Open Access
Add to BibSonomy
Abstract
When a thin film undergoes a percolative insulator-to-metal phase transition, the real part of the dielectric constant dramatically changes; it diverges close to the percolation threshold and becomes negative in the metallic phase. To date, the percolative nature of this phase transition has been monitored by near-field imaging or conventional spectroscopy. Although such methods are successful, they require laborious raster scanning or complicated theoretical fitting processes. In this study, using the strong coupling between slot antennas and a phase-transition material, a direct step-by-step investigation of the percolation transition can be demonstrated without any scanning or fitting processes. The percolation threshold can be identified in real time by monitoring the peak position, because the resonance transmission through the slot antenna array is highly affected by the dielectric environment. The work presented in this study could potentially contribute to the characterization of phase-transition materials to be used in memory devices or active metamaterials.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
When Au or Pb film is deposited on an insulating substrate by thermal evaporation, disordered nanometer-sized metal clusters are initially formed (Fig. 1(a)) [1,2]. As more metal evaporates, conducting channels are formed between the disordered clusters, and the electrons begin to percolate through the random network. Finally, a homogeneous layer is produced, and the film becomes metallic. In short, with the increase in thickness, the film undergoes an insulator-to-metal transition. These transitions are often referred to as percolation transitions, because the percolation process is present during the transition. The percolation threshold is defined as the critical thickness that separates the insulating and metallic regimes. Concerning the percolation transition, interestingly, the real part of the dielectric constant (ɛr) diverges near the percolation threshold [3,4]. In the insulating states, ɛr is a small positive number (∼10), whereas in the metallic state, it becomes negative. Therefore, as schematically shown in Fig. 1(c), ɛr becomes increasingly large with the increase in thickness, and eventually, it proves to be negative after crossing the percolation threshold. Such an increment of ɛr near the percolation threshold can be attributed to the increase in capacitive coupling between the metallic clusters [5]. In other words, as the thickness increases, the spacing between the metallic clusters decreases, and the effective capacitive coupling between the metallic clusters increases, inducing the enhancement of ɛr.
Fig. 1. Schematic diagrams of the percolative insulator-to-metal phase transition for (a) Au or Pb thin film and (b) VO2 thin film. (c) The conceptual real part of the dielectric constant (ɛr) as a function of the thickness or temperature of a thin film during the percolation transition. ɛr diverges near the percolation threshold and becomes negative in the metallic phase.
The divergence of ɛr has been also observed during the insulator-to-metal phase transition of a vanadium dioxide (VO2) thin film (Fig. 1(b)) [6,7]. The phase transition could be attributed to the breaking of the electron-lattice correlations that existed below the critical temperature (typically 68°C) [8,9]. Such a transition could also have been induced by femtosecond optical pulses, electric or magnetic fields [10–14]. More than a decade ago, M. M. Qazilbash et. al. imaged the near-field scattering amplitude directly at the infrared frequency with spatial resolution ≈20 nm and demonstrated that the insulating and metallic phases coexisted in the vicinity of the critical temperature [6]. This means that the VO2 phase transition has a percolative nature. They also extracted the dielectric constants during the phase transition using effective medium theory (EMT) and observed the divergence of ɛr near the percolation threshold. Therefore, in conclusion, the divergence of ɛr signaled the percolative nature of the insulator-to-metal phase transition.
The terahertz (THz) frequency range (0.1–2.0 THz) is appropriate for monitoring the anomalous behavior of dielectric constants during the percolation transition [1,15]. This is due to the transport length scales in metals being in the order of tens of nanometers in THz frequencies, which is comparable to the size of average metallic clusters and their spacing. Thus, it can be inferred from the response of the thin film to the THz waves, that the properties of the carrier motion are affected by the nanometer-scale disorder. Numerous efforts have been devoted to the characterization of the percolation transition of thin metal films or VO2 by THz-time-domain spectroscopy (THz-TDS) [15–17]. For instance, THz transmission through a VO2 film exhibits a gradual decrease as the thin films undergo an insulator-to-metal phase transition, this being indirect evidence of the coexisting of the insulating and metallic states [16,18]. In addition, the complex conductivity or dielectric constants have been extracted from the amplitude and phase spectra by applying the EMT or the Drude model, and the increments near the percolation threshold have been observed [5,15,16].
