Resonance Coupling in Heterostructures Composed of Silicon

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Resonance Coupling in Heterostructures Composed of Silicon Nanosphere and Monolayer WS2: A Magnetic-Dipole-Mediated Energy Transfer Process Hao Wang, Jinxiu Wen, Weiliang Wang, Ningsheng Xu, Pu Liu, Jiahao Yan, Huanjun Chen, and Shaozhi Deng ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b07826 • Publication Date (Web): 10 Jan 2019 Downloaded from http://pubs.acs.org on January 12, 2019

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Resonance Coupling in Heterostructures Composed of Silicon Nanosphere and Monolayer WS2: A Magnetic-Dipole-Mediated Energy Transfer Process Hao Wang,†,‡,# Jinxiu Wen,†,‡,# Weiliang Wang,‡,# Ningsheng Xu,† Pu Liu,§ Jiahao Yan,§ Huanjun Chen,†,* and Shaozhi Deng†,* †State

Key Laboratory of Optoelectronic Materials and Technologies, Guangdong Province Key

Laboratory of Display Material and Technology, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China. ‡School

of Physics, Sun Yat-sen University, Guangzhou 510275, China.

§School

of Materials Science and Engineering, Guangzhou 510275, China.

#These

authors contributed equally to the work.

*Address correspondence to: [email protected].; [email protected]. ABSTRACT Light−matter resonance coupling is a long-studied topic for both fundamental research and photonic and optoelectronic applications. Here we investigated the resonance coupling between the magnetic dipole mode of a dielectric nanosphere and 2D excitons in a monolayer semiconductor. By coating an individual silicon nanosphere with a monolayer of WS2, we theoretically demonstrated that, because of the strong energy transfer between the magnetic dipole mode of the nanosphere and the A-exciton in WS2, resonance coupling

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evidenced by anticrossing behavior in the scattering energy diagram was observed, with a mode splitting of 43 meV. In contrast to plexcitons, which involve plasmonic nanocavities, the resonance coupling in this all-dielectric heterostructure was insensitive to the spacing between the silicon nanosphere core and the WS2 shell. Additionally, the two split modes exhibited distinct light-scattering directionality. We further experimentally demonstrated the resonance coupling effect by depositing silicon nanospheres with different diameters onto a WS2 monolayer and collecting the scattering spectra of the resulting heterostructures under ambient conditions. We further demonstrated active control of the resonance coupling by temperature scanning. Our findings highlighted the potential of our all-dielectric heterostructure as a solid platform for studying strong light−matter interactions at the nanoscale. KEYWORDS： resonance coupling · silicon nanospheres · magnetic dipole modes · twodimension excitons · two-dimensional materials

Resonance coupling, a phenomenon of light−matter interaction between optical resonators and quantum emitters, has recently attracted intense research interest because of its importance in fundamental research as well as state-of-the-art nanophotonic applications such as exciton−polariton lasers, all-optical switches, and quantum information processing, among others.1−4 Such a coupling process can lead to a coherent and reversible energy exchange between the spectrally overlapped optical resonator and emitters. The occurrence of such hybridized states is usually characterized by mode splitting or quantized quenching dips on the optical extinction or scattering spectra of the systems.1,5−15 For an N-exciton system, the coupling strength refers to g  N  / V , where  is the transition dipole moment of the excitons and V is the mode volume of the optical resonator. Accordingly, a prerequisite for strong resonance


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coupling is a cavity with small V.12,14,15 Over the past several decades, because of their ultrasmall mode volumes, plasmonic nanocavities have been extensively used to achieve resonance coupling with various quantum emitters.1,5−15 These systems are well known as plexcitons.5,7,8,10 In particular, very recent studies have demonstrated that the resonance coupling with plasmonic nanocavities can even enter the strong coupling regime with only a single quantum emitter, which is important for quantum applications.13−15 High-refractive-index dielectric nanostructures are another type of optical nanocavities capable of confining free-space light into nanoscale volumes.16−18 In comparison with metals, these dielectrics usually exhibit a very small imaginary part of their dielectric functions across a broad spectral range. Furthermore, such dielectric nanostructures can exhibit intriguing optical magnetic and electric resonance modes that can be controlled through the manipulation of the nanostructures’ size and composition.19−23 Consequently, they impart resonance coupling with additional advantageous traits that cannot be accessed using individual pristine plasmonic nanostructures, such as low loss and unidirectional light scattering originating from the interferences between the spectrally overlapped excitons and magnetic dipole resonances.24−28 For example, several recent pioneering works have demonstrated resonance coupling with directional-light-scattering behaviors in dielectric nanostructures coupled with molecule excitons.29−32 From an application viewpoint, the compatibility of silicon nanostructures with modern semiconductor processing techniques can also make them excellent complements to plasmonic nanostructures in future nanophotonic devices. Another important parameter affecting the coupling strength is the transition dipole moment, μ, of the excitons. A large μ is favorable for strong resonance coupling of large mode splitting energy. Previous studies have utilized dye molecules, quantum dots, J-aggregates, and quantum


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wells as emitters; however, these materials exhibit relatively small μ values (4−36 Debye).12−15,33 In recent years, two-dimensional transition-metal dichalcogenides (TMDs) have been shown to exhibit a large μ (56 Debye) associated with their atomically thin thicknesses.34 In addition, TMDs with exotic external-stimulus-sensitive optical and optoelectronic responses have also been demonstrated.35−40 These properties make the TMDs ideal platforms for strong light−matter interactions with active control, similar to traditional exciton materials.41−45 Indeed, we and others have demonstrated resonance coupling at room temperature, including strong coupling and intermediate coupling, by coupling an individual plasmonic nanostructure to a monolayer TMD.46−51 In contrast to the aforementioned background, in the present work, from both theoretical and experimental aspects, we report on the resonance coupling between the magnetic dipole mode (MDM) and two-dimensional excitons by encapsulating an individual silicon nanosphere with monolayer WS2 (ML-WS2). The calculation results show that, when a silicon nanosphere is coated with ML-WS2, resonance coupling indicated by an anticrossing behavior in the energy diagram with a mode splitting of 43 meV is observed. This behavior is attributed to the coherent energy transfer between the magnetic dipole resonance and exciton transitions. In comparison with the resonance coupling in plexcitons, that in the all-dielectric heterostructure is less sensitive to the separations between the nanosphere core and the ML-WS2 shell. Furthermore, by utilizing single-particle dark-field scattering spectroscopy, we experimentally demonstrated the resonance coupling effect in an individual heterostructure composed of silicon nanosphere supported on ML-WS2. The resonance coupling revealed in our study is strongly related to the high-refractive-index (~3.5 in the visible region) silicon nanosphere, which can support a strong MDM. Such a coupling effect differs substantially from the enhancement of photoluminescence


