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Abstract
Excitation of ultraviolet (UV) range plasmon resonance with high quality (Q)-factor has been significantly challenging in plasmonics because of inherent limitations in metals like Au and Ag. Herein, we theoretically investigated UV-visible range plasmons in the topological insulator Bi1.5Sb0.5Te1.8Se1.2 (BSTS) nanosphere and nanoshell. In contrast to broad linewidth plasmon absorptions in the BSTS nanospheres, an ultra-sharp absorption peak with the Q-factor as high as 52 is excited at UV frequencies in the BSTS nanoshells. This peak is attributed to Dirac-type plasmon resonance originating from massless Dirac carriers in surface states of the BSTS. Furthermore, a tunable plasmon wavelength of the resonance is demonstrated by varying geometrical parameters of the BSTS nanoshells. This may find applications in surface enhanced Raman spectroscopies, nanolasers and biosensors in the UV regions.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmons (SPs) are quantized collective oscillations of free electrons resulting from the interaction of incident light with metals [1,2]. Due to their remarkable capabilities in enhancing the near-field intensity and overcoming the diffraction limit of light, SPs supported by metallic nanostructures have formed the basis of a wide range of research and technologies in the past two decades [3,4]. However, extending plasmon resonances with high quality (Q)-factor towards the ultraviolet (UV) region of the spectrum has been significantly challenging because of inherent limitations in metals like Au and Ag. Specifically, interband transitions in Au (Ag) introduce a strong dissipative channel for plasmon resonances at the wavelengths shorter than 550 nm (350 nm) [5]. Aluminum (Al) has low absorption down to a wavelength of 200 nm [6,7]. However, the value of the achievable Q-factors for state of the art Al nanostructures is still relatively low in UV region (approaching ∼ 15) [8–10]. This has inspired a search of alternative plasmonic materials beyond the metals. Candidates that are currently being investigated include highly doped semiconductors [11,12], metallic alloys [13], nitrides [14] and transparent conducting oxides [5] and, more recently, two-dimensional materials [15,16] and topological insulator (TI) materials.
TI represents a new class of material that behaves as an insulator in its bulk but whose surface contains conducting states [17]. The surface states of the TI are associated with massless Dirac quasiparticles and protected from backscattering by time-reversal symmetry. As a consequence, Dirac charge carriers in the surface states of the TI are free to move parallel to the surface. This means that the surface states of the TI have nearly-zero Drude losses. Therefore, TI is an ideal candidate to host high Q-factor plasmonic excitations across the whole EM spectrum. Recently, TI crystals such as Bi2Se3, Bi2Te3, Sb2Te3 and Bi1.5Sb0.5Te1.8Se1.2 (BSTS) have been reported as novel plasmonic materials in an ultra-broad spectral range from the terahertz to UV regions [18–26]. For example, Lupi et al. first experimentally demonstrated the excitation of Dirac-type plasmons in the microribbon arrays of a Bi2Se3 at terahertz frequencies [18]. Zheludev et al. reported the UV-visible range plasmon responses in the grating nanostructures of a BSTS [24]. However, in the UV-visible range, the observed plasmon responses in these TI nanostructures are mainly attributed to the bulk component and the contribution of Dirac charge carriers from surface states of the TI is often overwhelmed by that of bulk charge carriers from interband transitions due to an extremely small surface/bulk geometrical ratio. Then how to amplify the contribution from the surface states of the TI to collective plasmon response by engineering TI nanostructures? Despite the extreme interest, no investigation on this issue has been reported so far.
Nanospheres and nanoshells are relatively simple structures. Moreover, metallic nanoshells support rich resonant modes [27]. To date, the nanospheres and nanoshells of the TI have been rarely studied in the UV-visible range. In this paper, we theoretically presented a comparative investigation of UV-visible plasmons between the TI crystal BSTS nanospheres and nanoshells. In contrast to BSTS nanosphere, the BSTS nanoshell exhibits a Dirac-type plasmon resonance that originates from massless Dirac charge carriers in surface states of the BSTS and gets an ultra-high Q-factor in UV region due to significantly decreased Drude losses. The formation mechanism of the resonance was discussed based on plasmon hybridization theory. Finally, a tunable plasmon wavelength was demonstrated by changing geometrical parameters of BSTS nanoshells.