Despite infrared near-field nano-imaging and THz-TDS having been successfully adopted to monitor the percolation transition, there are several difficulties. Even though the near-field imaging allows direct observation of the formation and growth of the metallic nano-clusters throughout the percolative phase transition, a relatively long time is needed to take a single image due to the nanometer-scale scanning process. Therefore, thermal fluctuation should be carefully diminished throughout the long measurement time to obtain a reliable image. Meanwhile, complicated analysis processes are crucial for distinguishing the phase-transition stages using conventional THz-TDS. In addition, it remains debatable which analyzing method is appropriate for application because the results are highly dependent on the sample and dielectric models [16].
In this study, a novel method is proposed that allows direct real-time monitoring of the step-by-step percolation transition by peak-shift spectroscopy (tracking the resonance wavelength of the slot antennas). The strategy used is the strong plasmonic coupling between the metal slot antennas and the phase-transition material, for example, VO2 thin film, in the THz-frequency regime (Fig. 2(a)). The slot antennas are narrow rectangular apertures perforated in a thin metal film [19]. When the light the passes through the apertures, the electrons oscillate collectively and become highly concentrated at the gap, which is called the localized surface plasmon [20–22]. Generally, because the collective charge oscillation is dependent on the aperture geometry and frequency, complicated transmission spectra are expected. However, among these apertures, slot antennas exhibit a single resonance transmission as a result of their simple geometry when the incident light is polarized along the short side of the slot antennas. Furthermore, since most metal films can be regarded as perfect conductors in the THz-frequency range, the transmission can be obtained by analytic calculation. The resonance peaks, for free-standing slot antenna arrays, are located at wavelengths that are approximately twice the length of the aperture [23]. In the presence of the substrates, the resonance peak positions are strongly affected by the substrates’ refractive indices [24].
Fig. 2. (a) Upper panel: schematic diagram of the slot antenna arrays on a phase-transition material. Lower panel: conceptual resonance transmission in the insulating phase (black dotted line) and its red (red line) and blue (blue line) shifts depending on the variations of ɛr. (b) The calculated transmissions for the insulating phase (black line), percolation threshold (red line), and metallic phase (blue line) with $w = 25\; {\mathrm{\mu} \mathrm{m}},\; l = 150\; {\mathrm{\mu} \mathrm{m}},\; h = 70\; \textrm{nm},\; {p_x} = 150\; {\mathrm{\mu} \mathrm{m}},\; $ and ${p_y} = 180\; {\mathrm{\mu} \mathrm{m}}$. For clarity, 2 and 1 are added for the black and red line, respectively. The vertical dotted line represents the resonance position for the transmission of the insulating phase. (c) Summary table of the calculated transmission spectra in (b).
Recently, I investigated the analytical model for transmission especially when the slot antennas were fabricated on a thin film/substrate system (Fig. 2(a), upper panel) [25]. When the width, length, thickness, and period in the x and y directions of the metal slot antenna array are denoted by $w,\; l,\; {p_x}$, and ${p_y}$, respectively, the formula for the transmittance is given by
2. Theoretical analysis and discussion
For illustrative purposes, I calculated the transmission spectra for the three different cases: ɛr = 11 for the insulating phase, ɛr = 90 for the percolation threshold, and ɛr = −25 for the metallic phase. The thickness of the phase-transition material was set as $250\; \textrm{nm}$. The width ($w$), length ($l$), metal thickness ($h$), and the periods in the x- and y-directions (${p_x},{p_y}$) of the slot antenna array were given by $w = 25\; {\mathrm{\mu} \mathrm{m}},\; l = 150\; {\mathrm{\mu} \mathrm{m}},\; h = 70\; \textrm{nm},\; {p_x} = 150\; {\mathrm{\mu} \mathrm{m}},$ and ${p_y} = 180\; {\mathrm{\mu} \mathrm{m}}$, respectively (Fig. 2(a), upper panel). The metal film of the slot antenna array was assumed to be a perfect conductor. The calculated transmission spectra are shown in Fig. 2(b) for the black (ɛr = 11), red (ɛr = 90), and blue lines (ɛr = −25), respectively. For clarity, I added 2 to the black line graph and 1 to the red line graph. The black, dotted vertical line represents the resonance wavelength of the insulating phase (black line, ɛr = 11). As can be seen, a redshift for ɛr = 90 and a blueshift for ɛr = −25 are observed, meaning that the peak shift can be used to distinguish the phase-transition stages.