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(PL) in 2D perovskite using SiO2 microspheres with a low refractive index (1.45 in the visible region), where MDM was not involved.52 Moreover, it is noteworthy that the resonance coupling in a single silicon nanoparticle integrated with ML-WS2 was very recently reported, which claimed approaching the strong coupling regime.53 Although the authors of this previous study could modify the resonance coupling by placing the heterostructure in different dielectric environments, active control of the coupling effect remains unexplored. In the current study, using a similar heterostructure, we move a step forward by exploring active control of the resonance coupling effect via a temperature scanning technique. More importantly, by carefully scrutinizing the resonance coupling behaviors, we attribute the coupling between the MDM and two-dimensional excitons to a weak coupling regime mediated by an energy transfer process. We reveal a directional light-scattering characteristic, which is a typical fingerprint inherited from the MDM, in the heterostructures. RESULTS AND DISCUSSION To calculate the resonance coupling between the MDM and ML-WS2 excitons, we conceived a core−shell heterostructure comprising a silicon nanosphere coated with ML-WS2 (Figure 1a, inset). The diameter of the silicon nanosphere was 149 nm, and the thickness of the ML-WS2 shell was set to 1 nm on the basis of a previously reported experimental value.47 The scattering/absorption spectra of the silicon nanosphere, ML-WS2 shell, and core−shell heterostructures were then calculated analytically using the Mie theory.29,54 Figure 1a gives the theoretical scattering spectrum of the pristine silicon nanosphere, absorption spectrum of the hollow ML-WS2 shell, and the scattering spectrum of the corresponding core−shell heterostructure, which are excited by linearly polarized plane waves. The scattering spectrum of the pristine silicon nanosphere exhibits two typical resonance modes in the visible regime, which


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are dominated by the MDM at approximately 608 nm and by the electric dipole mode (EDM) at approximately 498 nm (Figure 1a, green line and Figure S1 in the Supporting Information).21,22,28 The scattering is negligible in the ML-WS2 hollow shell, whereas the absorption spectrum shows two prominent absorption peaks at 614 nm and 516 nm (Figure 1a, red line). These two absorption maxima are related to the A- and B-exciton transitions, respectively, which originate from the direct transitions at the K point of the ML-WS2 with a large spin−orbit coupling.38,43 The A-exciton absorption exhibits a narrow linewidth (γA) of 43 meV and a large absorption efficiency (Qabs, the absorption cross section divided by the geometrical cross section of the nanoparticle) of 57%; by contrast, the B-exciton absorption shows a relatively broad linewidth (γB) of 267 meV and a small Qabs of 32%. These results highlight the advantage of the A-exciton transition in the subsequent study of the strong light−matter interaction. The Qabs of the ML-WS2 shell is nearly four times that of the flat WS2 flake.43 This difference can be understood by considering that the surface area of a sphere is four times the area of its cross section.

Figure 1. Resonance coupling in the silicon nanosphere core−ML-WS2 shell heterostructure in free space. (a) Calculated scattering efficiency spectrum (Qsca, scattering cross section


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divided by the geometrical cross section of the particle) of the pristine silicon nanosphere (green line), absorption efficiency spectrum (Qabs, absorption cross section divided by the geometrical cross section of the nanoparticle) of the hollow ML-WS2 shell (red line), and scattering efficiency spectrum of the core−shell heterostructure (orange line). The diameter of the silicon nanosphere is 149 nm, and the thickness of the ML-WS2 shell is set to 1 nm. Inset: Scheme of the heterostructure. (b) Magnetic near-field and current intensity distributions of the pristine silicon nanosphere and the core−shell heterostructure. The images are, respectively, drawn at the magnetic dipole resonance (608 nm) of the pristine silicon nanosphere and A-exciton transition (614 nm). All of the contours are plotted at the central cross sections perpendicular to the magnetic field of the incidence light. When the silicon nanosphere is coated with the ML-WS2 shell, because of the relatively low absorption of the B-exciton as a result of its small oscillator strength, the interaction between the EDM of the silicon nanosphere and the B-exciton transition is negligible (Figure 1a, orange line). The effect of the coating is similar to that induced by a layer of a high-refractive-index dielectric material; that is, it leads to a small redshift of the EDM. By contrast, a distinct quenching dip appears in the scattering spectrum of the heterostructure around the A-exciton transition, accompanied by the emergence of two splitting peaks at the high- and low-energy sides (Figure 1a, orange line). These spectral features clearly indicate resonance coupling between the MDM of the silicon nanosphere and the A-exciton transition of ML-WS2. Notably, an energy difference of 20 meV exists between the MDM of the pristine silicon nanosphere and the A-exciton transition energy of the ML-WS2 shell. Because of the large refractive index of ML-WS2, the MDM will shift toward the A-exciton transition upon the formation of the heterostructure, which therefore ensures a strong spectral overlap for the resonance coupling.55