2. Simulation methods
The plasmonic absorptions of BSTS nanostructures were simulated by performing full-wave calculations using the finite element method with the commercial software COMSOL. In the numerical simulations, the TI crystal BSTS was treated as a material structure consisting of a semiconductive bulk with a thin metal layer on surface, namely a layer-on-bulk (LOB) model. The semiconducting layer was modeled using Tauc-Lorentz dispersion, while the metal surface layer was modeled with a 3D Drude-like dispersion. The values of the fitted parameters, such as the band-gap of the bulk, high frequency dielectric constant, 3D plasma frequencies and damping rate of the metal surface layer, are taken from the Ref. [24]. In addition, the thickness of the metal surface layer as an important fitting parameter was 1.5 nm in our simulations. It has to be noted that the modeling absorption spectra of BSTS nanostructures based on the LOB model agree quantitatively with the experimentally measured results [24,26].
A plane wave source (from 200 to 600 nm) was used to simulate the light incidence. Perfect matched layers were applied to the lateral boundaries of the simulation model in order to avoid spurious reflections. The surrounding of BSTS nanostructures was assumed to be air with the refractive index of n = 1 for simplifying calculation. The absorption cross section (CS) of BSTS nanostructures was calculated in the framework of the absorption formulation. Notice that the introduction of dielectric substrates or surface oxidations of the BSTS in practice would shift the resonances to the longer wavelengths, accompanied with a slight increase in the linewidths due to dielectric screening effect [28,29], thereby resulting in a slight decrease in practically achievable Q-factor.
3. Results and discussions
3.1 Plasmon response of BSTS nanospheres
Figure 1(a) depicts a schematic of the LOB model of BSTS nanosphere with the defined radius of R, where the blue region represents the semiconductive bulk and the yellow region represents the metal surface layer with a thickness of 1.5 nm. Based on the LOB model, the absorptions of BSTS nanospheres are calculated for different values of R in Fig. 1(b). When R = 20 nm, a single broad peak (denoted as “I”) is observed in the absorption spectrum. With the increase of R, the peak redshifts and becomes broader, meanwhile a new peak (denoted as “II”) appears at the shorter wavelength. With further increasing R, both peak “I” and “II” exhibit monotonous, clear redshifts and broadenings. The changing trends of peak “I” and “II” with R in the BSTS nanospheres are consistent with those of the dipolar and quadrupolar plasmon modes in metallic nanospheres [30]. Therefore, we assign peak “I” and “II” to dipolar and quadrupolar plasmon modes of BSTS nanospheres, respectively. The near-field distributions in Fig. 1(c) can further demonstrate the nature of plasmon modes. Obviously, the |E|-field distribution corresponding to peak “I” features two well defined maxima along the polarization direction, carrying a typical characteristic of dipolar localized surface plasmon mode excitation. As for peak “II”, it features four “hot spots” around the BSTS nanosphere. Moreover, the “hot spots” in the k-propagation direction has an obvious difference in intensity, implying the excitation of the quadrupolar plasmon mode by phase retardation effect.
Fig. 1. (a) A sketch of the LOB model of BSTS nanosphere. (b) Absorption spectra of BSTS nanospheres for different R. (c) Distributions of E-field amplitudes in E-k plane corresponding to peak “I” and “II”. (c) Absorption spectra of BSTS nanosphere with R = 50 nm for the overall, bare bulk and bare surface cases. Insets: illustrations of the simulation models for three cases.
The UV-visible range plasmons of BSTS nanostructures should be attributed to the combined contributions of bulk charge carriers from interband transitions and Dirac charge carriers from surface states of the BSTS [24]. To extract the contributions from the bulk and surface states, we calculate the absorptions of BSTS nanosphere with R = 50 nm for bare bulk and bare surface cases in Fig. 1(d), respectively. For the case of bare bulk, the absorptions are very similar to the overall absorptions in the wavelength range, except for that peak “II” has a slight blueshift in spectral position and a little decrease in resonant amplitude. However, for bare surface case, no plasmonic behaviors is observed in the considered wavelength range. Thus, we argue that both peak “I” and “II” are mainly attributed to interband absorptions in the bulk. The contribution of Dirac charge carriers in surface states of the BSTS is overwhelmed by of bulk charge carriers due to an extremely small surface/bulk geometrical ratio in the BSTS nanospheres. As a result, large intrinsic losses in the bulk results in relatively broad resonant linewidths for two peaks.
3.2 Plasmon response of BSTS nanoshells
Figure 2(a) depicts a schematic of the LOB model of BSTS nanoshell with defined parameters including the inner and outer radii of r and R, where the blue region represents the bulk part, the yellow regions represent the metal surface layers and the inner gray region is filled with a dielectric material of SiO2 with the refractive index of n = 1.46 used in numerical simulations [31]. The absorption spectrum of BSTS nanoshell with r = 40 nm and R = 50 nm is calculated based on LOB model in Fig. 2(b). In contrast to the BSTS nanosphere that exhibits two broad peaks, the BSTS nanoshell supports a relatively broad, low energy absorption peak (denoted as “I”) at the center wavelength of λ = 458 nm and an extremely narrow, high energy absorption peak (denoted as “II”) at the wavelength of λ = 205 nm. By fitting with the Lorentz-lineshape equation, peak “II” has a full width at half maximum (FWHM) of 3.9 nm. Consequently, an ultrahigh Q-factor of 52, the highest value reported in the UV region so far, is achieved in the BSTS nanoshells.