The table in Fig. 2(c) summarizes the calculated transmission spectra in Fig. 2(b). In the insulating phase (ɛr = 11), the resonance position was located at ${\mathrm{\lambda }_{\textrm{res}}} = 474\; {\mathrm{\mu} \mathrm{m}}$ (black line in Fig. 2(b) and the second row of the table in Fig. 2(c)). As the thin film underwent to the percolative phase (ɛr = 90), the resonance position shifted to ${\mathrm{\lambda }_{\textrm{res}}} = 530\; {\mathrm{\mu} \mathrm{m}}$, which means that it is redshifted by $\Delta {\mathrm{\lambda }_{\textrm{res}}} = 56\; {\mathrm{\mu} \mathrm{m}}$ (red line in Fig. 2(b) and the third row of the table in Fig. 2(c)). Finally, with the metallic phase (ɛr = −25), the resonant position experienced strong blueshift by an amount of $\Delta {\mathrm{\lambda }_{\textrm{res}}} ={-} 23\; {\mathrm{\mu} \mathrm{m}}$ compared to the insulating phase, so that it is located at a shorter wavelength ${\mathrm{\lambda }_{\textrm{res}}} = 451\; \mathrm{\mu m\;\ }$(blue line in Fig. 2(b) and the fourth row of the table in Fig. 2(c)). These simple example calculations demonstrate the potential of peak-shift spectroscopy to discriminate between percolative and metallic phases.
A more complex and practical example calculation was performed by assuming that the phase-transition material was a VO2 thin film whose ɛr changes by temperature as shown in Fig. 3(a) (green circles). The ɛr versus temperature data was taken from the ref. 6, exhibiting the percolative insulator-to-metal phase transition. In particular, the ɛr suddenly diverged near the percolation threshold and then became negative after the phase transition was complete. The transmission spectra were calculated at each temperature (Some selected spectra are plotted in the inset of Fig. 3.), and the resonance wavelengths (Fig. 3(b), purple circles) and the transmissions at the resonance positions (Fig. 3(c), yellow circles) were extracted. The transmission as a function of temperature (Fig. 3(c)) showed no singular point; it gradually decreased as the temperature increased. Therefore, we could not identify the percolation threshold solely by investigating the transmission. Such a monotonic decrease of the transmission has also been observed with bare VO2 thin film [16]. By contrast, tracking the resonance peak position (peak-shift spectroscopy) gives dramatic variations depending on the temperature. Before the critical temperature (343 K), the resonance shifts to the longer wavelength (redshift) as the temperature increases, while a strong blueshift is observed after the temperature far exceeds the critical point. In addition, surprisingly, the peak-position graph (Fig. 3(b)) has almost the same shape as the ɛr change graph (Fig. 3(a)). As a result, the step-by-step phase-transition stage is easily identified merely by observing the peak position. This means that peak-shift spectroscopy is an excellent tool for monitoring the percolation phase transition of VO2 thin film.
Fig. 3. (a) Change of the ɛr as a function of the temperature for the VO2 thin film. Data were read from ref. 6. (b) Calculated resonance wavelengths. (c) Calculated transmission at resonance. Inset: transmission spectra at some selected temperatures.
There are several works on VO2 coupled to plasmonic modes, where the phase change has been shown to induce the spectral shifts [26–28]. Theses references had studied percolative behavior of Au-VO2 nano composite systems and shift of the surface plasmon resonance during the phase transition of VO2. The main difference between the previous works and this study is whether Au and VO2 form a composite system or a coupling system. In the previous works, Au nano particles were embedded within VO2 to build a composite system, which strongly modifies the percolative nature of VO2 thin film. Therefore, both the hysteresis characteristics (transition temperature and hysteresis width) and the surface plasmon resonance change dramatically depending on the size of the Au nano particles. On the other hand, in this work, the uniform Au film (thickness 70 ∼ 100 nm) has been used to make the slot antenna arrays and such apertures are place on the homogeneous VO2 thin films to form an optically coupling system. Unlike the composite system, in this case, the transition temperature and hysteresis width are rarely changed regardless of the slot antennas [29], unless the width of the slot becomes sub-10 nm [30]. Consequently, the percolative nature of VO2 thin film itself can be monitored by peak shift spectroscopy.