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To elucidate the underlying physics associated with the resonance coupling, we deconvoluted the absorption spectra of the heterostructure and constituents, i.e., the hollow ML-WS2 shell and silicon nanosphere core, into the contributions from different resonance modes. The absorption spectrum of the ML-WS2 shell originates from both the EDM and the MDM; by contrast, in the case of the silicon nanospheres, the MDM dominates the light absorption across the whole investigated spectral range (Figure S2a and b in the Supporting Information). In addition, the absorption efficiency of the WS2 hollow shell is approximately one-half that of the pristine silicon nanosphere (Figure S2c in the Supporting Information). However, upon the formation of the core−shell heterostructure, the absorption efficiency of the WS2 shell is enhanced substantially, and the absorption of the WS2 shell overwhelms that of the silicon core (Figure S2d in the Supporting Information). Furthermore, a small quenching dip that coincides with the enhanced exciton transition of the shell is observed in the absorption spectrum of the silicon core (Figure S2d in the Supporting Information). The total absorption of the core−shell heterostructure is also enhanced to almost twice that of the pristine core. These behaviors clearly suggest that the two splitting peaks in the scattering spectrum of the heterostructure are features of the enhanced absorption resulting from the energy transfer from the silicon nanosphere core to the WS2 shell with intimate contact. This effect is seen more clearly by comparing the magnetic near-field distributions and the associated circular current intensities between the pristine silicon nanosphere and heterostructure. As shown in Figure 1b, at the scattering dip (614 nm) of the core−shell heterostructure, the magnetic field and current intensity inside the nanosphere core are strongly reduced in comparison with those of the MDM (608 nm) in the pristine silicon nanosphere. By contrast, the current intensity in the ML-WS2 shell is much stronger than that of


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the hollow ML-WS2 shell (Figure S3 in the Supporting Information), indicating that energy transfer occurred.56 The energy transfer is mediated by the interactions between the EDM and the MDM of the ML-WS2 shell and the MDM of the silicon core. Under excitations with linear polarization, the electron oscillations associated with the EDM in the shell can couple with the circular displacement current produced by the MDM in the silicon nanosphere core via Columbic interaction. Meanwhile, the MDMs in the shell and core can interact with each other via the Columbic interactions induced by their respective displacement currents. Although the MDM of the shell is much weaker than its EDM counterpart (Figure S2a in the Supporting Information), the MDM−MDM coupling should be stronger than the EDM−MDM coupling between the shell and core because of the similar orientations of the two magnetic dipoles and their associated electric field distributions.16 As a result, the scattering features of the core−shell heterostructure at resonance coupling are dominated by the MDM (Figure S4 in the Supporting Information). In this regard, we refer to the energy transfer in the heterostructure as an MDM-mediated energy transfer process. Notably, the scattering spectrum of the heterostructure shown in Figure 1a can originate from the Fano interference between the narrow exciton transition and the relatively broad MDM resonance.57 To further ascertain the origins of the spectral features, we used the coupled oscillators model (COM) to fit the simulated scattering spectrum of the heterostructures,58 whereby the coupling strength could be extracted to clarify the interaction type of the resonance coupling. According to the COM, the scattering cross section of a system with two coupled resonances can be stated as:


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(   A  iγA )  sca       iγMDM )(   A  iγA )    g  (   MDM

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



(1)

where g is the coupling strength between these two resonances, MDM and A are the energies of the uncoupled MDM and A-exciton, respectively, and γMDM and γA are the dissipation rates (linewidths) of the uncoupled MDM and A-exciton resonances, respectively. In the case of resonance coupling (MDM = A), the energies of the two normal modes are:

i ( γMDM  γA ) ( γMDM  γA )     A   g   

(2)

Because γMDM  γA , the splitting energy of the normal modes is:

( γMDM  γA )  ( γMDM  γA )    g   g    

(3)

According to the criteria proposed in previous studies,10,58−60 Fano interference will occur when  g  ( γMDM  γA ) /  , whereas mode splitting will occur when  g  ( γMDM  γA ) /  . We used Equation (1) to fit the simulation spectrum of the resonance coupling between the silicon nanosphere and ML-WS2. The scattering spectrum of the core−shell structure can be well described using the COM (Figure S5 in the Supporting Information). With the fitting parameters, g can be calculated to be 29 meV (Table S1 in the Supporting Information), which fulfills the criterion 2g > (γMDM − γA)/2. Such a result clearly indicates that mode splitting, rather than Fano resonance, occurs in the resonance coupling of the core−shell structure. In hybrid systems composed of two interacting resonance modes, the anticrossing behavior in the energy diagrams can usually be observed by continuously tuning the spectral overlaps between these two modes. In the current study, the MDM resonance energy can be tailored by tuning the diameters of the silicon nanospheres. Figure 2a shows the normalized scattering spectra of silicon nanospheres with various diameters; these spectra clearly indicate that the


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MDM resonance energy (MDM) varies from 2.16 eV to 1.86 eV as the diameters of the silicon nanosphere increase from 138 nm to 167 nm. In such a manner, the MDM can be scanned across the A-exciton transition energy (A) of the WS2 shell, giving rise to the distinct anticrossing behavior in the scattering spectra of the core−shell heterostructures (Figure 2b, color map). Two branches with strong scattering intensities are observed; they are termed the high-energy upper branch (UB, +) and low-energy lower branch (LB, −).

Figure 2. Anticrossing behavior of the resonance coupling in the silicon nanosphere core−ML-WS2 shell heterostructure. (a) Normalized scattering energy diagram of the silicon nanospheres with diameters ranging from 138 nm to 167 nm (color map). The white dashed line represents the magnetic dipole mode of the pristine silicon nanospheres. (b) Normalized scattering energy diagram of the heterostructures (color map) with silicon nanosphere cores corresponding to (a). The high-energy upper and low-energy lower branches are fitted using the coupled harmonic oscillator model (black solid lines). The red and white dashed lines represent the A-exciton transition and the magnetic dipole mode of the silicon nanosphere core, respectively. These spectral features can be well described using the following equation (Figure 2b, black solid lines)10,11:


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 

 MDM   A 2



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Ω   ( MDM   A ) 

(4)

2

Because of the redshift of the MDM upon the application of the WS2 shell, a modification factor  is applied in the model.11 Thus, detuning between the MDM and A-exciton is defined as

 = MDM − A. Parameter  is then fitted to be 0.986 (Table S1 in the Supporting Information). Parameter Ω is the mode splitting energy obtained from Equation (3) by fitting the scattering spectra at zero detuning (Figure 1a and Figure S5 in the Supporting Information); this parameter can be extracted as 43 meV. The mode splitting obtained here fulfills the criterion Ω  γMDM  γA , where γA and γMDM are 2

43 meV and 120 meV, respectively. Conventionally, such a criterion leads to the conclusion that the interacting system enters the strong coupling regime.10,58−60 However, if the mode splitting observed in the scattering spectra is, indeed, hybridized modes of part-light and part-matter because of the strong coupling effect, similar mode splitting should be observed in the absorption spectra of the core−shell structure,47,56 which contradicts our calculated results (Figure S2d in the Supporting Information). The absence of a splitting absorption spectrum at zero detuning unambiguously indicates that the resonance coupling observed in our study is in the weak coupling regime, which should be classified as enhanced absorption originating from the energy transfer process (see also the previous discussion).56 The absence of mode splitting in the absorption spectrum can be understood by considering the enhanced absorption of the WS2 shell. In the core−shell heterostructure, the absorption of the WS2 shell is sufficiently large to overwhelm those of the two split modes. As a result, an absorption spectrum characterized by a single peak will be obtained (Figure S2c and 2d in the Supporting Information).