Fig. 2. (a) A sketch of the LOB model of BSTS nanoshell. (b) Absorption spectrum of the BSTS nanoshell with r = 40 nm and R = 50 nm.
To reveal physical mechanisms of resonant peaks, the near-field distributions are presented in different planes in Fig. 3. For peak “I”, the |E|-field pattern features two maxima in E-k plane [See the top panel of Fig. 3(a)], showing a typical picture of dipolar localized surface plasmon mode excitation. Moreover, it exhibits an in-phase oscillation of induced charges on the inner and outer surfaces of the shell in the z-component of E-field distributions [See the bottom panel of Fig. 3(a)]. We assign these features to the bonding dipolar plasmon mode of BSTS nanoshell. As for peak “II”, it exhibits four “hot spots” around the nanosphere in E-k plane [See the top panel of Fig. 3(b)] and an out-of-phase oscillation of induced charges on both surfaces of the shell in E-H plane [See the bottom panel of Fig. 3(b)]. We thus assign peak “II” to the anti-bonding quadrupolar plasmon mode of BSTS nanoshell. In addition, it has to be noted that a giant enhancement factor of E-field intensity as high as ∼103 is produced by peak “II”. The value is comparable with or even higher than reported in metallic nanostructures proposed aiming at obtaining giant field enhancements [32,33].
Fig. 3. Distributions of |E|-field in E-k plane (top panel) and Ez in E-H plane (bottom panel) corresponding to peak (a) “I” and (b) “II”. Red dashed lines in E-k planes indicate the z-coordinate of E-H planes.
The formation process of plasmon modes can be intuitively elucidated based on plasmon hybridization theory [34]. In the nanoshell, the interaction between the primitive plasmons of the cavity (supported by the inner surface of the shell) and the sphere (supported by the outer surface of the shell) with the same multipolar index l can occur, consequently producing the hybridized bonding (denoted as “ω-”) and anti-bonding (denoted as “ω+”) modes. Peak “I”, corresponding to the bonding dipolar plasmon mode, is formed by a symmetric alignment of the cavity and sphere dipolar plasmons in the case of l = 1, as shown in Fig. 4(a). Peak “II”, corresponding to the anti-bonding quadrupolar plasmon mode, is formed by an anti-symmetric alignment of the cavity and sphere quadrupolar plasmons in the case of l = 2 as shown in Fig. 4(b). Additionally, the distributions of E-field vectors in the insets of Fig. 4 further demonstrate the excitation mechanisms of the bonding dipolar and anti-bonding quadrupolar plasmon modes.
Fig. 4. Plasmon hybridization diagrams illustrating the forming process of plasmon modes for the multipolar index (a) l = 1, and (b) l = 2. Insets: Distributions of E-field vectors in E-k plane corresponding to peak “I” and “II”.
3.3 Excitation of Dirac-type plasmon resonance in BSTS nanoshells
In order to separate the contributions from the bulk and surface states, the absorptions of the BSTS nanoshell with r = 40 nm and R = 50 nm are calculated for bare bulk and bare surface layers in Fig. 5, as has been done in BSTS nanospheres. For bare bulk case, it exhibits a broad peak that has the linewidth and spectral position approaching those of peak “I”. Thus, we argue that the bulk component of the BSTS plays a dominant role for the excitation of the bonding dipolar plasmon mode. For bare surface case, a sharp peak that has nearly the same linewidth as peak “II” appears near the position of peak “II”. This means that peak “II”, corresponding to the anti-bonding quadrupolar plasmon mode, is largely originated from Dirac charge carriers from surface states of the BSTS. For the anti-bonding quadrupolar plasmon mode, the near-field coupling of the primitive cavity and sphere plasmons associated with the inner and outer metal surface layers of the BSTS shell suppresses the excitation of bulk plasmons, thus enabling the excitation of a Dirac-type plasmon resonance.
Fig. 5. Absorption spectra of the BSTS nanoshell with r = 40 nm and R = 50 nm for the cases of the overall (black line), bare bulk (blue line) and bare surface (red line). Insets: illustrations of the simulation models for three cases.
