Supporting Information Tunable Resonance Coupling ...

Supporting Information Tunable Resonance Coupling in Single Si Nanoparticle-Monolayer WS2 Structures Sergei Lepeshov†,$, Mingsong Wang¶,$, Alex Krasnok‡,*,$, Oleg Kotov§, Tianyi Zhangǁ, He Liuǀ, Taizhi Jiang£, Brian Korgel£, Mauricio Terronesǁ,ǀ,%, Yuebing Zheng¶,*, and Andrea Alú‡,#,* † ITMO University, St. Petersburg 197101, Russia ¶ Department of Mechanical Engineering, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA ‡ Department of Electrical and Computer Engineering, The University of Texas at Austin, TX 78712, USA § N.L. Dukhov Research Institute of Automatics, Moscow 127055, Russia ǁ Department of Materials Science and Engineering and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, PA 16802, USA ǀ Department of Chemistry and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, PA 16802, USA % Department

of Physics, The Pennsylvania State University, University Park, PA 16802,

USA, Department of Materials Science and Engineering & Chemical Engineering, Carlos III University of Madrid, Avenida Universidad 30, 28911 Leganés, Madrid, Spain, and IMDEA Materials Institute, Eric Kandel 2, Getafe, Madrid 28005, Spain £ McKetta Department of Chemical Engineering and Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712, USA # Advanced Science Research Center, City University of New York, New York, NY 10031, USA $These authors contributed equally. S-1

*E-mail: [email protected]; [email protected]; [email protected]

Coupled mode theory In our coupled mode theory, each component (the Si nanoparticle and the exciton) of the coupled system is described as a harmonic oscillator with its own resonance frequency and damping. The coupling between the nanoparticle and WS2 excitations is mediated via inductive terms proportional to the oscillator velocities. Dynamics of the full system are therefore modeled by two coupled equations: 2 xmd  2 md xmd  md xmd  gxex  eE (t )

xex  2 ex xex  ex2 xex  gxmd  0

(S1)

where xmd and xex represent coordinates of the cavity (SiNP) and exciton oscillators, respectively, E (t ) is the driving electric field, e is the elementary charge, g is the MD resonance-exciton coupling strength, the parameters ex ,  ex and md ,  md are the resonant frequency and spectral width of the exciton and the MD resonance, respectively (bare, i.e. the initial ones). We assume that only the nanoantenna interacts directly with the incident field, which reflects the fact that the exciton extinction is negligible compared to that of the nanoantenna. The scattering cross-section of the coupled system, being dominated by the nanoparticle dipole moment radiation, can be estimated in this phenomenological approach as:

 scat   xmd 4

2

 2ex2  2 2 exmd   2 g 2

2

(S2)

2 2 Here ex2   2  ex2  i ex , md   2  md  i md . This model is used to obtain the results of

Figures 1 and 2 in the main text.

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Multipole decomposition

Figure S1. Results of multipole decomposition of the single SiNP with radius of 75 nm arranged in Air (a) and in Water (b).

Electric field enhancement for the SiNP on a SiO2 substrate

Figure S2. Enhancement factor of the tangential electric field near the SiNP on SiO2 substrate in air and in water environments. S-3

Fitting of spectra with Fano resonance We apply the the Fano resonance description proposed in Refs.1,2. The Fano resonance approach suggested in these works is an expansion of the original Fano model to nonHermitian systems (with losses). The essential part of this approach is that the scattering cross section spectra s t (w ) of a nanostructure supporting dark and bright modes can be presented in the following form:

 ( )   ex ( ) md ( )

(S3)

where the partial multipliers represent an interference between a continuum of radiative waves and a nonradiative (dark) mode  ex ( ) (excitonic state) and a continuum of radiative waves constricted from the radiative (bright) mode  md ( ) (magnetic dipole mode, in our case). These multipliers are giving by: 2

  2  ex2      q b   a2   ex ( )   ex ex ,  (  )  md 2 2   2  ex2    2  md 2      1     1   exex    md md 

(S4)

 ,  md  are the resonant frequency and spectral width (dressed, where ex ,  ex and md generally speaking, i.e. changed because of strong interaction) of exciton and MD resonances, respectively, q is the asymmetry Fano parameter, b is the damping parameter originating from intrinsic losses, a is the maximal amplitude of the resonance. We note that Equation S4 assuming that the restriction  ex

ex is fulfilled. Hence, the Fano resonance

results from the competition between the two modes, and thus the Fano lineshape depends on the coupling between the relative dipole strengths of those modes.

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Figure S3. (a) Fitting of the analytical and CMT results (blue curve) presented in Figure 1(c) via the Fano resonance model. (b) The same but for Figure 2(c). The black dashed curve and green dashed curve shows the fitting by Fano lineshape and additional Lorentzian, respectively. The red dashed line is a sum of black and green ones. Figures S3(a) and (b) demonstrate the results of fitting via the Fano resonance model of the analytical and CMT results (blue curve) presented in Figure 1(c) and Figure 2(c), respectively. The values of obtained resonant frequencies in the case of Figure S3(a) are

  493.96 THz (the corresponding wavelengths are 622.36 nm and ex  481.7 THz and md 606.91 nm), whereas their values before interaction were ex  md  487.4 THz (the wavelength is 615 nm). Further, the values of obtained resonant frequencies in the case of

  491.06 THz (the corresponding wavelengths are Figure S3(b) are ex  480.52 THz and md 623.8 nm and 610.5 nm), whereas their values before interaction were ex  482.0 THz and

md  487.7 THz (the wavelengths are 621 nm and 615 nm). Thus, we come to conclusion that in both cases the extracted resonant frequencies become changed due to their interaction, which is a typical fingerprint of strong coupling regime.

