#
Plasmonic Bound States in the Continuum to Tailor Exciton Emission of MoTe_{2}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

_{2}), the exciton emission of MoTe

_{2}in the PL spectrum split into two exciton-polariton modes, which is attributed to the high Q factor and strong interaction between the BIC mode and excitons of MoTe

_{2}.

## 1. Introduction

_{2}, WSe

_{2}) to explore exciton–polariton strong coupling and excitonic devices (e.g., excitonic lasers) [11,12,13,14,15,16]. However, because of the heat loss of metals, the quality factor (Q factor) of plasmon resonances is always smaller than 10 in the visible and near-infrared light region [17] and the line width is larger than that of the excitons [18,19]. As a result, photoluminescence spectral broadening is mainly observed in the plasmon exciton coupling system and it is hard to directly observe mode splitting in spectrum [20,21,22].

_{2}, the plasmonic BIC mode could adequately interact with the excitons of MoTe

_{2}. Due to the high Q factor and strong interaction between the BIC mode and excitons, the exciton emission of MoTe

_{2}was split into two modes in the photoluminescence spectrum.

## 2. Methods

_{2}wafer using standard electron beam lithography and metal deposition process, followed by a PMMA film spin coating on the gold nanorod array as a supporting layer. Then, the gold nanorod array could be transferred onto a prepared quartz (or other substrate) using the wet transfer process.

## 3. Result and Discussion

#### 3.1. Simulation

_{y}-polarization light with different rotation angles of gold nanorods. When the rotation angle was increased to 10 degrees, a narrow dip appeared at the wavelength of around 1280 nm, which was very close to the BIC mode. As the rotation angle increased, the linewidth of the dip was broadened slightly, while the depth became deeper. Ultimately, the dip was shifted to 1250 nm at the angle of 50 degrees. The electrical field distributions for the rotation angle of 0, 20 and 50 degrees are shown in (Figure 2b). For the 0 degree rotation angle, there was no electrical field enhancement found at the interface of the nanorods at the wavelength of around 1280 nm, because the BIC mode cannot be excited from far field. When this rotation angle was 20 degrees and 50 degrees, both the nanorod pairs exhibited electrical dipole resonance with opposite phases, like the BIC mode. However, as one of the nanorods was rotated, the condition for destructive interference in far field was no longer strictly satisfied. Therefore, this mode can be excited from far field. As the rotation angle was increased to 50 degrees, there was another broader dip at the wavelength of 1060 nm, which can be attributed to the plasmonic resonance mode of the rotated nanorod excited by the E

_{y}-polarization light. The transmission spectrum for E

_{x}-polarization light is shown in Figure 2c. The plasmonic resonance mode was clearly shown at the wavelength of 1080 nm with a linewidth of 210 nm. The simulated Re(E

_{z}) patterns of the plasmonic mode (Figure S1) for different rotations were almost the same with that for zero degrees, which is typical for electrical dipoles mode. When the rotation angle increased to 40 degrees, a slight dip was found at the wavelength of about 1260 nm, which can be attributed to the quasi-BIC mode.

#### 3.2. Experiment Results

_{y}-polarization light, the plasmonic quasi-BIC mode appeared when its rotation angle was higher than 20 degrees. As the rotation angle increased, the characteristic wavelength of the plasmonic quasi-BIC mode was little blue shifted from 1240 nm to 1210 nm and the Q factor of the quasi-BIC mode decreased from around 20 to 16, as shown in Figure 3d. At the large rotation angle (e.g., 50 degrees or 40 degrees), the Q factor was consistent with the simulation results. However, at small rotation angles, the experimental Q factor was lower than the simulation ones. One of the reasons was that the non-ideal edges (e.g., roughness) of the fabricated gold nanorods introduced additional loss for the system. For E

_{x}-polarization light, only plasmonic resonance mode was observed in the transmission spectra at small rotation angles, as shown in Figure 3c. The Q factor of the plasmonic resonance mode was about five, which was about three times lower than that of the plasmonic BIC mode.