3. Experimental evidence
The experimental evidence of my theory can be found in recently published research papers [29,31,32]. For example, in ref. 31, the THz transmission through the slot antennas on VO2 thin film during the phase transition had been measured. The schematic diagram of the experiment was displayed in Fig. 4(a). A 100-nm-thick VO2 thin film was grown by pulsed laser deposition onto a 430-µm-thick c-plane sapphire substrate. The array of slot antennas and the gold electrodes were simultaneously deposited on the VO2 film by standard E-beam lithography technique. The parameters of the slot antenna arrays were $w = 600\; \textrm{nm},\; l = 140\; {\mathrm{\mu} \mathrm{m}},\; h = 100\; \textrm{nm},\; {p_x} = 30\mathrm{\;\ \mu m}$ and ${p_y} = 150\; {\mathrm{\mu} \mathrm{m}}$. The gap between the electrode and the slot antenna array was $10\mathrm{\;\ \mu m}$. The 100-nm-thick gold film was sufficient to be regarded as a perfect conductor in the THz-frequency range [25]. At room temperature, the resonance peak was located at $577\; {\mathrm{\mu} \mathrm{m}}$. The phase transition of VO2 was induced by the electrical bias between the two electrodes and the transmitted THz pulses as a function of the applied voltage were recorded. The transmission amplitude as well as the phase can be extracted after Fourier transform of the measured THz time trace.
Fig. 4. (a) Schematic diagram of the experiments for the peak-shift spectroscopy. (b) Summary table of the experimental results: applied voltage, transmission, and resonance frequency data are extracted from the Fig. 3(a) in ref. 31.
The table in Fig. 4(b) summarizes the experimental results extracted from the Fig. 3(a) in ref. 31. At zero bias (insulating phase), a resonance peak was observed with a transmittance of 0.36 at 0.52 THz (577-${\mathrm{\mu} \mathrm{m}}$-wavelength) (the second row of the table in Fig. 4(b)). With increasing the voltage up to 350 V, the resonance peak position moved to 0.50 THz (600-${\mathrm{\mu} \mathrm{m}}$-wavelength) and the transmittance was 0.34 (the third row of the table in Fig. 4(b)). In other words, the peak position underwent a redshift by $\mathrm{\Delta }{\lambda _{\textrm{res}}} = 23\; {\mathrm{\mu} \mathrm{m}}$, while almost maintaining the transmittance. This is what we expect at the percolation threshold; strong redshift of the resonance peak with keeping high transmission. Meanwhile, with higher bias voltage 500 V (the fourth row of the table in Fig. 4(b)), the transmission significantly decreased down to 0.05 and the peak position located at 0.55 THz (545-${\mathrm{\mu} \mathrm{m}}$-wavelength). The sharp decrease in transmittance represents that the VO2 thin film has changed to a metallic state. In the metallic phase, the resonance peak experienced blueshift $\mathrm{\Delta }{\lambda _{\textrm{res}}} ={-} 32\; {\mathrm{\mu} \mathrm{m}}$, as expected in my theoretical discussion. Finally, by tracking the peak position, the percolative phase transition of VO2 thin film is directly identified without any raster scanning or complicated fitting process.
4. Conclusion and remark
In conclusion, peak-position spectroscopy was applied to investigate the percolative insulator-to-metal phase transition. Slot antenna arrays were employed to make the resonance peak. The resonance peak position moved to a longer wavelength on increasing the ɛr, whereas it moved to a shorter wavelength when the ɛr became negative. Unlike the peak position, the transmission at resonance showed a gradual decrease regardless of the behavior of the ɛr. Because the ɛr diverged near the threshold and then went below zero above the threshold during the percolation transition, peak-shift spectroscopy could be an effective tool for monitoring the phase transition. Our scheme was applied for monitoring the phase transition of a VO2 thin film and successfully identified the percolation threshold without any complicated analysis process or near-field scanning. Recently, phase-transition materials have been attracting attention due to the crucial role they play in switching devices, memory devices, and active metamaterials [18,33,34]. Therefore, I believe that my studies will help to realize phase-transition-based devices by offering efficient ways of analyzing the physical properties of phase-transition materials. Performing peak shift spectroscopy requires a transparent substrate and additional process to fabricate slot antennas on a phase transition material. As mentioned before, for VO2 thin film, such patterning process has little effect on the phase transition characteristics. However, in the case of other phase change materials, caution is required because patterning may affect the phase change process.
