Electrical Tuning of Exciton–Plasmon Polariton Coupling in Monolayer

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Electrical tuning of exciton-plasmon polariton coupling in monolayer MoS2 integrated with plasmonic nanoantenna lattice Bumsu Lee, Wenjing Liu, Carl H. Naylor, Joohee Park, Stephanie C Malek, Jacob S Berger, Alan T. Charlie Johnson, and Ritesh Agarwal Nano Lett., Just Accepted Manuscript • Publication Date (Web): 14 Jun 2017 Downloaded from http://pubs.acs.org on June 14, 2017

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Electrical tuning of exciton-plasmon polariton coupling in monolayer MoS2 integrated with plasmonic nanoantenna lattice

Bumsu Lee1†, Wenjing Liu 1†, Carl H. Naylor 2, Joohee Park1, Stephanie C. Malek1, Jacob S. Berger1, A.T. Charlie Johnson2 and Ritesh Agarwal1*

1

Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA

2

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA

†

These authors contributed equally to this work.

* To whom correspondence should be addressed. E-mail: [email protected]

Active control of light-matter interactions in semiconductors is critical for realizing next generation optoelectronic devices, with real-time control of the system’s optical properties and hence functionalities via external fields. The ability to dynamically manipulate optical interactions by applied fields in active materials coupled to cavities with fixed geometrical parameters opens up possibilities of controlling the lifetimes, oscillator strengths, effective mass and relaxation properties of a coupled exciton-photon (or plasmon) system. Here, we demonstrate electrical control of exciton-plasmon coupling strengths between strong and weak coupling limits in a two-dimensional semiconductor integrated with plasmonic nanoresonators assembled in a field-effect transistor device by electrostatic 1 ACS Paragon Plus Environment

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doping. As a result, the energy-momentum dispersions of such an exciton-plasmon coupled system can be altered dynamically with applied electric field by modulating the excitonic properties of monolayer MoS2 arising from many-body effects. In addition, evidence of enhanced coupling between charged excitons (trions) and plasmons was also observed upon increased carrier injection, which can be utilized for fabricating fermionic polaritonic and magnetoplasmonic devices. The ability to dynamically control the optical properties of a coupled exciton-plasmonic system with electric fields demonstrates the versatility of the coupled system and offers a new platform for the design of optoelectronic devices with precisely tailored responses.

Keywords: 2D TMDC, nanoplasmonics, electrical tuning, exciton plasmon polariton, trion plasmon, magnetoplasmons

Mono- and few-layered two-dimensional (2D) transition metal dichalcogenide (TMDC) semiconductors have been receiving great attention due to their very unique attributes originating from strong two-dimensional confinement and inadequate dielectric screening along with new potential applications including ultra-thin optoelectronic devices, exciton-polariton formation at high temperature, and spin-valley devices1-3. The strongly confined 2D excitons in monolayer TMDC semiconductors leads to several interesting optical features such as large exciton binding energy4-7 and oscillator strength8,9, and the observation of higher-order excitations such as charged excitons (trions)10,11. The optical properties of 2D excitons can be significantly altered when coupled to an external cavity, leading to enhancement of spontaneous emission rate and 2 ACS Paragon Plus Environment

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lasing in the weak exciton-photon coupling regime, and the formation of exciton-polaritons in the strong coupling regime12-23. Various types of optical cavities including distributed Bragg reflectors (DBRs)12-14, photonic crystals15 and plasmonic nanoresonators16-23 have been utilized to manipulate the optical properties of 2D excitons, demonstrating weak, intermediate and strong coupling regimes. Among different cavity types, plasmonic nanoantenna arrays offer unique opportunities for tailoring light-matter interactions in 2D materials with geometric compatibility, strong optical confinement as well as their ease of integration, which is also compatible with electrical injection or gating device configuration. Furthermore, plasmonic lattices depending on the lattice geometry allows for geometry-dependent tunable and intense resonances originating from localized surface plasmons (LSPs) coupled to the lattice dispersion known as “surface lattice resonances” or “lattice-LSP” modes24,25. The lattice-LSPs are propagating modes with strong electric fields, and relatively high-quality factors in comparison to LSP resonances from individual (uncoupled) nanoparticles. Recently, monolayer molybdenum disulfide (MoS2) integrated with plasmonic nanoantenna lattice has shown large enhancements of the Raman scattering and photoluminescence in the weak coupling regime17, Fano resonances in the intermediate coupling range17 and normal mode splitting with the formation of exciton-plasmon polaritons in the strong coupling regime22,23. On the other hand, owning to the atomically thin nature and the associated significantly reduced screening of the charge carriers, monolayer TMDC semiconductors provide a unique platform for electrically controlling their optoelectronic properties, via electrostatic doping in a field-effect transistor (FET) geometry. As a result, novel findings have been reported including the modulation of exciton binding energies and exciton-polaron coupling26-28, observation of charged trions11,12, and valley-contrast second-harmonic generation29. Here, by configuring the 3 ACS Paragon Plus Environment

