# Fileset

[s41377-023-01338-5.pdf](https://mdr.nims.go.jp/filesets/e23fcf29-6efa-4388-8698-cc23f72efbe4/download)

## Creator

Zhe Li, Xin-Yuan Zhang, Rundong Ma, Tong Fu, Yan Zeng, Chong Hu, Yufeng Cheng, Cheng Wang, Yun Wang, Yuhua Feng, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Ti Wang, Xiaoze Liu, Hongxing Xu

## Rights

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

## Other metadata

[Versatile optical manipulation of trions, dark excitons and biexcitons through contrasting exciton-photon coupling](https://mdr.nims.go.jp/datasets/12becc2e-36d9-420f-9695-4c95147ecd5b)

## Fulltext

Versatile optical manipulation of trions, dark excitons and biexcitons through contrasting exciton-photon couplingLi et al. Light: Science & Applications          (2023) 12:295 Official journal of the CIOMP 2047-7538https://doi.org/10.1038/s41377-023-01338-5 www.nature.com/lsaART ICLE Open Ac ce s sVersatile optical manipulation of trions, darkexcitons and biexcitons through contrastingexciton-photon couplingZhe Li1, Xin-Yuan Zhang1,2, Rundong Ma1, Tong Fu1, Yan Zeng1, Chong Hu1,2, Yufeng Cheng1, Cheng Wang1,Yun Wang3, Yuhua Feng3, Takashi Taniguchi 4, Kenji Watanabe 5, Ti Wang1✉, Xiaoze Liu1,2,6✉ andHongxing Xu 1,6,7,8✉AbstractVarious exciton species in transition metal dichalcogenides (TMDs), such as neutral excitons, trions (charged excitons),dark excitons, and biexcitons, have been individually discovered with distinct light-matter interactions. In terms ofvalley-spin locked band structures and electron-hole configurations, these exciton species demonstrate flexible controlof emission light with degrees of freedom (DOFs) such as intensity, polarization, frequency, and dynamics. However, itremains elusive to fully manipulate different exciton species on demand for practical photonic applications. Here, weinvestigate the contrasting light-matter interactions to control multiple DOFs of emission light in a hybrid monolayerWSe2-Ag nanowire (NW) structure by taking advantage of various exciton species. These excitons, including trions,dark excitons, and biexcitons, are found to couple independently with propagating surface plasmon polaritons (SPPs)of Ag NW in quite different ways, thanks to the orientations of transition dipoles. Consistent with the simulations, thedark excitons and dark trions show extremely high coupling efficiency with SPPs, while the trions demonstratedirectional chiral-coupling features. This study presents a crucial step towards the ultimate goal of exploiting thecomprehensive spectrum of TMD excitons for optical information processing and quantum optics.IntroductionIn the monolayer limit, the strong Coulomb interactionsand direct band gaps in transition metal dichalcogenides(TMDs) result in tightly bound excitons with strikingoptical signatures1–6. Excitons in the monolayers possesslarge binding energies of a few-hundred meV and arestable at room temperature. More interestingly, emergingexciton species, such as trions and biexcitons, are formedand spectrally separated with bound multiple-particleconfigurations7–13, offering many opportunities toinvestigate many-body interactions and related quantumphenomena. Meanwhile, some unique excitonic effectshave been discovered because of spin-valley locking bandstructures in TMD monolayers14–20. For the conservationof spin angular momentum, optical transitions of direct-gap excitons in K valleys can occur only with specificcircular polarizations17,21. This polarization selection ruleis also referred to valley polarization, acting as the coremechanism for the booming research of valleytronics. Onthe other hand, optical transitions of some excitons arespin-forbidden, leading to the discovery of dark excitonsin tungsten-based TMD monolayers. The dark excitonsare found to hold a much longer lifetime of a few nano-seconds than spin-allowed bright excitons, and unex-pectedly their transition dipoles are oriented along theout-of-plane direction22. In TMD monolayers, theseexciton species of spectral separations, different transition© The Author(s) 2023OpenAccessThis article is licensedunder aCreativeCommonsAttribution 4.0 International License,whichpermits use, sharing, adaptation, distribution and reproductionin any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate ifchangesweremade. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to thematerial. Ifmaterial is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtainpermission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.Correspondence: Ti Wang (wangti@whu.edu.cn) orXiaoze Liu (xiaozeliu@whu.edu.cn) or Hongxing Xu (hxxu@whu.edu.cn)1School of Physics and Technology, Center for Nanoscience andNanotechnology, and Key Laboratory of Artificial Micro- and Nanostructures ofMinistry of Education, Wuhan University, 430072 Wuhan, China2Wuhan University Shenzhen Research Institute, 518057 Shenzhen, ChinaFull list of author information is available at the end of the articleThese authors contributed equally: Zhe Li, Xin-Yuan