Funding
National Research Foundation of Korea (2009-0082580, 2020R1F1A1074832, 2021R1F1A1058307, K210309005); Dankook University (as a part of the University Innovation, Research-Focused Department Promotion Project, Support Program 2020 to Dankook University).
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1074832, No. 2021R1F1A1058307). This research has been done by the author(s) working at the Department of Physics of Dankook University. Department of Physics was supported by the Research-Focused Department Promotion Project as a part of the University Innovation Support Program 2020 to Dankook University. This research was supported by Nano·Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning. (2009-0082580) Project number: K210309005
Disclosures
The authors declare no conflicts of interest.
Data availability
Part of the data underlying the results presented in this paper are available in Ref. [6,31]. The rest of data are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Walther, D. G. Cooke, C. Sherstan, M. Hajar, M. R. Freeman, and F. A. Hegmann, “Terahertz conductivity of thin gold films at the metal-insulator percolation transition,” Phys. Rev. B 76(12), 125408 (2007). [CrossRef]
2. M. Hövel, B. Gompf, and M. Dressel, “Dielectric properties of ultrathin metal films around the percolation threshold,” Phys. Rev. B 81(3), 035402 (2010). [CrossRef]
3. H. Bakkali, E. Blanco, S. E. Lofland, and M. Domínguez, “Divergence of the dielectric constant in ultrathin granular metal films near the percolation threshold,” New J. Phys. 22(8), 083018 (2020). [CrossRef]
4. J. J. Tu, C. C. Homes, and M. Strongin, “Optical properties of ultrathin films: evidence for a dielectric anomaly at the insulator-to-metal transition,” Phys. Rev. Lett. 90(1), 017402 (2003). [CrossRef]
5. H. S. Choi, J. S. Ahn, J. H. Jung, T. W. Noh, and D. H. Kim, “Mid-infrared properties of a VO2 film near the metal-insulator transition,” Phys. Rev. B 54(7), 4621–4628 (1996). [CrossRef]
6. M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott transition in VO2 revealed by infrared spectroscopy and nano-imaging,” Science 318(5857), 1750–1753 (2007). [CrossRef]
7. H.-T. Kim, B.-G. Chae, D.-H. Youn, S.-L. Maeng, G. Kim, K.-Y. Kang, and Y.-S. Lim, “Mechanism and observation of Mott transition in VO2-based two- and three-terminal devices,” New J. Phys. 6, 52 (2004). [CrossRef]
8. H. Lu, S. Clark, Y. Guo, and J. Robertson, “The metal–insulator phase change in vanadium dioxide and its applications,” J. Appl. Phys. 129(24), 240902 (2021). [CrossRef]
9. F. J. Morin, “Oxides which show a metal-to-insulator transition at the Neel temperature,” Phys. Rev. Lett. 3(1), 34–36 (1959). [CrossRef]
10. E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing-A review,” Anal. Chim. Acta 706(1), 8–24 (2011). [CrossRef]
11. C. Kübler, H. Ehrke, R. Huber, R. Lopez, A. Halabica, R. F. Haglund, and A. Leitenstorfer, “Coherent structural dynamics and electronic correlations during an ultrafast insulator-to-metal phase transition in VO2,” Phys. Rev. Lett. 99(11), 116401 (2007). [CrossRef]
12. M. Nakajima, N. Takubo, Z. Hiroi, Y. Ueda, and T. Suemoto, “Photoinduced metallic state in VO2 proved by the terahertz pump-probe spectroscopy,” Appl. Phys. Lett. 92(1), 011907 (2008). [CrossRef]
13. H. Zhan, V. Astley, M. Hvasta, J. A. Deibel, D. M. Mittleman, and Y.-S. Lim, “The metal-insulator transition in VO2 studied using terahertz apertureless near-field microscopy,” Appl. Phys. Lett. 91(16), 162110 (2007). [CrossRef]