Based on plasmon hybridization theory [27], a nanoshell system exhibits two fundamental plasmon modes with resonant frequencies given by the equation:
3.4 Tunable plasmon wavelength by varying geometrical parameters
The absorption spectra of BSTS nanoshells are calculated by changing geometrical parameters in Fig. 6. With increasing r but keeping a fixed R = 30 nm, the increased interaction between the primitive cavity and sphere plasmons results in an obvious redshift of the bonding dipolar resonance (denoted as “I”) and a slight blueshift of the anti-bonding quadrupolar resonance (denoted as “II”), as shown in Fig. 6(a). Similarly, as the aspect ratio of the nanoshell becomes larger and larger at a shell thickness of 8 nm, the bonding dipolar resonance redshifts obviously and the anti-bonding quadrupolar resonance blueshifts slightly due to the increased interaction between the primitive plasmons, as shown in Fig. 6(b). With increasing r/R, the narrowing of the anti-bonding quadrupolar plasmon resonance is due to a more efficient cancellation of the moments of the primitive cavity and sphere plasmons, and the broadening of the bonding dipolar plasmon resonance is due to the increased radiative losses produced by enlarged dipole moments of the cavity and sphere. These observed spectral behaviors for peak “I” and “II” are very analogous those for bonding and anti-bonding plasmon resonances in metallic nanoshells [27].
Fig. 6. Absorption spectra of BSTS nanoshells by changing (a) the inner radius r (1: r = 12 nm, 2: r = 16 nm, 3: r = 20 nm, 4: r = 20 nm), and (b) the aspect ratio x = r/R (1: x = 0.6, 2: x = 0.73, 3: x = 0.8, 4: x = 0.84).
4. Conclusions
In summary, we theoretically investigated the UV-visible range plasmon responses in the BSTS nanospheres and nanoshells by employing the LOB model of the TIs. The BSTS nanosphere exhibits broad linewidth plasmon absorptions that largely originate from interband absorptions in the bulk. In contrast, the contribution from surface states of the BSTS to plasmon response can be amplified significantly in BSTS nanoshells due to the near-field coupling of plasmons associated with the inner and outer metal surface layers of the shell. As a consequence, a Dirac-type plasmon resonance originating from massless Dirac charge carriers in surface states of the BSTS is excited in UV region and gets a Q-factor as high as 52 due to significantly decreased Drude losses. Moreover, a tunable plasmon wavelength is demonstrated by varying geometrical parameters of the BSTS nanoshells. This may find applications in surface enhanced Raman spectroscopies, nanolasers and biosensors to sensitive to specific resonances in many organic molecules (e.g. proteins and DNA) in the UV regions.
Funding
National Natural Science Foundation of China (11704208); Key Research Project of Henan Higher Education Institutions (18A140006).
Disclosures
The authors declare no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. L. Novotny and B. Hecht, Principles of Nano-Optics, Cambridge University Press, 2006.
2. S. A. Maier, Plasmonics: Fundamentals and Applications, Springer, 2007.
3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
4. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef]
5. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010). [CrossRef]
6. M. W. Knight, N. S. King, L. Liu, H. O. Everitt, P. Nordlander, and N. J. Halas, “Aluminum for Plasmonics,” ACS Nano 8(1), 834–840 (2014). [CrossRef]
7. J. Martin and J. Plain, “Fabrication of aluminium nanostructures for plasmonics,” J. Phys. D: Appl. Phys. 48(18), 184002 (2015). [CrossRef]
8. Y. Ekinci, H. H. Solak, and J. F. Loffler, “Plasmon resonances of aluminum nanoparticles and nanorods,” J. Appl. Phys. 104(8), 083107 (2008). [CrossRef]
9. A. Sobhani, A. Manjavacas, Y. Cao, M. J. Mcclain, F. J. Garcia de Abajo, P. Nordlander, and N. J. Halas, “Pronounced Linewidth Narrowing of an Aluminum Nanoparticle Plasmon Resonance by Interaction with an Aluminum Metallic Film,” Nano Lett. 15(10), 6946–6951 (2015). [CrossRef]