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The resonance coupling of an optical resonator with quantum emitters is affected by the separations between them. In the silicon nanosphere core−ML-WS2 shell heterostructure, the resonance coupling is dominated by the MDM−MDM interaction. The MDM is of cavity type, where the magnetic field is mainly located inside the dielectric nanostructure. Therefore, we expected the resonance coupling to be insensitive to the separations between the core and shell. As shown in Figure 3a, for a 149-nm-diameter silicon nanosphere, the resonance coupling at zero detuning persists when the gaps (filled with air) between the core and shell are enlarged. Figure 3c (left panel) shows the normalized scattering spectrum diagram corresponding to heterostructures with different separations between the core and shell. The Ω remains at 43 meV when the gap is increased from 0 to 50 nm. The mode splitting is visible even when the gap is increased to 150 nm (Figure S6 in the Supporting Information). However, if the silicon nanosphere core is replaced with a gold nanosphere, the resonance coupling is instead mediated by the dipolar interactions between the plasmonic dipole mode (PDM) of the gold nanosphere and the exciton transition of the WS2. Because the PDM is of surface type with enhanced electric fields mainly localized at two apexes of the nanosphere, the dipolar interaction is of a near-field nature; it is thus strongly dependent on the separation between the core and shell (Figure 3b). As shown in Figure 3c (right panel), when the separation between the gold nanosphere and the WS2 shell is enlarged, the scattering dip induced by the resonance coupling is smeared out quickly, becoming negligible when the separation is larger than 30 nm. These results suggest that the resonance coupling in the heterostructure with a silicon nanosphere core is less sensitive to the separations between the core and shell.


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Figure 3. Dependence of the resonance coupling on core−shell separations. (a) Calculated scattering spectra of the silicon nanosphere core−ML-WS2 shell. The diameter of the silicon nanosphere is 149 nm. (b) Calculated scattering spectra of the gold nanosphere core−MLWS2 shell. The diameter of the gold nanosphere is 200 nm. (c) Normalized scattering spectrum diagrams of heterostructures with different separations between the core and shell. Left: heterostructure with a silicon nanosphere core. Right: heterostructure with a gold nanosphere core. The separations vary from 0 nm to 50 nm (color map). In all of the calculations, the gaps between the core and shell are filled with air (n = 1). The aforementioned theoretical calculations can, in principle, be verified by collecting the scattering spectra from individual heterostructures with silicon nanosphere cores of various diameters. However, fabricating the silicon nanosphere core−ML-WS2 shell heterostructures proposed in our calculations is difficult. We therefore employ another type of heterostructure where the silicon nanosphere is directly placed onto the two-dimensional ML-WS2 (particle-onfilm structure: POF) to demonstrate the resonance coupling effect. We emphasize that the purpose of using the POF is not to directly compare the experimental results with the numerical simulations but instead to reveal the resonance coupling between the silicon nanosphere and the ML-WS2 with another geometry that is easier to access. Therefore, a quantitative comparison between the scattering spectra of the POF and core−shell structures is inappropriate because, in


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the POF, the flat ML-WS2 cannot sustain MDM resonance. As a result, only the resonance coupling mediated by the interaction between the MDM of the silicon nanosphere and electric dipolar exciton transition of ML-WS2 will be recorded. In a typical measurement, silicon nanospheres of various sizes were deposited onto the MLWS2 grown on the silicon substrate with a 300-nm oxide layer using the chemical vapor deposition (CVD) method (Figure 4a and 4b).47,50 In such a manner, the silicon nanosphere has an intimate contact with ML-WS2. After the circulating displacement current associated with the MDM goes through the contact point, effective interactions between the MDM and exciton transition can be built up. The as-grown WS2 is a monolayer flake with a thickness of ~1 nm (Figure S7 in the Supporting Information).47 The exciton transition of ML-WS2 was manifested by its PL spectrum, which exhibits an emission maximum at 1.94 eV (639 nm), with a linewidth (γA) of 80 meV (Figure 4d, upper panel). The emission maximum is attributable to the direct-gap transition of the A-exciton.38,43 Notably, the γA is much larger than that used in our calculation. In addition, the PL peak exhibits a redshift of 80 meV relative to the theoretical peak position. Such discrepancies can be explained by considering that the parameters used in the theoretical calculations were directly adopted from those measured on mechanically exfoliated samples.53 Usually, the crystalline quality of CVD-grown WS2 is inferior to that of exfoliated WS2, which therefore results in a relatively broad PL spectrum.37


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Figure 4. Scattering spectra from silicon nanospheres deposited onto flat ML-WS2 flake. (a) Schematic showing the heterostructures composed of individual silicon nanospheres supported on the surface of a flat WS2 monolayer. (b) Scanning electron microscope image of the various silicon nanospheres deposited onto the WS2 monolayer. (c) Dark-field scattering images of the various heterostructures corresponding to the region in (b). Five typical heterostructures composed of silicon nanospheres of different sizes are marked with colored dashed lines. (d) Photoluminescence spectrum of the monolayer WS2 (upper). Scattering spectrum of a typical heterostructure (lower). Single-particle dark-field scattering spectroscopy was then used to measure the scattering spectra from the various individual silicon nanospheres supported on the ML-WS2 flake, eliminating the average effect from the ensemble measurements.28,29,47,50 The pattern-matching method was used to correlate the morphology of each heterostructure with its scattering spectrum. Figure 4c shows the dark-field images of various individual heterostructures, where