Zhang1234567890():,;1234567890():,;1234567890():,;1234567890():,;www.nature.com/lsahttp://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/0000-0003-3701-8119http://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/0000-0002-1718-8834http://orcid.org/0000-0002-1718-8834http://orcid.org/0000-0002-1718-8834http://orcid.org/0000-0002-1718-8834http://orcid.org/0000-0002-1718-8834http://creativecommons.org/licenses/by/4.0/mailto:wangti@whu.edu.cnmailto:xiaozeliu@whu.edu.cnmailto:hxxu@whu.edu.cndipoles, unique valley polarization dependence, and dis-tinct carrier dynamics provide flexible approaches tocontrol the emission light with degrees of freedom (DOFs)such as frequency, intensity, polarization, and dynamics.TMDs have been demonstrated as a versatile platformto manipulate the excitonic emissions with differentDOFs when coupled with various photonic nanos-tructures. In optical cavities, the bright excitonic emissionintensities could be significantly amplified with acceler-ated dynamics by the Purcell effect and even get into thestimulated regime for coherent lasing actions23–26.Remarkably, these bright excitons could also reach thestrong coupling regime by controlling the couplingstrength, giving rise to intriguing polaritonic phenom-ena27–35. In deliberate photonic structures, the excitonicvalley polarization could be well preserved and evenenhanced16,30,36,37; via chiral photonic designs, the valleypolarization could be utilized as a novel DOF for sortingand routing optical signals38–41. With considerable spec-tral separations, it is worth noting that different excitons(e.g., trions, dark excitons, and biexcitons) of specificelectron-hole configurations provide great opportunitiesto investigate many-body interactions and related quan-tum phenomena9,10,12,42. Moreover, dark excitons withspin-forbidden transitions are found to couple with pho-tons in a totally different way because of their out-of-plane transition dipoles22. The above-mentioned pro-gresses indicate the tremendous potential to exploit TMDexcitons with different DOFs, establishing one ultimategoal to exploit the comprehensive spectrum of TMDexcitons for optical information processing and quantumoptics43,44. However, towards this goal, there is still aconsiderable gap because it remains elusive to fullymanipulate all the excitons simultaneously on demand.In this work, we showcase the optical versatile manip-ulation of various excitons in a hybrid monolayer WSe2-Ag nanowire (NW) structure by harnessing the con-trasting photon-exciton interactions with dependences ofdipole orientations, diffusion, and chirality. Here the AgNW is taken as the photonic structure for two-fold rea-sons: (i) The surface plasmon polaritons (SPPs) in AgNWs can largely enhance the light-matter interactions forall the exciton species of WSe2. The enhancement can beensured by the highly confined electromagnetic fields;excitons with different transition dipole orientations canall couple to different SPP modes22,24,31,41,45–47. (ii) Thevalley polarization-dependent coupling of excitonicemissions is possible in Ag NWs. By breaking the modesymmetry, the chiral coupling and routing of SPP modesprovide a convenient way to manipulate the valleypolarized emissions39. In this experimental configuration,the excitons (including trions), dark excitons (includingdark trions), and biexcitons (including charged biexci-tons), are found to couple independently with propagatingSPPs in quite different ways. Consistent with the simu-lations, the dark excitons and dark trions show extremelyhigh coupling efficiency with SPPs, while the trionsdemonstrate highly directional chiral-coupling features asthe valley polarization is present. The detailed experi-ments and result discussions are elaborated as follows.ResultsDesign and characterization of the hybrid structureThe schematic of the sample structure is shown inFig. 1a. It consists of an Ag NW with ~8 μm length and amonolayer WSe2 encapsulated between two hexagonalboron nitride (hBN) thin films, which are sitting on aSiO2/Si substrate (see Methods and Fig. S1 for moredetails). The exciton species of monolayer WSe2 could bedistinguished via the hBN encapsulation, as the photo-luminescence (PL) spectrum shows in Fig. 1b (pumped bya continuous-wave (CW) laser of 685 nm at 4 K). Thereappear multiple narrow PL peaks, which are labeled as theneutral A exciton (X0), biexciton (XX0), trion (X-), darkexciton (XD), charged biexciton (XX-), dark trion X�D� �.The lower energy peaks besides X�D are considered asexciton complexes (XC), which are not the focus of thisresearch48. These exciton species are identified by theirpeak energies, pump-power dependence, and valleypolarization (see more details in Figs. S2 and S3), whichare consistent with previous reports42,49–51. The valleypolarization of these excitons is examined with circularpolarization degree as ρ=(I+-I-)/(I++I-), where I+ and I-represent the right and left circular polarized PL intensity.Under right-circular polarized (σ+) pump light of 685 nmCW laser, the ρ of X0, XX0, and X- are 27%, 79 and 92%,respectively (see Fig. S2 and Table S2 for detailed analysisfor the ρ of XD, XX- and X�D, see Fig. S4 for the σ- pumpcase). Moreover, the sample structure also enables effi-cient coupling between the SPPs of NWs and the