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plasmonic lattice-monolayer MoS2 system in an FET device geometry, we demonstrate active control of the coupling strengths between the MoS2 excitons and lattice-LSP resonances, with continuous and reversible transition between the strong and weak exciton-plasmon coupling regimes achieved by electron injection or depletion in the active MoS2 monolayer. Furthermore, under certain doping conditions, evidence of enhanced coupling between negatively charged excitons (trions) and plasmons was also observed, which are fermionic exciton-plasmon polaritons that can provide a novel platform for quantum optics. Therefore, we demonstrated that the spin classification of the exciton-plasmon system can be switched back and forth between bosonic (neutral exciton-plasmon) and fermionic (trion-plasmon) polaritonic states by simply applying an external electric field to the system.

To fabricate the optoelectronic device (Figure 1a), monolayer MoS2 was grown directly on Si/SiO2 substrate by chemical vapor deposition30 followed by the fabrication of source and drain electrodes and silver plasmonic nanodisk arrays (see Materials and Methods). A 285 nmthick thermally grown SiO2 layer sandwiched between MoS2 and highly-doped Si substrate produces a metal-oxide-semiconductor FET with a capacitance of ~12 nF/cm2. Charge carriers were injected or depleted from the electrical contacts depending on the gate electrostatic potential (VG) with respect to MoS2. For example, a VG of ~100 V can lead to a carrier density of ~8×1012/cm2 in the MoS2 monolayer, estimated from the capacitance of the device. As a result, the chemical potential (Fermi level) of MoS2 can be altered by ~50 meV depending on the carrier density. Figure 1b shows a typical transconductance curve obtained from a MoS2 FET device, displaying n-type channel performance. The plasmonic lattice cavities were fabricated with the diameters of the silver nanodisks varied between 110 and 140 nm, with a constant thickness of 4 ACS Paragon Plus Environment

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50 nm and with a lattice parameter of a × b = 460 nm × 460 nm. These cavity geometries allow tuning the LSP energies near the MoS2 excitonic region to enable strong exciton-plasmon coupling22. To characterize the evolution of the coupling between the MoS2 excitons and latticeLSPs, the dispersions of the coupled MoS2-plasmonic lattice system were measured by a homebuilt angle-resolved setup31 while tuning the gate voltage (see Materials and Methods). The angle-resolved differential reflectance spectra (∆R/R = (Rsample-Rsubstrate)/Rsubstrate) measured at 77 K for MoS2 monolayer integrated with silver nanodisk array with disk diameters, d = 110 nm are presented in Figures 2a-c at three representative gate voltages. The lattice was carefully designed to tune the LSP mode of the nanodisks nearly in resonance with the A excitons to allow maximum exciton-plasmon coupling22. As a result, strong coupling of the lattice-LSP modes to both the neutral excitons (Ao) and negatively charged excitons (trions, A-) was observed at different applied voltages, leading to the formation of their own discrete polariton branches. The dark and bright regions in the angle-resolved ∆R/R plots are lower and higher values of the reflected light over the background reflection, and as in our previous work,22 we have identified that the dark features (dips) are related to the absorption-dominated response of the exciton-plasmon polaritons. At VG = 0 V (Figure 2a), the system’s dispersion shows an anti-crossing behavior near the MoS2 Ao exciton state (yellow (green) dashed-lines express the positions of Ao (A-) excitons in Figure 2a-c), indicating strong coupling between the MoS2 excitons and lattice-LSPs; When gate bias was applied, significant changes in the angle-resolved spectra were observed (Figure 2b and c). Upon sweeping the VG from 0 to 80 V, the anti-crossing gradually disappeared in the dispersion curves, indicating that the strong Ao exciton-lattice LSP coupling was gradually changed to weak coupling upon carrier injection. Interestingly, starting from VG = 40 V (Figure 2b and c), new spectral features show up near 650 nm, which matches 5 ACS Paragon Plus Environment