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the silicon nanospheres exhibit strong light scattering with vivid colors because of the strong EDM and MDM resonances (dashed circles in Figure 4c). For a typical silicon nanosphere with an MDM energy similar to the A-exciton transition energy, the scattering spectrum features two shoulders separated by a scattering minimum (Figure 4d, lower panel) coinciding with the exciton emission maximum, suggesting resonance coupling. To further ascertain the resonance coupling between the silicon nanosphere and ML-WS2 flake, the scattering spectra from various individual heterostructures with different detuning between the MDM and exciton transition frequencies were measured. To this end, silicon nanospheres with diameters ranging from 153 nm to 183 nm were selected and measured (Figure 5a). As shown in Figure 5b, the scattering spectra of the heterostructures are strongly dependent on the sizes of the silicon nanospheres. In particular, for the large silicon nanospheres with an MDM located at the low-energy side of the A-exciton transition (Figure 5b, gray vertical line), two shoulders near the MDM are clearly observed in the scattering spectrum of each heterostructure (Figure 5b, purple, orange, and pink). In particular, for the silicon nanosphere with a diameter of 169 nm, the MDM is in resonance with the A-exciton transition, giving rise to almost equivalent magnitudes of the two shoulders (Figure 5b, pink). The low-energy shoulder dominates the spectra of heterostructures with large silicon nanospheres. When the sizes of the silicon nanospheres become smaller, the low-energy shoulder blueshifts and vanishes eventually, whereas the high-energy shoulder is always present and located near the A-exciton transition (Figure 5b, blue and green).


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Figure 5. Scattering spectra from heterostructures with silicon nanospheres of various diameters deposited onto ML-WS2 flake. (a) Scanning electron microscopy and dark-field images of five typical heterostructures. The diameters of the silicon nanospheres from bottom to top are 153 nm, 165 nm, 169 nm, 175 nm, and 183 nm, respectively; the scale bars are 100 nm. (b) Dark-field scattering spectra of the various heterostructures corresponding to (a). The pink dashed line represents the fitting obtained using the coupled oscillator model. (c) Calculated backward scattering spectra of the silicon nanospheres with various diameters supported on ML-WS2 flake. The diameters of the silicon nanospheres from bottom to top are 144, 146, 150, 151, and 152 nm, respectively. The gray vertical bars indicate the A-exciton transition wavelength of ML-WS2. The scattering spectra from the POF structures were then calculated using finite-difference time-domain (FDTD) simulations. The silicon nanospheres were placed onto an ML-WS2 flake on top of a 300-nm-thick SiO2 layer. A dielectric constant of 2.25 was used for the SiO2 substrate. The backward scattering spectra from various POF structures were inspected according to the dark-field scattering measurement geometry. Because of the difference in the exciton


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emission energy between the CVD-grown and mechanical exfoliated ML-WS2 flakes (Figure 5b and 5c, gray lines), the diameters of the silicon nanospheres used in the FDTD simulations were reduced from the experimental ones to give a better description of the influence of the particle diameters on the resonance coupling spectra. As shown in Figure 5c, the main features of the experimental spectra can be well reproduced from the corresponding simulated ones. The interaction type of the resonance coupling in the POF can be revealed using the COM. In particular, by fitting the experimental spectrum in pink (POF with zero detuning) using the COM, we obtained a g of 17.5 meV. The γMDM and γA obtained by fitting are 300 meV and 80 meV, respectively (Table S1 in the Supporting Information), indicating a condition of 2g < (γMDM − γA)/2. In such a circumstance, the scattering spectrum represents a Fano lineshape. Therefore, the resonance coupling observed in the experiments originates from the Fano interference between the exciton and the MDM. Compared with the coupling strength of the core−shell structure, that of the POF structure is much smaller. This difference in coupling strength can be understood from several aspects. First, the point contact between the silicon nanosphere and the ML-WS2 flake in the experimental characterizations leads to a very small coupling area, where only a few excitons participate in the resonance coupling process. Second, as previously discussed, only the resonance coupling mediated by the interaction between the MDM of the silicon nanosphere and electric dipolar exciton transition of ML-WS2 will be recorded in the dark-field scattering measurements. Third, the linewidth of the A-exciton transition of the CVD-grown WS2 (80 meV) is much larger than that used in the calculations (43 meV). Therefore, the energy transferred from the silicon nanosphere to ML-WS2 will be dissipated rapidly. The coupling strength between the MDM and the A-exciton cannot compete


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with such an energy dissipation, giving rise to the relatively weak resonance coupling effects observed in the experiments. The excitonic characteristics of the TMDs are sensitive to an external stimulus, which enables active control of the light−matter interactions where they are involved.45,47,48,61,62 In particular, the exciton emission of ML-WS2 is strongly dependent on the environmental temperature.63 When the temperature is varied from 293 K to 433 K, the emission energy of the A-exciton can be tailored from 1.94 eV (639 nm) to 1.88 eV (660 nm), which can be reversibly tuned upon reducing the temperature (Figure S8 in the Supporting Information). Such a capability can be used for active control of the resonance coupling between the MDM and exciton transition in the silicon nanosphere−ML-WS2 heterostructures. To this end, we investigated the spectral evolutions of the light scattering from different individual silicon nanospheres supported on MLWS2 upon temperature scanning.

Figure 6. Active control over resonance coupling by temperature scanning. (a−c) Scattering spectra recorded at different temperatures for silicon nanospheres supported on ML-WS2. The silicon nanospheres have diameters of (a) 153 nm, (b) 169 nm, and (c) 175 nm. The