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Figure S4. (a) Fitting of the experimentally measured scattering spectra (blue curve) for the single SiNP-monolayer WS2 heterostructure in air (a) and water (b) via the Fano resonance model. The black dashed curve and green dashed curve shows the fitting by Fano lineshape and additional Lorentzian, respectively. The red dashed line is a sum of black and green ones. The results of fitting of the experimentally measured scattering spectra for the single SiNP-monolayer WS2 heterostructure in air (a) and water (b) via the Fano resonance model are presented in Figure S4. These results demonstrate a significant change of the asymmetry Fano parameter q from -0.157 (air) to 0.127 (water) caused by altering of Mie resonances with replacing of air by water and variations in 1L-WS2 excitonic properties.

Monolayer WS2 preparation Atmospheric-pressure chemical vapor deposition (APCVD) method was used to prepare monolayer WS2 on SiO2/Si wafers. A tube furnace with Argon as the carrier gas (the flow rate is 150 sccm, during the synthesis) was employed. Two freshly cleaned SiO2/Si wafers with ~10 mg WO3 powders sandwiched by them were placed in a 2 cm-diameter quartz tube. Then, WO3 powders was heated up to 700 °C and held for 15 min in the tube furnace, and simultaneously sulfur powders were separately heated up to 250 °C with a heating belt. Following the APCVD fabrication, the as-grown monolayer WS2 was transferred onto a glass substrate. The transfer process began by spin coating a layer of PMMA on as-grown monolayer WS2 on the SiO2/Si wafer. Then, the SiO2/Si wafer was etched away by 1 M S-6

sodium hydroxide (NaOH) aqueous solution. After being rinsed by DI-water for several times, the detached PMMA+WS2 film was fished onto a pre-cleaned glass substrate. Finally, the PMMA layer was removed by immersing the whole specimen into acetone.

Figure S5. (a) An atomic force microscope (AFM) image of monolayer WS2. The scale bar is 2.4 μm. (b) The height profile of the back dashed line in (a). (c) A SEM image of the single aSi:H nanoparticle on monolayer WS2. The scale bar is 500 nm. Figure S5a shows an atomic force microscope (AFM) (Park Scientific) image of a representative WS2 monolayer used in our study. The thickness of monolayer WS2 is confirmed by the height profile of the back dashed line in Figure S5b. A micro-Raman system (Witec Micro-Raman Spectrometer Alpha 300) with a 488-nm excitation laser was used to examine the degree of crystalline of the monolayer WS2 in air. The Raman spectrum in Figure 1 3c shows two peaks centered at 362 cm-1and 424 cm-1, which represent out-of-plane E2g

mode, and the in-plane A2g mode of monolayer WS2, respectively3. The PL spectrum in Figure 3d shows a single intense peak centered at 622 nm (1.99 eV), which matches with the reported exciton emission of the CVD-grown monolayer WS2 4.

Synthesis of Si nanoparticles Hydrogenated amorphous silicon (a-Si:H) nanoparticles were synthesized in supercritical n-hexane, as described previously

5,6.

A 10 mL titanium batch reactor purchased from High

Pressure Equipment Company (HiP Co.) was brought in a nitrogen filled glove box. 21 µL trisilane (Si3H8, 100%, Voltaix) and a certain amount of n-hexane (anhydrous, 95%, Sigma-

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Aldrich) were added in the reactor. (Caution: trisilane is a pyrophoric liquid and should be handled in the glovebox with an inert atmosphere during all the processes.) The amount of n-hexane is related to the reaction pressure inside the reactor later during heating. The pressure with a specific temperature and amount of hexane can be determined by the n-hexane phase diagram. In all reactions, the pressure was kept at 34.5 MPa (5000 psi). Different reaction temperatures lead to different H contents in these a-Si:H nanoparticles 6.

In this experiment, the a-Si:H nanoparticles with H content of 40% were synthesized at a

temperature of 380 oC.[4] After loading the reagents, the reactor was first sealed using a wrench inside the glove box. Then it was tightly sealed using a vice after removed from the glove box. The reactor was then inserted into a heating block and heated to the target temperature for 10 min to allow complete decomposition of trisilane. After the reaction, the reactor was cooled to room temperature by an ice bath. The reactor was then opened and the colloidal a-Si:H nanoparticles were extracted from the reactor. The nanoparticles were washed using chloroform (99.9%, Sigma-Aldrich) by centrifuging at 8000 rpm for 5 min. The precipitate was collected and dispersed in chloroform before use. A SEM image of the a-Si:H nanoparticles on monolayer WS2 is shown in Figure S5c.

Optical measurement SiNPs were drop coasted on the bare glass substrate or the top of monolayer WS 2. The scattering spectra of single SiNPs on the bare glass substrate or monolayer WS2 were measured by an inverted microscope (Ti-E, Nikon) with a spectrograph (Andor), an EMCCD (Andor) and a halogen white light source (12V, 100 W), as schematically shown in Figure S67,8. To measure the scattering spectra in the solvent with a big dielectric constant, water was sandwiched between the sample and a cover glass 9. The Witec Micro-Raman Spectrometer was also used to measure PL spectra of monolayer WS 2 in different surrounding media.

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Figure S6. Schematic of the optical setup.

PL spectra fitting

Figure S7. Fitting of PL spectra of 1L-WS2 in air (a) and in water (b).

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