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the A- exciton (trion) resonance, implying the appearance of the trion state and their strong coupling with the lattice-LSP modes upon carrier injection. Figure 2d-f show a series of ∆R/R line-cuts extracted at different angles from the individual angle-resolved spectra (Figure 2a-c, orange-dashed rectangular areas) at VG = 0, 40, and 80 V. Positions of uncoupled Ao and A- exciton resonances of bare MoS2 are also indicated as arrows in Figure 2d-f. These ∆R/R spectra show clearly resolved exciton-plasmon polariton dispersions originated from both Ao and A- exciton-plasmon coupling at different gate voltages. At VG = 0 V, distinct polariton branches resulting from strong Ao exciton-plasmon coupling can be observed, as indicated by the gray-dashed lines in Figure 2d. The strong Ao exciton-plasmon coupling and the absence of the spectral features of A- excitons indicate that the sample was lightly doped. As the carrier concentration increased upon applying a positive VG = 40 V, new polariton mode (~650 nm) corresponding to A- exciton-plasmon coupling appeared in the ∆R/R spectra (Figure 2b and e), accompanied by a slight blue-shift of the preexisting polariton branches. Upon increasing VG to 80 V (Figure 2c and f), the polariton modes originating from Ao exciton-plasmon coupling vanished while the A- (trion) polariton gained oscillator strength, resulting in more enhanced reflection features and mode splitting, which suggests that the system changed progressively from strong Ao exciton-plasmon coupling to A- exciton-plasmon coupling regime with increasing carrier concentration. The polariton modes cross their corresponding uncoupled Ao or A- excitons of bare MoS2 (indicated as arrows in Figure 2d-f) because our system consists of multiple-coupled oscillators (exciton, trion, LSP, lattice mode) with their intercoupling rather than simple two-coupled oscillators, in which the energies of the polariton modes are determined depending on their relative coupling strengths and detuning (see Supporting Information). These experiments demonstrate that plasmon coupling to the excitonic 6 ACS Paragon Plus Environment

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resonances can be finely tuned between the weak and strong coupling limits via electric control of carrier density in the active medium of 2D semiconductors. In addition, the possibility of creating trion-plasmon polaritons, a unique type of fermionic light-matter hybrids, in which the spin structure of the trion can effectively couple to the plasmon, can enable a new class of magnetoplasmonic systems. In order to quantitatively characterize the observed tuning phenomena of the excitonplasmon coupling, the angle-resolved spectra were fitted to a coupled oscillator model (COM) to calculate the exciton-plasmon coupling strengths as a function of VG, as shown in Figure 3 (see Supporting Information). Red dots in angle-resolved ∆R/R plots were extracted from the experimental data, tracking the exciton-plasmon polariton modes and gray solid-lines overlaid on top of red dots are from the COM results. These COM fitting results are in very good agreement with the experimental data, capturing all the features of the recorded dispersions over large wavelength and angle ranges at different applied VG (a set of full angle-resolved ∆R/R simulation images are also presented in the Supporting Information). The VG-dependent excitonLSP coupling strengths are presented in Figure 3f, while the exciton-diffractive order coupling strengths were found to be nearly negligible in this device (See Supporting Information for all the matrix elements obtained from COM fitting). At VG = 0 V, only the Ao exciton-plasmon strong coupling was observed in the reflectance spectrum, as indicated by clear anti-crossing behaviors of the dispersion curves (Figure 2d and 3a) with a coupling strength of 63 meV. As the carrier concentration increased upon applying positive VG, the Ao exciton state displayed a slight blue shift in its energy (yellow dashed-lines in Figure 3a-e) and linewidth broadening in the ∆R/R spectra attributed to many-body effects upon carrier doping26 (see also Supporting Information). As a result, it gradually decoupled from the lattice-LSP modes, and eventually 7 ACS Paragon Plus Environment