#### 3.3. Coupling with MoTe_{2}

_{2}. The monolayer MoTe

_{2}was mechanically exfoliated from bulk crystal on quartz and the array of gold nanorod pairs with a rotation angle of 50 degrees was transferred to the top of MoTe

_{2}. An image of MoTe

_{2}integrated with the quasi-BIC structure is shown in Figure 4a. For comparison, we divided the monolayer MoTe

_{2}into two parts: with and without the quasi-BIC structure. The whole structure was covered with PMMA film to protect the monolayer MoTe

_{2}from the oxidation by air. The photoluminescence spectra of MoTe

_{2}with and without the quasi-BIC structure are shown in Figure 4b,c. For pure MoTe

_{2}, there was one emission peak at the wavelength of 1144 nm, which corresponded to the exciton emission of monolayer MoTe

_{2}[35,36]. For MoTe

_{2}with the quasi-BIC structure, there were two peaks in the PL spectrum. The peak at the wavelength of 1205 nm corresponded to the plasmonic quasi-BIC mode, which had lower energy than the excitons of MoTe

_{2}. The other one, at the wavelength of 1141 nm, was very close to the exciton of MoTe

_{2}, but the intensity was lower than that of pure MoTe

_{2}. The PL mapping and the transmission spectrum of the device are shown in Figures S2 and S3. Figure 4d shows the enhancement of the PL spectrum (by dividing the PL spectrum of MoTe

_{2}with and without the plasmonic structure). The enhancement of the PL spectrum was a Fano-like curve, which means that the plasmonic BIC mode not only directly enhanced the PL emission at the wavelength of the plasmonic mode, but also repartitioned the radiation channel of excitons through the exciton–plasmon coupling. The coupling system corresponded to the open cavity−exciton system, in which both excitons and plasmons can directly interact with the external field. It was different from excitons coupled with a closed cavity, such as the Fabry−Perot cavity, in which excitons are encapsulated within the cavity and cannot directly interact with the external field. Based on the cavity-quantum electrodynamic method, the total optical intensity of the hybrid exciton–plasmon system is given by: $I={I}_{0}FM$, where ${I}_{0}$ is a typical Lorentz term describing the optical response of excitons uncoupled with plasmons, $M$ is a Rabi term describing the Rabi splitting when the excitons are coupled with plasmons and $F$ is a Fano function $F=\frac{{({\omega}_{0}-\omega +q)}^{2}+{{\gamma}_{0}}^{2}}{{({\omega}_{0}-\omega )}^{2}+{{\gamma}_{0}}^{2}}$. In the Fano function, $q=g/({\mu}_{p}/{\mu}_{e})$, where g is the coupling strength between excitons and plasmons, $\frac{{\mu}_{\mathrm{p}}}{{\mu}_{\mathrm{e}}}$ presents the ration of coupling strength of the plasmons and excitons to the external field and ${\gamma}_{0}$ is the linewidth of the cavity mode. In the coupling system, the original exciton mode split into two exciton-polariton modes, which is described by Rabi term M. The low energy mode was dominated by plasmons, while the high energy mode was dominated by excitons. Then, the Fano term further redistributed the radiation channel through enhancing the low energy mode and reducing the high energy mode. In detail, after excitons excited in MoTe

_{2}, part of exciton energy transferred to the low energy mode and was emitted through the plasmon BIC mode, resulting in the lower emission intensity of the high energy mode. More discussion of this phenomenon is shown in Figure S4.

_{2}and a higher coupling strength g. Therefore, the clear mode splitting in the PL spectrum and Fano line shape in the normalized PL spectrum were observed.

## 4. Summary

_{2}, the exciton emission of MoTe

_{2}in the PL spectrum split into two exciton-polariton modes, coupling monolayer MoTe

_{2}with the plasmonic quasi-bound state. We believe that the plasmonic quasi-BIC with a high Q factor and small mode volume would provide promising nanophotonic structures to study strong coupling of exciton polaritons in two-dimensional van der Waals systems.

## Supplementary Materials

_{2}exciton, Figure S3: the transmission spectrum of the ML MoTe

^{2}covering by plasmonic BIC structure, Figure S4: The diagram for PL spectrum of MoTe