WSe2monolayer. The thin hBN could not only prevent thecharge transfer between WSe2 and Ag NWs withoutsuppressing the PL quantum efficiency, but also ensuresufficient coupling strength as shown in Fig. 1c, d andSupplementary Fig. S5. The effect of hBN is further ver-ified by the control sample without hBN between theWSe2 and Ag NW (Supplementary Fig. S6).For the distinct properties of these exciton species, theircoupling with SPPs of NW occurs in quite different ways.The most distinct properties of these excitons lie at theorientations of transition dipoles. For instance, the dipolesof exciton (X0) and trion (X-) are in-plane oriented52,while those of dark excitons (XD) are out-of-planeoriented22,24,52. Based on these differences, numericalsimulations are carried out to look into their couplingwith NW SPPs. In Fig. 1c, the simulated electromagneticfield of an out-of-plane dipole source with NWs is pro-filed as a function of position (the cross-section electricLi et al. Light: Science & Applications          (2023) 12:295 Page 2 of 9field distribution is shown in Fig. S7). Along the NWs (x-axis) at both directions, the uniform wave-like spread-outindicates the efficient coupling and thus can support long-range propagation towards both ends of the NW. Tobetter characterize the coupling, normalized SPP powerξ=P/Pmax is defined to represent the strength. Along they-axis, however, the coupling becomes more efficient atthe NW edges and slightly weaker in the center. When thedipole source goes outside the NWs range, the couplingdiminishes drastically. On the contrary, the simulatedfield of the in-plane dipole source is profiled in Fig. 1d.The field is much weaker than that of the out-of-planedipole. For the normalized SPP power, the coupling ismore efficient around the edge of the NWs and becomesextremely weak at the center.Experimental observation of the contrasting exciton-photon couplingPL spectroscopy is carried out to observe the couplingfeatures of these different excitons. The pump CW laserof 685 nm is focused onto the middle point of the NWand the PL are collected in the pump area (at the middle)and at both ends of the NW. For convenience, thepolarization of pump and PL collections are all set to beright circularly polarized (the polarization analysis is dis-cussed in Figs. 4 and S2). In the PL image of Fig. 2a, thewhite spots in the middle and at both ends correspond tothe scattered signals from the in-situ excitons, and thepropagating SPP coupled excitons, respectively. The PLspectra of these two areas are then plotted in Fig. 2a.Apparently, the PL spectrum in the middle is consistentwith Fig. 1b, where the exciton (X0) emission dominates.In contrast, the PL at the right end shows a totally dif-ferent profile, where the emissions of dark excitons (XD)and dark trions X�D� �dominate but those of X0, X- andXX0 decrease drastically. This could be well explained bythe simulation of Fig. 1c, where the transition dipoles ofXD and X�D are out-of-plane oriented and are expected tocouple more efficiently than those in-plane orienteddipoles of X0 and X-.The pump-power dependent PL spectroscopy is takento further look into the contrasting coupling behaviors.The power-dependent PL spectra at both areas are plottedin Fig. 2b, d (those for the left end are shown in Fig. S8). Inthe PL spectra of right end, the intensities of XD and X�Dare already quite prominent at low pump powers, andtheir linewidths are considerably narrower than PLspectra in the middle. As the power increases, otherexciton peaks, such as biexcitons (XX0) and chargedbiexcitons (XX-), become visible for different power-lawdependence. By normalizing the end spectrum (PLintensity IR(L) at the right (left) end) with respect to themiddle one (PL IM in the middle), the coupling efficiencyfor each exciton species is defined as (κ=IR/IM). ThisabAg nanowireTop hBNWSe2SiO2/Si substrateBottom hBNzyx5 �mBright field760750740730720710PL intensity (a.u.)Wavelength (nm)1.75 1.72 1.69 1.66 1.63Energy (eV)�+�-�+ excitationX0X-XX0XX-c-2000200y (nm)Out-of-plane dipole18 (A/m) 0-1000 -500 0 500 1000x (nm)�H � �H �x (nm)0 50-50-200020004ξd0 50-50-200020001In-plane dipoleξXD-XDXC-2000200y (nm)y (nm)-1000 -500 0 500 1000x (nm)6 (A/m) 0 y (nm)x (nm)Fig. 1 Contrast exciton-photon coupling of various excitons in WSe2. a Schematic of the Ag NW-WSe2 sample structure. The inset shows thebright field microscopic image. b Helicity-resolved PL spectra of monolayer WSe2 far away from Ag NW at 4 K under σ+ excitation at 685 nm.c Simulated electromagnetic field (left) and normalized SPP power ξ (right) of out-of-plane dipoles coupled with NWs as a function of position,respectively. d Simulated electromagnetic field (left) and normalized SPP power ξ (right) of in-plane dipoles coupled with NWs as a function ofposition, respectivelyLi et al. Light: Science & Applications          (2023) 12:295 Page 3 of 9efficiency κ at three typical powers is then summarized inFig. 