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disappeared in the dispersion spectra. Upon increasing the positive gate voltage, an additional polariton branch emerged (Figure 3b), resulting from the splitting of the initial polariton branch 2 at the A- exciton state, indicating A--plasmon coupling. With a further increase in VG (Figure 3bd), the new polariton branch 2 progressively blue shifted, suggesting increased mode splitting between the polariton branches 2 and 3 near the A- state (increase in A- plasmon coupling), and decreased mode splitting between polariton branches 1 and 2 near the A0 state (decrease in Ao plasmon coupling). At VG = 80 V (Figure 3e), the polariton branches 1 and 2 merged into one branch, which indicates that the coupling between Ao excitons and the lattice-LSP modes vanished, owing to the collapse of their oscillator strengths under high doping conditions. The evolution in the exciton-plasmon coupling strengths is simulated by the COM fitting. Upon applying positive VG, the Ao exciton-LSP coupling strength undergoes a large change from 63 meV to almost zero, while the coupling between trions and lattice-LSP modes gradually increased with increased doping and reached a maximum coupling strength of 42 meV at VG = 80 V, caused by a partial transition of the oscillator strengths from neutral excitons to negatively charged trions. At intermediate VG (Figure 3c), the observed polariton modes originated from both the A- (lower energy) and Ao (higher energy) excitons indicated by gray arrows. The lower value in the maximum coupling strength of A- excitons can be explained by their weaker oscillator strengths than Ao excitons. However, given that the typical oscillator strengths of trions found in 2D quantum wells or bulk materials are more than an order of magnitude lower than that of the neutral excitons10,32, this finding is intriguing since the magnitude of the coupling strength of trions with plasmons is comparable to neutral exciton-plasmon coupling, which further illustrates the enhanced interaction between excitons and charged carriers due to significantly reduced screening and large overlap between electron and hole wave functions from

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their extreme 2D confinement15. In control experiments (see Supporting Information), reflectance spectra of bare monolayer MoS2 FET device also revealed a decrease (increase) of the oscillator strength of the Ao (A-) exciton transition upon electrostatic doping and only a very small shift of their resonance energies due to many-body effects26-28. These results are consistent with our observation of the evolution of the exciton-plasmon coupling with increased doping, as will be discussed later in more detail. To further study the modulation of light-matter coupling of the system and its active control via external fields, measurements were carried out on nanodisk arrays with different disk diameters (d =120 and 140 nm) patterned on the same large area MoS2 monolayer. LSP resonances arising from different sized silver disks resulted in different coupling strengths with Ao and A- excitons (Figure 4) due to different LSP-exciton detuning22. Unlike the previous device with the LSP in resonance with the A- exciton (d = 110 nm, Figure 3 and 4a-c), these two lattices have their LSP resonances more detuned from the excitonic region at 670 nm and 685 nm (blue-dashed lines in Figure 4f-h and k-m) respectively. Especially, the 685 nm mode is largely detuned from the excitonic region with >150 meV detuning. The tuning of the mode dispersions (Figure 4f-h and k-m) with different VG was observed in both devices, with qualitatively similar trends (Figure 3i and n) as observed for the device in Figure 3 and Figure 4a-d. However, the exciton-plasmon coupling strengths of the array with LSP in resonance with the excitons (d = 110 nm) were significantly higher than the array with detuned LSP resonance (d = 140 nm) at the same VG. The different LSP resonances in these two different arrays not only quantitatively changed the exciton-plasmon coupling strengths, but more importantly, altered the nature of the exciton-plasmon coupling of the system. Figure 4e, j and o show a series of line-cuts obtained at different VG, extracted from the angle-resolved spectra of the three arrays at the angles where the 9 ACS Paragon Plus Environment

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lattice-LSP modes have zero detuning with the Ao exciton (sinθ = 0.34, 0.32, and 0.27 for d = 110, 120 and 140 nm, respectively). For d = 110 and 120 nm devices (Figure 4e and j), evolution of the exciton-plasmon dispersion indicated by grey-dashed lines with VG suggests that the system changed progressively from strong Ao exciton-plasmon coupling to strong A- excitonplasmon coupling regime. In contrast, the d = 140 nm device (Figure 4o) showed two polariton modes observed at VG = 0 V gradually merged into one broad dip with increasing VG, indicating that the system evolved from strong to weak coupling regime. These results, consistent with other similar devices, also provide more insights about design strategies for obtaining precisely tailored optoelectronic responses in 2D polaritonic devices.