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photoluminescence spectra of the ML-WS2 flake at different temperatures are included for reference (red curves). The temperature is scanned from 293 K to 433 K. Three representative results are illustrated in Figure 6. For a small-diameter (153 nm) silicon nanosphere, its MDM is located away from the exciton emission at the short-wavelength side. Because of the large detuning at room temperature, no resonance-coupling spectral features are observed (Figure 6a). When the temperature is steadily increased, the exciton emission will be tailored farther away from the MDM to the long-wavelength side. As a result, the scattering spectra of the silicon nanospheres at different temperatures are nearly unchanged. For a larger silicon nanosphere (169 nm) with MDM in resonance with the A-exciton at room temperature, the quenching dip due to the resonance coupling redshifts and blurs with increasing temperature (Figure 6b). At temperatures higher than 400 K, the quenching dip disappears, and the scattering spectrum of the silicon nanosphere recovers to that of the pristine one. This behavior is attributed to the A-exciton transition located at the long-wavelength side of the MDM in this silicon nanosphere, where the spectral overlap between these two resonances becomes smaller as the exciton transition redshifts at higher temperature. Figure 6c shows the temperature-dependent scattering spectra of a heterostructure where the silicon nanosphere (173 nm) exhibits an MDM resonance at the long-wavelength side of the exciton transition. In this scenario, as the temperature was varied from 293 to 433 K, the WS2 exciton was scanned across the MDM resonance. As a result, the quenching dip and the two scattering shoulders were always observed. These results clearly indicate that the resonance coupling between the silicon nanosphere and ML-WS2 can be actively controlled by temperature scanning. One peculiar characteristic of the silicon nanosphere is that coupling of its MDM resonance with the spectrally overlapped EDM resonance of comparable strength (either from the


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nanosphere or the adjacent species) can give rise to unidirectional scattering with enhanced forward scattering and suppressed backward scattering.26,28,29 For example, we have demonstrated directional light scattering due to the resonance coupling in a silicon nanosphere coated with a J-aggregate shell.29 Given that the resonance coupling between the silicon nanosphere and ML-WS2 in the present study is mediated by the interaction between the MDM of the nanosphere and EDM as well as by that between the MDM of the nanosphere and the MDM of the hollow shell, we predicted that the heterostructure should exhibit unidirectional scattering behaviors. As a proof-of-concept study, we calculated the distribution of the light scattering from the heterostructure with zero detuning between the exciton transition and the MDM resonance. Figure 7a gives the far-field scattering distributions of the pristine silicon nanosphere and the core−shell heterostructure, which are, respectively, drawn at the MDM resonance (pristine silicon nanosphere) and two split peaks (heterostructure). The light-scattering behaviors of these three modes under plane-wave excitation with linear polarization are distinctly different (Figure 7b and c). In particular, the MDM resonance of the pristine silicon nanosphere exhibits anisotropic light scattering with directionality (F/B), defined as the logarithm of the forward-to-backward scattering intensity ratio, of 1.55 dB. In the heterostructure, the F/B of the high-energy peak is suppressed (0.27 dB), whereas that of the low-energy peak is enhanced (2.74 dB; Figure 7b and c). The opposite behavior of the directional scattering in the core−shell heterostructure at the two split peaks is attributed to the phase differences between the EDM and MDM modes that contribute to these two scattering peaks (Figure S4 in the Supporting Information). According to the Mie theory, the effective electric dipolar polarizability (α1e) and magnetic dipolar polarizability (α1m) of a spherical nanoparticle are54


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1e 

3i 3i a , 1m  3 b1 3 1 2k 2k

(5)

where a1 and b1 are the Mie scattering coefficients of EDM and MDM, respectively, and k is the vacuum wave vector. The backward scattering can then be calculated as

 b  4k 4 I [1  V cos(  Δ  )] 2

2

where I  1e  1m , V 

(6)

2 1e 1m I

is a parameter determined by the polarizabilities of the

EDM and the MDM, and Δ is the phase difference between the EDM and the MDM. The parameters V at the split peaks are similar to each other (Figure S9 in the Supporting Information). However, the phase differences between the EDM and the MDM are −0.99 rad (the low-energy peak) and −1.53 rad (the high-energy peak), respectively. These phase differences can therefore result in a reduced backscattering intensity of the low-energy peak because of its stronger destructive interference between the EDM and the MDM,25 giving rise to an enhanced F/B value.

Figure 7. Directional scattering in the silicon nanosphere core−ML-WS2 shell heterostructure. (a) Calculated scattering spectra of the pristine silicon nanosphere (solid green line) and heterostructure (solid orange line). The diameter of the silicon nanosphere is 149 nm. Middle: Far-field scattering patterns corresponding to the MDM of the pristine


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silicon nanosphere and high- (HEM) and low-energy (LEM) peaks of the core−shell heterostructure. (b) Polar plots of the far-field scattering distributions corresponding to the three modes in (a). (c) Directionality of the three modes in (a). The directionality, F/B, is defined as 10log10(IF/IB), where IF and IB represent the forward and backward scattering intensities, respectively. The directional light-scattering behaviors can, in principle, be verified experimentally. However, as we mentioned in previous discussions, fabricating the silicon nanosphere core−MLWS2 shell heterostructures as proposed in Figure 7 is difficult. As a compromise, we demonstrate the unidirectional light scattering of the resonance coupling between the silicon nanosphere and ML-WS2 using the POF structure. To this end, ML-WS2 was transferred from the silicon substrate with a 300-nm oxide layer to a transparent quartz-glass substrate. Upon deposition of the silicon nanospheres, both the forward and backward light scattering spectra from various individual POF structures were measured using dark-field microscopy (Figure 8a and b). The scattering spectra of three representative POF heterostructures are shown in Figure 8c−e. Both the forward (orange curves) and backward (green curves) scattering spectra exhibit Fano-like lineshapes because of the resonance coupling. In addition, the forward scattering overwhelms the backward scattering over a broad spectral range, suggesting the occurrence of unidirectional scattering enabled by the coupling between the MDM and the WS2 exciton in the POF structure. The main features of the experimental spectra are quite similar to those of the numerically simulated spectra (Figure 8f−h). The discrepancies between the spectral lineshapes can be ascribed to imperfections in the experimental samples, such as nonideal nanosphere shapes and surface contaminants on the nanospheres.28 We speculate that the directional light scattering


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revealed in the heterostructure can benefit various optoelectronic applications such as solar cells, ultrasensitive sensing, and light-emitting devices.