^{2}without and with plasmonic BIC mode.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Pala, R.A.; White, J.; Barnard, E.; Liu, J.; Brongersma, M.L. Design of plasmonic thin-film solar cells with broadband absorption enhancements. Adv. Mater.
**2009**, 21, 3504–3509. [Google Scholar] [CrossRef] - Clavero, C. Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices. Nat. Photonics
**2014**, 8, 95–103. [Google Scholar] [CrossRef] - Ding, S.Y.; Yi, J.; Li, J.F.; Ren, B.; Wu, D.Y.; Panneerselvam, R.; Tian, Z.Q. Nanostructure-based plasmon-enhanced raman spectroscopy for surface analysis of materials. Nat. Rev. Mater.
**2016**, 1, 16021. [Google Scholar] [CrossRef] - Li, J.-F.; Li, C.-Y.; Aroca, R.F. Plasmon-enhanced fluorescence spectroscopy. Chem. Soc. Rev.
**2017**, 46, 3962–3979. [Google Scholar] [CrossRef] [PubMed] - Kale, M.J.; Avanesian, T.; Christopher, P. Direct photocatalysis by plasmonic nanostructures. Acs Catal.
**2014**, 4, 116–128. [Google Scholar] [CrossRef] - Zhang, X.; Chen, Y.L.; Liu, R.-S.; Tsai, D.P. Plasmonic photocatalysis. Rep. Prog. Phys.
**2013**, 76, 046401. [Google Scholar] [CrossRef] [Green Version] - Chen, Z.; Li, X.; Wang, J.; Tao, L.; Long, M.; Liang, S.-J.; Ang, L.K.; Shu, C.; Tsang, H.K.; Xu, J.-B. Synergistic effects of plasmonics and electron trapping in graphene short-wave infrared photodetectors with ultrahigh responsivity. ACS Nano
**2017**, 11, 430–437. [Google Scholar] [CrossRef] - Sun, Z.; Lionel, A.; Chen, Z. Plasmonic-enhanced perovskite–graphene hybrid photodetectors. Nanoscale
**2016**, 8, 7377–7383. [Google Scholar] [CrossRef] - Ho, J.; Dong, Z.; Leong, H.S.; Zhang, J.; Tjiptoharsono, F.; Daqiqeh Rezaei, S.; Goh, K.C.H.; Wu, M.; Li, S.; Chee, J.; et al. Miniaturizing color-sensitive photodetectors via hybrid nanoantennas toward submicrometer dimensions. Sci. Adv.
**2022**, 8, eadd3868. [Google Scholar] [CrossRef] - Salamin, Y.; Ma, P.; Baeuerle, B.; Emboras, A.; Fedoryshyn, Y.; Heni, W.; Cheng, B.; Josten, A.; Leuthold, J. 100 GHz Plasmonic Photodetector. ACS Photonics
**2018**, 5, 3291–3297. [Google Scholar] [CrossRef] [Green Version] - Stührenberg, M.; Munkhbat, B.; Baranov, D.G.; Cuadra, J.; Yankovich, A.B.; Antosiewicz, T.J.; Olsson, E.; Shegai, T. Strong light–matter coupling between plasmons in individual gold bi-pyramids and excitons in mono-and multilayer WSe2. Nano Lett.
**2018**, 18, 5938–5945. [Google Scholar] [CrossRef] [PubMed] - Fernandez, H.A.; Withers, F.; Russo, S.; Barnes, W.L. Electrically tuneable exciton-polaritons through free electron doping in monolayer WS2 microcavities. Adv. Opt. Mater.
**2019**, 7, 1900484. [Google Scholar] [CrossRef] [Green Version] - Han, X.; Wang, K.; Xing, X.; Wang, M.; Lu, P. Rabi splitting in a plasmonic nanocavity coupled to a WS2 monolayer at room temperature. ACS Photonics
**2018**, 5, 3970–3976. [Google Scholar] [CrossRef] - Schneider, C.; Glazov, M.M.; Korn, T.; Höfling, S.; Urbaszek, B. Two-dimensional semiconductors in the regime of strong light-matter coupling. Nat. Commun.
**2018**, 9, 2695. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, X.; Galfsky, T.; Sun, Z.; Xia, F.; Lin, E.-C.; Lee, Y.-H.; Kéna-Cohen, S.; Menon, V.M. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photonics
**2015**, 9, 30–34. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Chen, Z.; Tao, L.; Sun, B.; Xu, X.; Zheng, J.; Xu, J. Investigation on the fano-type asymmetry in atomic semiconductor coupled to the plasmonic lattice. ACS Photonics
**2021**, 8, 3583–3590. [Google Scholar] [CrossRef] - Kravets, V.G.; Kabashin, A.V.; Barnes, W.L.; Grigorenko, A.N. Plasmonic surface lattice resonances: A review of properties and applications. Chem. Rev.
**2018**, 118, 5912–5951. [Google Scholar] [CrossRef] - Wen, J.; Wang, H.; Wang, W.; Deng, Z.; Zhuang, C.; Zhang, Y.; Liu, F.; She, J.; Chen, J.; Chen, H.; et al. Room-temperature strong light–matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals. Nano Lett.
**2017**, 17, 4689–4697. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef] - Rodriguez, S.; Feist, J.; Verschuuren, M.; Garcia-Vidal, F.; Rivas, J.G. Thermalization and cooling of plasmon-exciton polaritons: Towards quantum condensation. Phys. Rev. Lett.
**2013**, 111, 166802. [Google Scholar] [CrossRef] [Green Version] - Wersall, M.; Cuadra, J.; Antosiewicz, T.J.; Balci, S.; Shegai, T. Observation of mode splitting in photoluminescence of individual plasmonic nanoparticles strongly coupled to molecular excitons. Nano Lett.
**2017**, 17, 551–558. [Google Scholar] [CrossRef] [PubMed] - Kleemann, M.-E.; Chikkaraddy, R.; Alexeev, E.M.; Kos, D.; Carnegie, C.; Deacon, W.; de Pury, A.C.; Große, C.; de Nijs, B.; Mertens, J.; et al. Strong-coupling of wse2 in ultra-compact plasmonic nanocavities at room temperature. Nat. Commun.
**2017**, 8, 1296. [Google Scholar] [CrossRef] [Green Version] - Von Neumann, J.; Wigner, E. On some peculiar discrete eigenvalues. Phys. Z.
**1929**, 30, 465–467. [Google Scholar] - Herrick, D.R. Construction of bound states in the continuum for epitaxial heterostructure superlattices. Phys. B+C
**1976**, 85, 44–50. [Google Scholar] [CrossRef] - Joseph, S.; Pandey, S.; Sarkar, S.; Joseph, J. Bound states in the continuum in resonant nanostructures: An overview of engineered materials for tailored applications. Nanophotonics
**2021**, 10, 4175–4207. [Google Scholar] [CrossRef] - Bogdanov, A.A.; Koshelev, K.L.; Kapitanova, P.V.; Rybin, M.V.; Gladyshev, S.A.; Sadrieva, Z.F.; Samusev, K.B.; Kivshar, Y.S.; Limonov, M.F. Bound states in the continuum and fano resonances in the strong mode coupling regime. Adv. Photonics
**2019**, 1, 016001. [Google Scholar] [CrossRef] [Green Version] - Hsu, C.W.; Zhen, B.; Stone, A.D.; Joannopoulos, J.D.; Soljačić, M. Bound states in the continuum. Nat. Rev. Mater.
**2016**, 1, 16048. [Google Scholar] [CrossRef] [Green Version] - Overvig, A.; Yu, N.; Alù, A. Chiral quasi-bound states in the continuum. Phys. Rev. Lett.
**2021**, 126, 073001. [Google Scholar] [CrossRef] - Gorkunov, M.V.; Antonov, A.A.; Kivshar, Y.S. Metasurfaces with maximum chirality empowered by bound states in the continuum. Phys. Rev. Lett.
**2020**, 125, 093903. [Google Scholar] [CrossRef] - Koshelev, K.; Lepeshov, S.; Liu, M.; Bogdanov, A.; Kivshar, Y. Asymmetric metasurfaces with high-q resonances governed by bound states in the continuum. Phys. Rev. Lett.
**2018**, 121, 193903. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liang, Y.; Koshelev, K.; Zhang, F.; Lin, H.; Lin, S.; Wu, J.; Jia, B.; Kivshar, Y. Bound States in the Continuum in Anisotropic Plasmonic Metasurfaces. Nano Lett.
**2020**, 20, 6351–6356. [Google Scholar] [CrossRef] [PubMed] - Dong, Z.; Jin, L.; Rezaei, S.D.; Wang, H.; Chen, Y.; Tjiptoharsono, F.; Ho, J.; Gorelik, S.; Ng, R.J.H.; Ruan, Q.; et al. Schrödinger’s red pixel by quasi-bound-statesin-the-continuum. Sci. Adv.
**2022**, 8, abm4512. [Google Scholar] [CrossRef] - Dong, Z.; Mahfoud, Z.; Paniagua-Domínguez, R.; Wang, H.; Fernández-Domínguez, A.I.; Gorelik, S.; Ha, S.T.; Tjiptoharsono, F.; Kuznetsov, A.I.; Bosman, M.; et al. Nanoscale mapping of optically inaccessible bound-states-in-the-continuum. Light Sci. Appl.
**2022**, 1, 20. [Google Scholar] [CrossRef] - Koshelev, K.; Bogdanov, A.; Kivsha, Y. Meta-optics and bound states in the continuum. Sci. Bull.
**2019**, 12, 836–842. [Google Scholar] [CrossRef] [Green Version] - Ruppert, C.; Aslan, B.; Heinz, T.F. Optical properties and band gap of single-and few-layer mote2 crystals. Nano Lett.
**2014**, 14, 6231–6236. [Google Scholar] [CrossRef] [PubMed] - Biswas, S.; Champagne, A.; Haber, J.B.; Pokawanvit, S.; Wong, J.; Akbari, H.; Krylyuk, S.; Watanabe, K.; Taniguchi, T.; Davydov, A.V.; et al. Rydberg excitons and trions in monolayer MoTe
^{2}. ACS Nano**2023**, 17, 7685–7694. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Schematic figure of the array of gold nanorod pairs supporting the plasmonic BIC mode. The parameters of the gold nanorod pair are shown on the right, where d