Enhanced many-body effects are one of the unique characteristics of highly confined TMDC monolayers even at moderate doping levels, which can be easily achieved from Si/SiO2 back-gated devices7,10,26-28. Greatly reduced screening due to the lack of large bulk polarization leads to enhanced Coulomb interaction and scattering process, which, along with phase-space filling (Pauli blocking) effect, influences the exciton oscillator strength and binding energy26-28,33. The increased charge carrier concentration under positive electrostatic gating results in the reduction of the Ao oscillator strength due to exciton bleaching, giving rise to weaker interactions between excitons and plasmons, which drives the system towards weak coupling regime. On the contrary, the depletion of charge carriers makes MoS2 more intrinsic, resulting in stronger exciton-plasmon coupling. Thus, in TMDC monolayers, continuous and reversible switching between strong and weak exciton-plasmon coupling regimes can be achieved in response to the

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variation of charge carrier concentration (Fermi level shift), which can be easily controlled by external fields, owing to the unique attributes of the 2D excitonic systems. In summary, we demonstrated active control of the coupling strengths between 2D MoS2 excitons and plasmonic lattices integrated in an FET device, via charge carrier injection/depletion. Continuous and reversible transition between the strong and weak excitonplasmon coupling regimes was achieved by tuning the gate voltage. Furthermore, we also showed that the trion resonances could also couple with the lattice plasmons at high electron doping concentration, showing their own dispersion properties. Our work demonstrates that unique opportunities exist in 2D monolayer semiconductors to electrically control light-matter interactions, owing to the lack of bulk polarization in these ultrathin materials, which reduces carrier screening, and hence leads to extraordinarily strong exciton oscillator strengths and binding energies, as well as enhanced many body effects. Electrical control of light-matter interactions in photonic devices is very attractive for designing modulators, switches, sensors, and other functional polaritonic devices. Furthermore, stronger trion-plasmon coupling can be an attractive platform for studying the strongly coupled spin and plasmon systems, i.e., magnetoplasmons, in which the combination of plasmonics and magnetism can enable the control of plasmonic properties by magnetic fields, giving rise to novel magneto-optical responses in these class of materials.

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Materials and Methods MoS2 growth and device fabrication. Monolayer MoS2 flaks were grown on Si/SiO2 substrate (285 nm thick SiO2 layer) via chemical vapor deposition (CVD) method. Silver nanodisk array and the source and drain electrodes were patterned directly on the as-grown MoS2 substrate by electron beam lithography, followed by the deposition of 50 nm silver by electron-beam evaporation. More detailed information for both MoS2 growth and fabrication of the plasmonic nanostructures and electrical contacts have been described in references (17), (22) and (30). The device (on the substrate) was then attached to a chip carrier with electrical pins designed for our optical microscopy cryostat (Janis ST-500) and the sample electrodes were connected to electrical pads of the chip carrier by wire-bonding for the electrical measurements. Optical and electrical measurements. Angle-resolved reflectance spectra were acquired from our home-built angle-resolved optical setup. The setup configuration and the detailed information about the measurements are described elsewhere in our previous study (references (22) and (31)). For electrical measurements, two Keithley 2400 voltage sources were used to apply the source-drain bias and the gate voltage, and the channel current was recorded through Keithley 6517 electrometer.

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Supporting Information Gate voltage-dependent reflectivity in bare MoS2, coupled oscillator model, fitting parameters for the COM model for different MoS2-plasmon cavity devices and full scale dispersions of devices via the COM model.

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(21) Sobhani, A.; Lauchner, A.; Najmaei, S.; Ayala-Orozco, C.; Wen, F.; Lou, J.; Halas, N. J. Appl. Phys. Lett. 2014, 104, 031112. (22) Liu, W.; Lee, B.; Naylor, C. H.; Ee, H. S.; Park, J.; Johnson, A. C.; Agarwal, R. Nano Lett. 2016, 16, 1262-1269. (23) Wang, S.; Li, S.; Chervy, T.; Shalabney, A.; Azzini, S.; Orgiu, E; Hutchison, J. A.; Genet, C.; Samorì, P; Ebbesen, T.W. Nano Lett. 2016,16, 4368-4374. (24) Zou, S.; Janel, N.; Schatz, G. C. J. Chem. Phys. 2004, 120, 10871-10875. (25) Auguié, B.; Barnes, W. L. Phys. Rev. Lett. 2008, 101, 143902. (26) Chernikov, A.; van der Zande, A. M.; Hill, H. M.; Rigosi, A. F.; Velauthapillai, A.; Hone, J.; Heinz, T. F. Phys. Rev. Lett. 2015, 115, 126802. (27) Gao, S.; Liang, Y.; Spataru, C. D.; Yang, L. Nano Lett. 2016, 16, 5568-5573. (28) Sidler, M.; Back, P.; Cotlet, O.; Srivastava, A.; Fink, T.; Kroner, M.; Demler, E.; Imamoglu, A. Nature Phys. 2017, 13, 255-261. (29) Seyler, K. L.; Schaibley, J. R.; Gong, P.; Rivera, P.; Jones, A. M.; Wu, S.; Yan, J.; Mandrus, D. G.; Yao, W.; Xu, X. Nature Nanotech. 2015, 10, 407-411. (30) Han, G. H.; Kybert, N. J.; Naylor, C. H.; Lee, B. S.; Ping, J.; Park, J. H.; Kang, J.; Lee, S. Y.; Lee, Y. H.; Agarwal, R.; Johnson, A. C. Nature Commun. 2015, 6, 6128. (31) Sun, L.; Ren, M. L.; Liu, W.; Agarwal, R. Nano Lett. 2014, 14, 6564-6571. (32) Combescot, M.; Tribollet, J. Solid State Commun. 2003, 128, 273-277. (33) Schmitt-Rink, S.; Chemla, D. S.; Miller, D. A. B. Adv. Phys. 1989, 38, 89-188.

