake. Both theWS2 andhBN flakes were mechanically exfoliated from their bulk counterparts. TheML-WS2 flakes were qualitatively identified by optical color contrast andfurther confirmed by PL and Raman spectroscopy. We employed theconventional dry-transfer method using polydimethylsiloxane stamps totransfer theflakes on topof eachother56.Wealsonoticedwrinkles formationduring the top-thin hBN transfer because of the high elastic modulus of thehBN57 compared toML-WS258.As a standardprotocol of sample processing,we employed vacuum annealing at 200 °C for 5 h, followed by naturalcooling in a rapid-thermal-annealing system for Samples 1 and 359.PL and Raman spectroscopyPL and Raman signals from all three samples were collected using a home-built confocal microscopy setup equipped with a microscope objective(NA = 0.75), yielding diffraction-limited spatial resolutions. The sampleswere mounted on an XY scanner combined with a ±2.5 mm XYZ nano-positioner stack (Attocube). For generating the spacemaps of PL signals, thesamplesweremovedusing the scannerprovidinga scanning rangeof 50 μm.Adiode-pumped solid-stateCWlaser emitting atλ = 532 nmwasused as anexciting source for both PL and Ramanmeasurements. An ultra-steep longpass filter designed at an edge of 533.3 nm (Semrock) was used to suppressthe laser light from entering into the spectrometer. All the spectra wereacquired with a 0.5m focal length spectrometer combined with a water-cooled charge-coupled device camera providing a best spectral resolution of~125 μeV at λ = 532 nm on an 1800 lines/mm grating. A grating with150 lines/mmgiving a spectral resolutionof 2.5 meVatλ = 532 nmwasusedfor acquiring large wavelength range spectra.Data availabilityThe data that support the findings of this study are available from thecorresponding author upon reasonable request.Received: 21 November 2024; Accepted: 17 April 2025;References1. Mak, K. F., Lee,C.,Hone, J., Shan, J. &Heinz, T. F. Atomically thinMoS2:a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).2. Butler, S. Z. et al. Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano 7, 2898 (2013).3. Mak, K. F. et al. 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I.D.P. thanks The Council of Scientific &Industrial Research (CSIR), New Delhi, for the doctoral fellowship. K.W. andT.T. acknowledge support from the JSPS KAKENHI (Grant Numbers21H05233and23H02052) andWorldPremier InternationalResearchCenterInitiative (WPI), MEXT, Japan.Author contributionsY.W. and S.S. carried out μ-PL and μ-Raman measurements supported byI.D.P. and J.T.S. under the supervision of S.K. S.S. fabricated the samplessupported by J.T.S under the supervision of S.K. K.W. and T.T. prepared thehBNmaterial. Y.W.andS.K.analyzed thedatasupportedbyJ.T.S.and I.D.P.S.K. led the interpretationof the results. Y.W. andS.K.wrote themanuscript.All authors discussed the results and contributed to the manuscript. S.K.conceived and coordinated the project.https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 7www.nature.com/commsmatCompeting interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-025-00809-z.Correspondence and requests for materials should be addressed toSantosh Kumar.Peer review information Communications Materials thanks ElizabethPeterson and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. Primary Handling Editors: Zakaria Al Balushi andAldo Isidori. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s43246-025-00809-z ArticleCommunications Materials |            (2025) 6:86 8https://doi.org/10.1038/s43246-025-00809-zhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/commsmat Large trion binding energy in monolayer WS2 via strain-enhanced electron–phonon coupling Results Nanoparticle-induced local-strain effects on X0 and X− emission energies Quantification of NP-induced local strain Excitons’ (X0 and X−) energy gauge-factors and X− BE tuning rate X− tuning-rates verification across various samples Correlation of enhanced X− BE with electron–phonon coupling Discussion Methods Sample preparation PL and Raman spectroscopy Data availability References Acknowledgements Author contributions Competing interests Additional information