2c. It is apparent that the coupling efficiency κ isdominant for XD and X�D, which is far larger than all theother excitons which have strong in-plane dipoles.Although the efficiency κ decreases as the pump powerincreases, it is always the unambiguously highest for theXD and X�D. The dominant efficiency κ of XD and X�D isabout 2.8 times larger than the κ for in-plane dipoles, i.e.,the trions under 320 μW pump power. The 2.8 timesstronger coupling efficiency is consistent with the simu-lation, where the coupling strength is calculated to be 2.5times stronger. Moreover, time-resolved photo-luminescence (TRPL) and numerical simulation are car-ried out to further characterize the efficient couplingbetween the XD, X�D and Ag NW (Fig. S9). Interestingly,the efficiency κ for trions (X-) reveals more fine features ofthe trions. This directly helps resolve two peaks at theoriginal X- position as inter-valley trion X�1� �and intra-valley trion X�2� �because of different valley-indexedthree-particle configurations, as reported by the magneto-optical measurements53,54. The efficiency κ is close tozero for neutral excitons and biexcitons (X0 and XX0).The case of XX0 may be just resulted from the lowemission yield and low coupling strength here; the case ofX0 is attributed to the low coupling strength and muchhigher propagation loss of SPPs with large re-absorptionat the exciton resonance. Due to the narrow absorptionlinewidth of hBN encapsulated WSe2, this SPP loss of re-absorption mainly affects the X0 resonance. The light-matter coupling with SPPs thus shows contrasting beha-viors for each specific excitons, rendering versatileapproaches to control their light emissions.Manipulate the light emissions of different excitons bytuning the couplingOnce the light-matter coupling is established for thesedistinct excitons, their light emissions can be flexiblymanipulated by taking advantage of their distinct char-acteristics. For demonstration, the excitonic emissionintensity, and directional coupling with polarizationdependence would be deliberately controlled with specificspectral signatures. This controllability is exemplified byexploiting the spectral separations, different excitons’diffusion lengths and valley DOF.We first demonstrate that the spectral profiles for eachexciton can be intentionally altered and even some exci-tonic emissions can be selectively turned off, as we tunethe photonic coupling of different excitons. This isLorbda1280 �W320 �W80 �W0.3MiddleRight endXD-XD-MiddleRight endX1-X2-cPL imagePL intensity (a.u.)Right end/middle750740730720 750740730720710 7101000100Power (�W)Power (�W)PL intensity (cts.)PL intensity (cts.)10100010010Wavelength (nm) Wavelength (nm)750740730720710Wavelength (nm)X0X0XX-XX-XX0XX0XX0X0XDXDXCXCXX-XX-XD-XD-X-XX0X2-X2-XDXDX1-X1-Wavelength (nm)75074073072071010001001001010Fig. 2 Power-dependent PL spectra from the middle and the right end of the Ag NW. a In-situ (collected at the middle point of NW) andpropagated PL spectra (collected at right end) with the excitation power of 160 μW (pumped at the middle), the inset shows the corresponding PLimage. Color map of in-situ (b) and propagated PL spectra (d) as a function of pump powers. For better demonstration, the data is acquired at 4 Kwith σ+ excitation and σ+ detection. c Spectral coupling efficiency κ at the pump powers of 80, 320, and 1280 μWLi et al. Light: Science & Applications          (2023) 12:295 Page 4 of 9realized by moving the pump spot around the vicinity ofthe middle point NW. In Fig. 3a, the PL spectra collectedat right end (see Fig. S10 for the left end) are mapped byindexing the pump positions along the y-axis (the direc-tion perpendicular to the NW axis). As the pump spotmoves away from the center point (y= 0), XD and X�Dwould preserve their emission intensity even at the posi-tion y > 1.0 μm, while the trions (X�1 and X�2 ) and chargedbiexcitons (XX-) decrease their intensity much morerapidly. Detailed spectra are shown as the two line-cuts ofthe PL map at the positions of y= 0 and y=−0.5 μm as inFig. 3b. As a function of pump position, the emissions ofXX-, X�1 and X�2 can be selectively turned off. To quan-titatively analyze this dependence for accurate control, wemap out the wide-spread coupling efficiency by normal-izing all the spectra with respect to the spectrum at y= 0as in Fig. 3c. With this normalization, XD and X�D have themost wide-spread efficiency while the XX- has the least.This efficiency is largely determined by the diffusionlength, as well as the intrinsic coupling behaviors of thedipole orientations as discussed in Fig. 2. The normalizedPL intensity for typical excitons (X�1 , X�2 , XD, X�D and XX-)is then plotted as a function of pump position fordiffusion length analysis in Fig. 3d, where a diffusionmodel is employed to fit the data. As excited by a CWlaser, the exciton concentration n can be depicted by asimple steady-state diffusion equation55,56Pα2πhvw2 e�r2=w2 ¼ nðrÞτX� DX2nðrÞ ð1ÞWhere P is the excitation power,α the absorptioncoefficient at the photo energy hv, e�r2=w2the Gaussianprofile, τX and DX are the exciton lifetime and diffusioncoefficient, respectively. The analytical solution to Eq. (1)in a 2D crystal isnðrÞ /Z 1�1K0ðr0=LXÞe� r�r0ð Þ2=w2dr0 ð2Þwhere K0 is the modified Bessel function of the secondkind, LX ¼ ffiffiffiffiffiffiffiffiffiffiffiDXτXpis the diffusion