_{y}= 80 nm, d

_{x}= 210 nm and φ is the rotation angle. The periodic parameters of the nanorod pair array are P

_{x}= 400 nm and P

_{y}= 600 nm. (

**b**) The electrical field intensity ${\left|E\right|}^{2}$ of a probe placed 2 nm from surface one of the gold nanorods; meanwhile, a dipole source for excitation is placed on the terminal of the other gold nanorod. The inset shows the simulated Re(E

_{z}) patterns at the wavelength of 1280 nm. (

**c**) The transmission spectrum of gold nanorod pairs being excited by plane wave incidence condition with Ex polarization. The inset shows the simulated Re(Ez) patterns at the wavelength of 1090 nm.

**Figure 2.**(

**a**) Transmission spectra of plasmonic BIC structures being excited by plane wave incidence conditions with Ey polarization. (

**b**) simulated Re(Ez) patterns of plasmonic BIC mode with nanorod rotation angles of 20 and 50 degrees at the dip wavelength in figure (

**a**). For the rotation of 0 degrees, the simulation wavelength was set at 1280 nm. (

**c**) Transmission spectra of plasmonic BIC structures being excited by plane wave incidence condition with Ex polarization.

**Figure 3.**(

**a**) SEM images of the gold nanorod pair arrays with different rotation angles. (

**b**) Transmission spectra of the gold nanorod pair arrays under the incident light of E

_{y}-polarization. (

**c**) Transmission spectra of the gold nanorod pair arrays under the incident light of E

_{x}polarization. (

**d**) Experimental and simulation Q factor and the wavelength of the plasmonic quasi-BIC mode extracted from the transmission dips.

**Figure 4.**(

**a**) Image of MoTe

_{2}integrated with plasmonic quasi-BIC structure, in which the rotation angle of nanorods is 50 degrees. (

**b**) PL spectrum data and the corresponding fitting curve of pure MoTe

_{2}. (

**c**) PL spectrum data and the corresponding fitting curve of MoTe

_{2}with plasmonic quasi-BIC structure. (

**d**) The enhancement of PL intensity of MoTe

_{2}integrated with plasmonic quasi-BIC structure.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jin, Y.; Wu, K.; Sheng, B.; Ma, W.; Chen, Z.; Li, X.
Plasmonic Bound States in the Continuum to Tailor Exciton Emission of MoTe_{2}. *Nanomaterials* **2023**, *13*, 1987.
https://doi.org/10.3390/nano13131987

**AMA Style**

Jin Y, Wu K, Sheng B, Ma W, Chen Z, Li X.
Plasmonic Bound States in the Continuum to Tailor Exciton Emission of MoTe_{2}. *Nanomaterials*. 2023; 13(13):1987.
https://doi.org/10.3390/nano13131987

**Chicago/Turabian Style**

Jin, Yuxuan, Kai Wu, Bining Sheng, Wentao Ma, Zefeng Chen, and Xiaofeng Li.
2023. "Plasmonic Bound States in the Continuum to Tailor Exciton Emission of MoTe_{2}" *Nanomaterials* 13, no. 13: 1987.
https://doi.org/10.3390/nano13131987