Figure 8. Experimental measurements and numerical simulations of the unidirectional light-scattering characteristics of the POF structures. Schematic showing the (a) backward and (b) forward light-scattering measurements using dark-field microscopy. (c−e) Experimental forward (orange) and backward (green) scattering spectra of three typical POF structures. (f−h) Simulated forward (orange) and backward (green) scattering spectra of three POF structures corresponding to (c−e). The diameters of the silicon nanospheres in the simulation are 148 nm, 151 nm, and 152 nm. The gray bars represent the exciton transition energy. Another interesting aspect of using the silicon nanosphere as a nanocavity in the resonance coupling is that it enables directional PL from ML-WS2. In fact, a very recent study has demonstrated unidirectional light emission by coupling monolayer MoS2 to silicon Mie resonators.64 To demonstrate such an effect in the case of resonance coupling, we measured the


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light emissions from various POF structures. However, because of the large size difference between the excitation light spot (~1 μm in diameter) and a POF heterostructure (~150 nm in diameter), the PL signals from the POF structures were immersed into the background of the WS2 and could not be extracted for further characterization (Figure S10 in the Supporting Information). This circumstance precludes measuring the intrinsic PL signal from the POF structure and characterizing its directions. Revealing the PL behaviors of the POF structure requires characterization techniques with high spatial resolution, such as scanning near-field optical microscopy, which will be the subject of a future report. CONCLUSIONS In summary, we have revealed the resonance coupling between the MDM of a silicon nanosphere and two-dimensional excitons in ML-WS2 via both theoretical and experimental approaches using different geometries. In the theoretical calculations, we constructed a silicon nanosphere core−ML-WS2 shell heterostructure and showed that resonance coupling, manifested by the anticrossing behavior in the scattering diagram with mode splitting of 43 meV, can be observed. Such an effect originates from the strong energy transfer between the MDM of the silicon nanosphere and the A-exciton of ML-WS2. This process belongs to the weak coupling regime, in contrast to the conclusion in a recent study on a similar structure.53 The resonance coupling in this all-dielectric core−shell heterostructure is insensitive to the gaps between the core and shell. Additionally, because of the involvement of the MDM, the two split modes exhibit directional light-scattering behaviors, which is a distinctive characteristic associated with the dielectric nanostructures. From the experimental aspect, we employed a POF structure by depositing various silicon nanospheres onto a flat ML-WS2 flake. The resonance coupling in the POF structure is a Fano interference effect; this coupling also exhibits unidirectional light


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scattering and can be actively tailored by temperature scanning. We believe that these findings can not only further the understanding of strong light−matter interactions at the nanoscale but also benefit future nanophotonics applications based on all-dielectric nanostructures, such as signal transmission and detection, light routing, sensing, and nonlinear optical processes. METHODS Numerical simulations. Numerical simulations of the core−shell heterostructure were performed using the commercial software package COMSOL Multiphysics v4.3b in the frequency domain. The dielectric function of ML-WS2 was adopted from previous reported values.55 The dielectric functions used for silicon and gold were based on previous measurements.65 A linearly polarized plane wave with a wavelength ranging from 475 to 825 nm was launched into a box containing the target nanostructure. A maximum mesh size of 5 nm was applied to the nanostructure, and the surrounding medium was divided using fine meshes. The surrounding medium was set as vacuum with a refractive index of 1.0. Perfectly matched layers were used at the boundary to absorb the scattered radiation in all directions. The absorption spectra of the core and shell were obtained by integrating the power loss density over their volumes. The magnetic field and current density distributions were inspected at the central cross section perpendicular to the magnetic field of the incident light. The FDTD method was used to calculate the forward and backward scattering spectra of the POF structures. The silicon nanospheres were placed on a monolayer WS2 flake on top of a 300nm-thick SiO2 layer. A dielectric constant of 2.25 was used for the SiO2 substrate. The thickness of the monolayer WS2 was kept as 1 nm. Sample preparation. The monolayer WS2 was grown directly onto the silicon substrate capped with a 300-nm oxide layer (Nanjing MKNANO Tech. Co., Ltd., www.mukenano.com).


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Silicon nanospheres with various diameters were synthesized using femtosecond laser ablation in liquid. Briefly, a single-crystalline silicon wafer was used as a target and was immersed in deionized water. A Legend Elite Series ultrafast laser (Coherent Inc.) was used as the ablation source (λ = 800 nm). The pulsewidth was 35 fs, the energy of a single pulse was 4 mJ, and the repetition rate was 1 kHz. The silicon nanosphere colloidal solution was obtained after laser ablation of the silicon wafer in water; this solution was subsequently drop-cast onto the monolayer WS2 flake. Various heterostructures were obtained after the deposit was allowed to naturally dry under ambient conditions. To measure the forward and backward light scattering spectra from the POF structure, MLWS2 was transferred from the silicon substrate with a 300-nm oxide layer to a transparent quartzglass substrate. A layer of polystyrene (PS, 10 wt% in toluene) was first cast onto the as-grown ML-WS2 supported on a SiO2/Si substrate. After heating under 120 °C for 1 h, ML-WS2 was peeled from the substrate via the PS layer assisted by the tension of water and then transferred to a pre-cleaned quartz-glass substrate. The PS layer was removed by immersing the sample into toluene. The POF structures were then formed by depositing silicon nanospheres onto ML-WS2. Dark-field scattering imaging and spectroscopy. The scattering spectra of the heterostructures were recorded on a dark-field optical microscope (Olympus BX51) equipped with a quartz-tungsten-halogen lamp (100 W), a monochromator (Acton SpectraPro 2360), and a charge-coupled device camera (Princeton Instruments Pixis 400BR_eXcelon). The camera was thermoelectrically cooled to −70 °C during the measurements. A dark-field objective (100×, numerical aperture of 0.80) was used both to illuminate the heterostructures with the white excitation light and to collect the backward-scattered light. The incidence angle was ~55°. To characterize the forward-scattering light, an oil-immersion dark-field condenser with a numerical


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aperture of 1.4 was used for illumination from the bottom of the sample, and the light scattering in the forward direction was recorded using the 100× dark-field objective. The scattered spectra from the heterostructures were corrected by first subtracting the background spectra taken from the adjacent regions without the nanostructures and then dividing them by the calibrated response curve of the entire optical system. Color scattering images were captured using a color digital camera (ARTCAM-300MI-C, ACH Technology Co., Ltd., Shanghai) mounted onto the imaging plane of the microscope. Characterization. The PL and Raman spectra of ML-WS2 were acquired using a Renishaw inVia Reflex system integrated into a dark-field microscope (Leica). The 532-nm excitation laser was focused onto the samples with a diameter of ~1 μm through a 50× objective (numerical aperture of 0.80). Scanning electron microscopy imaging was performed using an FEI Quanta 450 microscope. The thickness of ML-WS2 was measured by atomic force microscopy (AFM; NTEGRA Spectra). ASSOCIATED CONTENT Supporting Information Contributions from the EDM and MDM of the silicon nanosphere in free space with a diameter of 149 nm; contributions from the EDM and MDM to the absorption spectra of a silicon nanosphere, hollow ML-WS2 shell, and core−shell heterostructure, as well as the corresponding core and shell in the heterostructure; current intensity distributions of the hollow WS2 shell and core−shell heterostructure at A-excitonic transition; contributions from the EDM and MDM to the scattering spectra of a silicon nanosphere core−ML-WS2 shell heterostructure; COM fitting of the scattering spectrum of the core−shell heterostructure; calculated scattering cross section of the core−shell heterostructure with different gaps between the core and shell; Raman spectrum