length. Equation (2) isemployed to obtain the diffusion length in Fig. 3d. Thediffusion lengths of XD and X�D are then estimated to be0.59 ± 0.10 μm and 0.84 ± 0.13 μm, while those of trionsand XX- cannot be quantified as they are too smallcompared to the beam spot size (see Supplementary S11a b710 720 750 7507407307207101.00.80.60.40.20.0-1.0 -0.5 0.0 0.5 1.0Normalized PL Intensity7407301.00.50.0-0.5-1.0ycRight endRight end80040000 �m-0.5 �mdy (�m)1.00.50.0-0.5-1.0y (�m)XDXX-XD-X2-X1-y (�m)LaseryxWavelength (nm) Wavelength (nm)710 720 750l y / l 0740730Wavelength (nm)PL intensity (cts.)PL intensity (cts.)1001.20.6010XX0 X1- X2-XDXX-XX0 X1- X2-XDXX-XD-XD-XCXCXD-XX-XX0X2-XDXCX1-Fig. 3 Controlling the light emissions by tuning the exciton-photon coupling. a Color map of PL spectra as a function of the pump position yunder σ+ excitation and σ+ detection. The excitation laser is at 685 nm with power of 1 mW. The position y corresponds to the coordinates of the axisperpendicular to the axis of NW, and y= 0 represents the center point of NW. The inset indicates the scan direction in the sample schematics. b PLspectra for y= 0 and y=−0.5 μm as the line-cuts of red and blue dashed lines in (a). c Color map of coupling efficiency, Iy/I0 as a function ofwavelength and position. d The normalized PL of 5 typical excitons as a function of y position. The dark excitons and dark trions have the largestexpansions along the y axisLi et al. Light: Science & Applications          (2023) 12:295 Page 5 of 9for more details). The diffusion length thus provides anefficient approach to tune the exciton-photon coupling tomanipulate the spectral profiles of each exciton. Note herethat only this SPP coupling with diffusion model can wellexplain the observed features. The possibility of the in-plane propagation via substrate waveguide is excludedwith a detailed discussion in Supplementary Section 12.To demonstrate the control of polarization DOF, thedirectional coupling of some excitons is then shown to bepossible with polarization dependence. Away from theNW center (y= 0), the excitation scheme can supporttransverse optical spin angular momentum (t-OSAM) fordirectional coupling of circularly polarized light, i.e. spin-momentum locking of light with time reversal sym-metry38,39. The circular polarized light can be emittedfrom excitons, trions, and biexcitons in the studiedstructure (Fig. 1b). To investigate the directional coupling,the PL spectra as a function of pump position y at bothright and left ends are compared and analyzed for direc-tionality (Fig. 4a). The directionality D is defined asD=(IL-IR)/(IL+IR), where IL and IR represent the intensityat the left and right ends, respectively. All these mea-surements are pumped by a right-circularly polarized σ+CW laser at 685 nm with 1 mW power. Primarily, X�1 andX�2 show clear pump position-dependent directionality: asthe position y moves from the positive to negative values,the directionality changes its sign. This is due to thet-OSAM with time reversal symmetry as elaborated later.But the directionality for other excitons does not showsuch features. To take a closer look, the PL spectra at bothleft and right ends at y= 0.4 μm are plotted in Fig. 4b. Thedirectionality of XX- without such features is due to thesmall valley polarization (Fig. S2); the directionality ofXX0 is attributed to the extremely low coupling efficiencyinduced low directionality contrast, and the X0 emission isinvisible here as discussed above. In contrast, the XD andX�D with strong emission intensity have smaller direc-tionality without such clear pump-position dependence.To confirm that the directional coupling of X�1 and X�2 isresulted from the t-OSAM, the directionality is measuredas a function of pump polarization by changing the exci-tation half-wave plate (see “Methods” section and Fig. S13for details) as in Fig. 4c. When the polarization changesfrom linear polarization to right/left circular polarization,the directionality starts from 0 and reaches its positive/negative maximum for both X�1 and X�2 . This observationdirectly proves the mechanism of the t-OSAM, consistentwith other similar t-OSAM configurations38,39. In contrast,dbace10000300-3000300-300-1000 -500 0 5001000-1000 -500 0 50002006In-plane circular dipole (A/m)(A/m)�H��H�Out-of-plane linear dipole1.00.50.0-0.5710 720 730 740 750DirectionalityDirectionality0.150.004002000710 720 730 740 750-0.15Left endRight end-0.10.00.1-0.10.00.1HWP angle (degree)0 20 40 60 80 100y(nm)y(nm)y(μm)x (nm)x (nm)Wavelength (nm) Wavelength (nm)XD-XD-XX-XX-XX0XX0X2-X2-XDXDXCXCX1-X1-PL intensity (cts.)X2-X1-Fig. 4 Directional coupling with polarization dependence. a Position and wavelength dependent directionality D under σ+ excitation of 685 nmCW laser with 1 mW power. b PL spectra from the left and right ends of the Ag NW with y ~ 0.4 μm, as indicated by the black dashed line in (a).c Polarization dependent directionality of X�1 and X�2 , the polarization of the laser is modified by a half wave-plate (HWP). With HWP angle increases,the polarization is set from linear to right/left circular polarization. d, e are magnetic field distributions of