Acknowledgements This work was supported by the NSF under the NSF 2-DARE program (EFMA1542879), NSF-MRSEC (LRSM) seed grant under award number DMR11-20901 and by the US Army Research Office under Grant No. W911NF-12-R-0012-03. S.C.M acknowledges the NSF Graduate Research Fellowship Program for its support. Nanofabrication and electron microscopy characterization was carried out at the Singh Center for Nanotechnology at the University of Pennsylvania.

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Figures Figure 1.

Figure 1. Electrical tuning of monolayer MoS2 coupled with plasmonic nanodisk array configured in a field-effect transistor geometry. (a) Schematic diagram of the MoS2 monolayer-plasmonic lattice system integrated with an FET device which enables carrier injection and depletion. (b) Typical transconductance data obtained from a MoS2 FET device. Inset: SEM images of the MoS2-plasmonic lattice FET device.

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Figure 2.

Figure 2. Tuning of exciton-plasmon coupling between the lattice-LSP modes to both neutral (Ao) and charged (A-) excitons via gate voltage. (a-c) Angle-resolved ∆R/R spectra at three different gate voltages (VG = 0, 40 and 80 V), showing Ao and Aexciton-plasmon coupling. (d-f) Line cuts extracted from the orange dashed-rectangular area of the angle-resolved spectra at each gate voltage in (a-c). Angles of line cuts are described in (d). Evolution of the system’s eigenmodes are shown by grey-dashed lines.

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The positions of uncoupled Ao and A- excitons are indicated as arrows. The ∆R/R spectra are offset for clarity. Lattice constant is (a × b) = (460 nm × 460 nm).

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Figure 3.

Figure 3. Coupled Oscillator Model fitting of the evolution of the exciton-plasmon coupling under different electron doping conditions. (a-e) Angle-resolved ∆R/R spectra and the corresponding coupled oscillator model (COM) fits at different gate voltages. Red dots express the eigenmodes extracted from our experimental data and gray solidlines overlaid with red dots are the fitting results from the COM model. At VG = 40 V, polariton modes are observed from both Ao and A- excitons as indicated in (c). The 19 ACS Paragon Plus Environment

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positions of uncoupled Ao and A- excitons, and LSP resonances are indicated as yellow-, green- and blue-dashed lines, respectively in (a-e). (f) Calculated coupling strengths between LSP and both Ao and A- excitons obtained from the COM as a function of the gate voltage.

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Figure 4.

Figure 4. Gate-voltage dependent exciton-plasmon coupling in three different silver nanodisk arrays with different exciton-LSP detuning values. (a-c) d = 110 nm. (f-h) d = 120 nm. (k-m) d = 140 nm. The positions of uncoupled Ao and A- excitons, and LSP resonances are indicated as yellow-, green- and blue-dashed lines, respectively. (d,i,n) Comparison of the exciton-plasmon coupling strengths between LSPs and both Ao and A- excitons obtained from the COM as a function of the gate voltage. (e,j,o) Line cuts (vertical white-dashed lines, sinθ = 0.34 in (a-c), sinθ = 0.32 in (f-h), and sinθ = 0.27 in (k-m), respectively) from the angle-resolved spectra at different VG. Grey-dashed lines in (e), (j) and (o) trace the evolution of the system’s eigenstates upon carrier doping.

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The ∆R/R spectra are offset for clarity. Lattice constants of all devices are (a × b) = (460 nm × 460 nm).

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