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and AFM characterization of the ML-WS2 flake; temperature-dependent PL of the CVD-WS2 monolayer; dependence of Vα on the wavelengths in the silicon nanosphere core−ML-WS2 shell heterostructure; bright-field optical microscope image and PL mapping image of the ML-WS2 flake. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].; [email protected]. Author Contributions H.W., J.X.W., and W.L.W. contributed equally to this work. H.J.C., S.Z.D., and N.S.X. conceived the study, designed the experiments, and initiated the study. H.W. and J.X.W. conducted the experimental measurements and analyzed the data. W.L.W. carried out the numerical calculations and modeling. P.L. and J.H.Y. provided the silicon nanosphere samples. H.W., J.X.W., W.L.W., N.S.X., H.J.C., and S.Z.D. participated in the discussion of the data. H.W., S.Z.D., and H.J.C. co-wrote the manuscript. All authors have given approval to the final version of the manuscript. The authors declare no competing financial interest. ACKNOWLEDGMENT This work was financially supported by the National Natural Science Foundation of China (grant nos. 51290271, 11474364), the Guangdong Natural Science Funds for Distinguished Young Scholars (grant no. 2014A030306017), the Science and Technology Department of Guangdong Province, Pearl River S&T Nova Program of Guangzhou (grant no. 201610010084), the


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Guangdong Special Support Program (grant no. 201428004), and the Fundamental Research Funds for the Central Universities (grant no. 17lgzd05). REFERENCE 1. Törmä, P.; Barnes, W. L. Strong Coupling between Surface Plasmon Polaritons and Emitters: A Review. Rep. Prog. Phys. 2015, 78, 013901. 2. Imamoğlu, A.; Ram, R. J.; Pau, S.; Yamamoto, Y. Nonequilibrium Condensates and Lasers without Inversion: Exciton-Polariton Lasers. Phys. Rev. A 1996, 53, 4250−4253. 3. Volz, T.; Reinhard, A.; Winger, M.; Badolato, A.; Hennessy, K. J.; Hu, E. L.; Imamoğlu, A. Ultrafast All-Optical Switching by Single Photons. Nat. Photonics 2012, 6, 605−609. 4. Sanvitto, D.; Kena-Cohen, S. The Road towards Polaritonic Devices. Nat. Mater. 2016, 15, 1061−1073. 5. Fofang, N. T.; Park, T.-H.; Neumann, O.; Mirin, N. A.; Nordlander, P.; Halas, N. J. Plexcitonic Nanoparticles: Plasmon−Exciton Coupling in Nanoshell−J-Aggregate Complexes. Nano Lett. 2008, 8, 3481−3487. 6. Ni, W.; Ambjornsson, T.; Apell, S. P.; Chen, H.; Wang, J. Observing Plasmonic−Molecular Resonance Coupling on Single Gold Nanorods. Nano Lett. 2010, 10, 77−84. 7. Fofang, N. T.; Grady, N. K.; Fan, Z.; Govorov, A. O.; Halas, N. J. Plexciton Dynamics: Exciton−Plasmon Coupling in a J-Aggregate−Au Nanoshell Complex Provides a Mechanism for Nonlinearity. Nano Lett. 2011, 11, 1556−1560. 8. Manjavacas, A.; Garcia de Abajo, F. J.; Nordlander, P. Quantum Plexcitonics: Strongly Interacting Plasmons and Excitons. Nano Lett. 2011, 11, 2318−2323.


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9. Chen, H.; Shao, L.; Woo, K. C.; Wang, J.; Lin, H.-Q. Plasmonic−Molecular Resonance Coupling: Plasmonic Splitting versus Energy Transfer. J. Phys. Chem. C 2012, 116, 14088−14095. 10. Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in Individual Metallic Dimers. Nano Lett. 2013, 13, 3281−3286. 11. Eizner, E.; Avayu, O.; Ditcovski, R.; Ellenbogen, T. Aluminum Nanoantenna Complexes for Strong Coupling between Excitons and Localized Surface Plasmons. Nano Lett. 2015, 15, 6215−6221. 12. Zengin, G.; Wersäll, M.; Nilsson, S.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Realizing Strong Light-Matter Interactions between Single-Nanoparticle Plasmons and Molecular Excitons at Ambient Conditions. Phys. Rev. Lett. 2015, 114, 157401. 13. Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Vacuum Rabi Splitting in a Plasmonic Cavity at the Single Quantum Emitter Limit. Nat. Commun. 2016, 7, 11823. 14. Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Single-Molecule Strong Coupling at Room Temperature in Plasmonic Nanocavities. Nature 2016, 535, 127−130. 15. Liu, R.; Zhou, Z. K.; Yu, Y. C.; Zhang, T.; Wang, H.; Liu, G.; Wei, Y.; Chen, H.; Wang, X. H. Strong Light-Matter Interactions in Single Open Plasmonic Nanocavities at the Quantum Optics Limit. Phys. Rev. Lett. 2017, 118, 237401. 16. Decker, M.; Staude, I. Resonant Dielectric Nanostructures: A Low-Loss Platform for Functional Nanophotonics. J. Opt. 2016, 18, 103001.


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Table of Contents Graphic

Resonance coupling between the magnetic dipole mode of a silicon nanosphere and 2D excitonic transitions in monolayer WS2, which originates from the energy transfer between these two modes, is demonstrated from both theoretical and experimental perspectives.


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Resonance Coupling in Heterostructures Composed of Silicon

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