SPPs excited by an in-plane circular dipolesource and out-of-plane linear dipole source at y= 30 nm, respectivelyLi et al. Light: Science & Applications          (2023) 12:295 Page 6 of 9the XD and X�D show negligible polarization dependence(see Fig. S14). To corroborate this conclusion, the time-averaged power flows of SPPs toward the NW ends forboth in-plane and out-of-plane dipole sources are simu-lated in Fig. 4d, e. The in-plane dipole is set to right cir-cularly polarized σ+ for trions and out-of-plane dipole is setto linearly polarized for dark excitons and dark trions (see“Methods” section). For the in-plane σ+ dipole, the SPPpower flows to the right end when the position y is set to bepositive, and vice versa for the negative y position. For theout-of-plane linear dipole, the SPP power flows evenly forboth ends without dependence on the position y. Thisconfirms the polarization dependence for XD and X�D. Theobserved non-zero directionality in Fig. 4a may beexplained by the simulation of Fig. S15, where tilted out-of-plane dipole orientation is introduced by the inhomo-geneity of the sample. Nevertheless, the reason of inho-mogeneity for non-zero directionality needs furtherexperimental investigations. Based on these detailed ana-lyses, the directional coupling via t-OSAM is well estab-lished for the trions.DiscussionIn summary, this work presents versatile opticalmanipulation of trions, dark excitons, and biexcitons ina monolayer WSe2 via contrasting exciton-photoncoupling with dependences of dipole orientations, dif-fusion, and chirality. By leveraging the photonic modesin Ag NWs, the exciton-photon coupling behaves quitedifferently for various excitons, including X�1 , X�2 , XD,X�D. and XX− according to the excitonic transitiondipole orientations. By the established contrastingexciton-photon coupling, the DOFs of intensity, fre-quency, and polarization can simultaneously bemanipulated on the excitonic spectrum. With the dif-fusion lengths of various excitons, the exciton-photoncoupling could be flexibly tuned to control the fullspectral profiles. Via the t-OSAM, the X�1 , and X�2 of in-plane transition dipoles can support directional chiralcoupling with polarization dependence. Toward the goalof full manipulation of the comprehensive excitonicspectrum on-demand, this work presents a crucial stepfor exploiting various excitons with multiple DOFssimultaneously.For practical applications based on versatile manipula-tion, the parameters of the photonic structures can betuned and optimized. In the studied plasmonic NWs here,for example, the diameters of the Ag NW and the thick-ness of the top hBN can be tuned to adjust the couplingstrength and the polarization dependence. As shown inFigs. S5 and S16, the optical contrast for the selectiveturn-on/turn-off, optical sorting, and directional routingof excitonic emissions could be optimized for realisticoptical information process.Materials and methodsSample fabricationMonolayer WSe2 was prepared by mechanical exfolia-tion of bulk materials (HQ graphene). The dry transfermethod was conducted with a home-build transfer stage.The top hBN thin film (~ 5 nm), WSe2, and bottom hBNwere picked up in sequence and transferred the hetero-structure to a cleaned 285 nm SiO2/Si substrate. Chloro-form was utilized to dissolve the polycarbonate (PC) filmthat was used for the 2D materials transfer. The chemi-cally synthesized Ag NWs were first spin-coated onanother clean substrate and then transferred to the hBN/WSe2/hBN heterostructure by the same dry transfermethod. After removing the residual PC film, the samplewas deposited with 10 nm aluminum oxide immediatelyby atomic layer deposition to prevent oxidation of the AgNW in the air.Spectroscopy measurementFor the PL measurement, a CW 685 nm laser wasemployed to excite the sample. Before reaching the 50×dark-field objective (Olympus, 0.5 NA), the laser passedthrough a half-wave plate (HWP) and/or a quarter-waveplate (QWP) to alter its polarization. The PL signal fromthe sample was collected by the same objective and guidedto a spectrometer (Andor, Kymera 328i). For the PLspectra in Figs. 1, S2, and S4, the spectrometer wasswitched to spectrum mode to collect a single spectrum.For the PL spectra in other figures, the spectrometer wasswitched to image mode. In this mode, the PL signal fromthe entire Ag NW was diffracted by a grating (300 line/mm) and recorded by an electron multiplying charge-coupled device (Andor, DU970P). The recorded imageshave two dimensions that contain the information of the xposition and wavelength, separately. The integration timewas 30 s. The spectra from the left and right ends of theAg NW can be extracted from the same image byselecting different interested areas. All the spectra werecollected at a sample temperature of 4 K (Montana,Cryostation S50).Electromagnetic simulationThe electromagnetic simulations were carried out usingCOMSOL Multiphysics 5.2a. Johnson and Christy’sexperimental data was adopted to determine thefrequency-dependent permittivity of Ag57. The refractiveindex of SiO2 was considered as 1.5. In the model, the AgNW was constructed with a pentagonal cross-section