10. J. Zheng, W. Yang, J. Wang, J. Zhu, L. Qian, and Z. Yang, “An ultranarrow SPR linewidth in the UV region for plasmonic sensing,” Nanoscale 11(9), 4061–4066 (2019). [CrossRef]
11. J. W. Cleary, R. E. Peale, D. J. Shelton, G. D. Boreman, C. W. Smith, M. Ishigami, R. Soref, A. Drehman, and W. R. Buchwald, “IR permittivities for silicides and doped silicon,” J. Opt. Soc. Am. B 27(4), 730–734 (2010). [CrossRef]
12. R. Soref, J. Hendrickson, and J. W. Cleary, “Long-wave infrared tunable thin-film perfect absorber utilizing highly doped silicon-on-sapphire,” Opt. Express 20(4), 3814–3824 (2012). [CrossRef]
13. M. G. Blaber, M. D. Arnold, and M. J. Ford, “A review of the optical properties of alloys and intermetallics for plasmonics,” J. Phys.: Condens. Matter 22(14), 143201 (2010). [CrossRef]
14. U. Guler, V. W. Shalaev, and A. Boltasseva, “Nanoparticle plasmonics: going practical with transition metal nitrides,” Mater. Today 18(4), 227–237 (2015). [CrossRef]
15. G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative Plasmonic Materials: Beyond Gold and Silver,” Adv. Mater. 25(24), 3264–3294 (2013). [CrossRef]
16. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]
17. M. Z. Hasan and C. L. Kane, “Colloquium Topological Insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010). [CrossRef]
18. P. D. Pietro, M. Ortolani, O. Limaj, A. D. Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013). [CrossRef]
19. Y. Deshko, L. Krusin-Elbaum, V. Menon, A. Khanikaev, and J. Trevino, “Surface plasmon polaritons in topological insulator nano-films and superlattices,” Opt. Express 24(7), 7398–7410 (2016). [CrossRef]
20. M. Autore, F. D. Apuzzo, A. D. Gaspare, V. Giliberti, O. Limaj, P. Roy, M. Brahlek, N. Koirala, S. Oh, F. J. García de Abajo, and S. Lupi, “Plasmon–phonon interactions in topological insulator microrings,” Adv. Opt. Mater. 3(9), 1257–1263 (2015). [CrossRef]
21. Y. P. Lai, I. T. Lin, K. H. Wu, and J. M. Liu, “Plasmonics in Topological Insulators,” Nanomater. Nanotechnol. 4(13), 1–8 (2014). [CrossRef]
22. M. Zhao, M. Bosman, M. Danesh, M. Zeng, P. Song, Y. Darma, A. Rusydi, H. Lin, C. W. Qiu, and K. P. Loh, “Visible Surface Plasmon Modes in Single Bi2Te3 Nanoplate,” Nano Lett. 15(12), 8331–8335 (2015). [CrossRef]
23. J. Yin, H. N. S. Krishnamoorthy, G. Adamo, A. M. Dubrovkin, Y. Chong, N. I. Zheludev, and C. Soci, “Plasmonics of topological insulators at optical frequencies,” NPG Asia Mater. 9(8), e425 (2017). [CrossRef]
24. J. Y. Ou, J. K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2,” Nat. Commun. 5(1), 5139 (2014). [CrossRef]
25. Z. Yue, B. Cai, L. Wang, X. Wang, and M. Gu, “Intrinsically core-shell plasmonic dielectric nanostructures with ultrahigh refractive index,” Sci. Adv. 2(3), e1501536 (2016). [CrossRef]
26. A. M. Dubrovkin, G. Adamo, J. Yin, L. Wang, C. Soci, Q. J. Wang, and N. I. Zheludev, “Visible Range Plasmonic Modes on Topological Insulator Nanostructures,” Adv. Opt. Mater. 5(3), 1600768 (2017). [CrossRef]
27. E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004). [CrossRef]
28. M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, “Nanosphere Lithography: Effect of Substrate on the Localized Surface Plasmon Resonance Spectrum of Silver Nanoparticles,” J. Phys. Chem. B 105(12), 2343–2350 (2001). [CrossRef]
29. A. Pinchuk, A. Hilger, G. Von Plessen, and U. Kreibig, “Substrate effect on the optical response of silver nanoparticles,” Nanotechnology 15(12), 1890–1896 (2004). [CrossRef]
30. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]
31. E. D. Palik, Handbook of optical constants of solids, Academic press, 1998.
32. J. N. He, C. Z. Fan, P. Ding, S. M. Zhu, and E. J. Liang, “Near-field engineering of Fano resonances in a plasmonic assembly for maximizing CARS enhancements,” Sci. Rep. 6(1), 20777 (2016). [CrossRef]
33. J. Q. Wang, Y. N. Wu, C. Z. Fan, E. J. Liang, Y. Li, and P. Ding, “Unmodified hot spot in hybridized nanorod dimer for extended surface-enhanced Raman scattering,” J. Phys. Chem. Solids 136, 109152 (2020). [CrossRef]
34. E. Prodan, C. Radloff, and N. J. Halas, “A Hybridization Model for the Plasmon Response of Complex Nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef]