anda corner rounding of 10 nm. The length of the Ag NW isaround 8 μm. To simulate an infinite length condition,200 nm perfect matched layers were added to both ends ofthe Ag NW. An electric dipole was positioned 5 nmunderneath the center of Ag NW to simulate variousexcitons in WSe2. The dipole’s polarization can beLi et al. Light: Science & Applications          (2023) 12:295 Page 7 of 9controlled by modulating the amplitude and phasebetween linear dipoles in different directions. Finally, timeaveraged-power flow SPPs to both ends of the Ag NWwere collected to calculate the total coupling strength ξand directionality D of different excitons.AcknowledgementsThis research was supported by National Key R&D Program of China (Grant No.2021YFA1401100), National Natural Science Foundation of China (NSFC, GrantNo. 62005202, 12074297, 62261160386), the Fundamental Research Funds forthe Central Universities (No. 2042023kf0195), Guangdong Basic and AppliedBasic Research Foundation (No. 2023A1515011222), China PostdoctoralScience Fund, No.4 Special Funding (Pre-Station) – 2022TQ0235, ChinaPostdoctoral Science Fund, No.2 Special Funding (Pre-Station) – 2020TQ0234.K.W. and T.T. acknowledge support from JSPS KAKENHI (Grant Numbers19H05790, 20H00354, and 21H05233) and A3 Foresight by JSPS. We thank theCore Facility of Wuhan University for the AFM measurements.Author details1School of Physics and Technology, Center for Nanoscience andNanotechnology, and Key Laboratory of Artificial Micro- and Nanostructures ofMinistry of Education, Wuhan University, 430072 Wuhan, China. 2WuhanUniversity Shenzhen Research Institute, 518057 Shenzhen, China. 3Institute ofAdvanced Synthesis, School of Chemistry and Molecular Engineering, NanjingTech University, 211816 Nanjing, China. 4International Center for MaterialsNanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, 305-0044 Tsukuba, Japan. 5Research Center for Functional Materials, NationalInstitute for Materials Science, 1-1 Namiki, 305-0044 Tsukuba, Japan. 6WuhanInstitute of Quantum Technology, 430206 Wuhan, China. 7School ofMicroelectronics, Wuhan University, 430072 Wuhan, China. 8Henan Academyof Sciences, 450046 Zhengzhou, ChinaConflict of interestThe authors declare no competing interests.Supplementary information The online version contains supplementarymaterial available at https://doi.org/10.1038/s41377-023-01338-5.Received: 12 July 2023 Revised: 8 November 2023 Accepted: 12 November2023References1. Thureja, D. et al. Electrically tunable quantum confinement of neutral excitons.Nature 606, 298–304 (2022).2. Sun, B. S. et al. Evidence for equilibrium exciton condensation in monolayerWTe2. Nat. Phys. 18, 94–99 (2022).3. Jia, Y. Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93(2022).4. Mak, K. F. et al. Atomically thin MoS2: a new direct-gap semiconductor. Phys.Rev. Lett. 105, 136805 (2010).5. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. NanoLett. 10, 1271–1275 (2010).6. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg seriesin monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).7. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12,207–211 (2013).8. You, Y. et al. Observation of biexcitons in monolayer WSe2. Nat. Phys. 11,477–481 (2015).9. He, Y. M. et al. Cascaded emission of single photons from the biexciton inmonolayered WSe2. Nat. Commun. 7, 13409 (2016).10. Soavi, G. et al. Exciton-exciton annihilation and biexciton stimulated emissionin graphene nanoribbons. Nat. Commun. 7, 11010 (2016).11. Huang, P. et al. Nonlocal interaction enhanced biexciton emission in largeCsPbBr3 nanocrystals. eLight 3, 10 (2023).12. Barbone, M. et al. Charge-tuneable biexciton complexes in monolayer WSe2.Nat. Commun. 9, 3721 (2018).13. Ross, J. S. et al. Electrical control of neutral and charged excitons in amonolayer semiconductor. Nat. Commun. 4, 1474 (2013).14. Guddala, S. et al. Valley selective optical control of excitons in 2D semi-conductors using a chiral metasurface [Invited]. Opt. Mater. Express 9, 536–543(2019).15. Yu, H. Y. et al. Valley excitons in two-dimensional semiconductors. Natl Sci. Rev.2, 57–70 (2015).16. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductortransition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).17. Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055(2016).18. Qi, P. et al. Phonon scattering and exciton localization: molding exciton flux intwo dimensional disorder energy landscape. eLight 1, 6 (2021).19. Zhang, X. X. et al. Experimental evidence for dark excitons in monolayer WSe2.Phys. Rev. Lett. 115, 257403 (2015).20. Rivera, P. et al. Interlayer valley excitons in heterobilayers of transition metaldichalcogenides. Nat. Nanotechnol. 13, 1004–1015 (2018).21. Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater.14, 290–294 (2015).22. Zhou, Y. et al. Probing dark excitons in atomically thin semiconductors vianear-field coupling to surface plasmon polaritons. Nat. Nanotechnol. 12,856–860 (2017).23. Shi, W. B. et al. Hybrid coupling enhances photoluminescence of monolayerMoS2 on plasmonic nanostructures. Opt. Lett. 43, 4128–4131 (2018).24. Park, K. D. et al. Radiative control of dark excitons at room temperature bynano-optical antenna-tip Purcell effect. Nat. Nanotechnol. 13, 59–64 (2018).25. Wu, S. F. et al. Monolayer semiconductor nanocavity lasers with ultralowthresholds. Nature 520, 69–72 (2015).26. Shang, J. Z. et al. Room-temperature 2D semiconductor activated vertical-cavity surface-emitting lasers. Nat. Commun. 8, 543 (2017).27. Baranov, D. G. et al. Ultrastrong coupling between nanoparticle plasmons andcavity photons at ambient conditions. Nat. Commun. 11, 2715 (2020).28. Zhao, J. X. et al. Ultralow threshold polariton condensate in a monolayersemiconductor microcavity at room temperature. Nano Lett. 21, 3331–3339(2021).29. Liu, X. Z. et al. Control of coherently coupled exciton polaritons in monolayertungsten disulphide. Phys. Rev. Lett. 119, 027403 (2017).30. Cai, T. et al. Coupling emission from single localized defects in two-dimensional semiconductor to surface plasmon polaritons. Nano Lett. 17,6564–6568 (2017).31. Datta, B. et al. Highly nonlinear dipolar exciton-polaritons in bilayer MoS2. Nat.Commun. 13, 6341 (2022).32. Sanvitto, D. & Kéna-Cohen, S. The road towards polaritonic devices. Nat. Mater.15, 1061–1073 (2016).33. Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys.10, 803–813 (2014).34. Gibbs, H. M., Khitrova, G. & Koch, S. W. Exciton–polariton light–semiconductorcoupling effects. Nat. Photon. 5, 273 (2011).35. Kasprzak, J. et al. Bose-Einstein condensation of exciton polaritons. Nature 443,409–414 (2006).36. Shreiner, R. et al. Electrically controllable chirality in a nanophotonic interfacewith a two-dimensional semiconductor. Nat. Photon. 16, 330–336 (2022).37. Sun, L. Y. et al. Separation of valley excitons in a MoS2 monolayer using asubwavelength asymmetric groove array. Nat. Photon. 13, 180–184 (2019).38. Gong, S. H. et al. Nanoscale chiral valley-photon interface through optical spin-orbit coupling. Science 359, 443–447 (2018).39. Guo, Q. B. et al. Routing a chiral Raman signal based on spin-orbit interactionof light. Phys. Rev. Lett. 123, 183903 (2019).40. Chen, Y. et al. Chirality-dependent unidirectional routing of WS2 valley pho-tons in a nanocircuit. Nat. Nanotechnol. 17, 1178–1182 (2022).41. Chen, P. G. et al. Long-range directional routing and spatial selection of high-spin-purity valley trion emission in monolayer WS2. ACS Nano 15,18163–18171 (2021).42. Ye, Z. L. et al. Efficient generation of neutral and charged biexcitons inencapsulated WSe2 monolayers. Nat. Commun. 9, 3718 (2018).43. Turunen, M. et al. Quantum photonics with layered 2D materials. Nat. Rev.Phys. 4, 219–236 (2022).44. Montblanch, A. R. et al. Layered materials as a platform for quantum tech-nologies. Nat. Nanotechnol. 18, 555–571 (2023).Li et al. Light: Science & Applications          (2023) 12:295 Page 8 of 9https://doi.org/10.1038/s41377-023-01338-545. Luo, Y. et al. Deterministic coupling of site-controlled quantum emitters inmonolayer WSe2 to plasmonic nanocavities. Nat. Nanotechnol. 13, 1137–1142(2018).46. Zhang, Y. X. et al. Simultaneous surface-enhanced resonant Raman andfluorescence spectroscopy of monolayer MoSe2: determination of ultrafastdecay rates in nanometer dimension. Nano Lett. 19, 6284–6291 (2019).47. Niu, Y. J., Xu, H. X. & Wei, H. Unified scattering and photoluminescencespectra for strong plasmon-exciton coupling. Phys. Rev. Lett. 128, 167402(2022).48. Lin, K. Q. et al. High-lying valley-polarized trions in 2D semiconductors. Nat.Commun. 13, 6980 (2022).49. Steinhoff, A. et al. Biexciton fine structure in monolayer transition metaldichalcogenides. Nat. Phys. 14, 1199–1204 (2018).50. Liu, E. F. et al. Landau-quantized excitonic absorption and luminescence in amonolayer valley semiconductor. Phys. Rev. Lett. 124, 097401 (2020).51. Li, Z. P. et al. Revealing the biexciton and trion-exciton complexes in BNencapsulated WSe2. Nat. Commun. 9, 3719 (2018).52. Wang, G. et al. Colloquium: excitons in atomically thin transition metaldichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).53. Tang, Y. H., Mak, K. F. & Shan, J. Long valley lifetime of dark excitons in single-layer WSe2. Nat. Commun. 10, 4047 (2019).54. Lyons, T. P. et al. The valley Zeeman effect in inter- and intra-valley trions inmonolayer WSe2. Nat. Commun. 10, 2330 (2019).55. Cadiz, F. et al. Exciton diffusion in WSe2 monolayers embedded in a van derWaals heterostructure. Appl. Phys. Lett. 112, 152106 (2018).56. Ma, X. J. et al. Superior photo-carrier diffusion dynamics in organic-inorganichybrid perovskites revealed by spatiotemporal conductivity imaging. Nat.Commun. 12, 5009 (2021).57. Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev.B 6, 4370–4379 (1972).Li et al. Light: Science & Applications          (2023) 12:295 Page 9 of 9 Versatile optical manipulation of trions, dark excitons and biexcitons through contrasting exciton-photon coupling Introduction Results Design and characterization of the hybrid structure Experimental observation of the contrasting exciton-photon coupling Manipulate the light emissions of different excitons by tuning the coupling Discussion Materials and methods Sample fabrication Spectroscopy measurement Electromagnetic simulation Acknowledgements