14. Y. H. Matsuda, D. Nakamura, A. Ikeda, S. Takeyama, Y. Suga, H. Nakahara, and Y. Muraoka, “Magnetic-field-induced insulator–metal transition in W-doped VO2 at 500 T,” Nat. Commun. 11(1), 3591 (2020). [CrossRef]
15. T. L. Cocker, L. V. Titova, S. Fourmaux, H.-C. Bandulet, D. Brassard, J.-C. Kieffer, M. A. El Khakani, and F. A. Hegmann, “Terahertz conductivity of the metal-insulator transition in a nanogranular VO2 film,” Appl. Phys. Lett. 97(22), 221905 (2010). [CrossRef]
16. P. Mandal, A. Speck, C. Ko, and S. Ramanathan, “Terahertz spectroscopy studies on epitaxial vanadium dioxide thin films across the metal-insulator transition,” Opt. Lett. 36(10), 1927–1929 (2011). [CrossRef]
17. P. U. Jepsen, B. M. Fischer, A. Thoman, H. Helm, J. Y. Suh, R. Lopez, and R. F. Haglund, “Metal-insulator phase transition in a VO2 thin film observed with terahertz spectroscopy,” Phys. Rev. B 74(20), 205103 (2006). [CrossRef]
18. J.-H. Shin, S.-P. Han, M. Song, and H.-C. Ryu, “Gradual tuning of the terahertz passband using a square-loop metamaterial based on a W-doped VO2 thin film,” Appl. Phys. Express 12(3), 032007 (2019). [CrossRef]
19. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001). [CrossRef]
20. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]
21. J. Kyoung and Y. G. Roh, “Extraordinary optical transmission induced by strong plasmon-phonon coupling: shape resonance versus non-shape resonance,” J. Appl. Phys. 120(19), 193104 (2016). [CrossRef]
22. Y.-M. Bahk, D. J. Park, and D.-S. Kim, “Terahertz field confinement and enhancement in various sub-wavelength structures,” J. Appl. Phys. 126(12), 120901 (2019). [CrossRef]
23. J.-H. Choe, J.-H. Kang, D.-S. Kim, and Q.-H. Park, “Slot antenna as a bound charge oscillator,” Opt. Express 20(6), 6521 (2012). [CrossRef]
24. J. H. Kang, J.-H. Choe, D. S. Kim, and Q.-H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17(18), 15652 (2009). [CrossRef]
25. J. Kyoung, “Anomalous blueshift of aperture resonance enabled by the loss of a thin film,” Sci. Rep. 10(1), 22100 (2020). [CrossRef]
26. M. Maaza, O. Nemraoui, C. Sella, A. C. Beye, and B. Baruch-Barak, “Thermal induced tunability of surface plasmon resonance in Au–VO2 nano-photonics,” Opt. Commun. 254(1-3), 188–195 (2005). [CrossRef]
27. H. Zhou, X. Cao, M. Jiang, S. Bao, and P. Jin, “Surface plasmon resonance tunability in VO2/Au/VO2 thermochromic structure,” Laser Photon. Rev. 8(4), 617–625 (2014). [CrossRef]
28. I. Balin, S. Wang, P. Wang, Y. Long, and I. Abdulhalim, “Enhanced transition-temperature reduction in a half-sphere Au/VO2 core-shell structure: local plasmonics versus induced stress and percolation effects,” Phys. Rev. Appl. 11(3), 034064 (2019). [CrossRef]
29. M. Seo, J. Kyoung, H. Park, S. Koo, H. T. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. S. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef]
30. Y.-G. Jeong, S. Han, J. Rhie, J.-S. Kyoung, J.-W. Choi, N. Park, S. Hong, B.-J. Kim, H.-T. Kim, and D.-S. Kim, “A vanadium dioxide metamaterial disengaged from insulator-to-metal transition,” Nano Lett. 15(10), 6318–6323 (2015). [CrossRef]
31. Y.-G. Jeong, H. Bernien, J.-S. Kyoung, H.-R. Park, H.-S. Kim, J.-W. Choi, B.-J. Kim, H.-T. Kim, K. J. Ahn, and D.-S. Kim, “Electrical control of terahertz nano antennas on VO2 thin film,” Opt. Express 19(22), 21211 (2011). [CrossRef]
32. J. Kyoung, M. Seo, H. Park, S. Koo, H. Kim, Y. Park, B.-J. Kim, K. Ahn, N. Park, H.-T. Kim, and D.-S. Kim, “Giant nonlinear response of terahertz nanoresonators on VO2 thin film,” Opt. Express 18(16), 16452 (2010). [CrossRef]
33. J. J. Yang, D. B. Strukov, and D. R. Stewart, “Memristive devices for computing,” Nat. Nanotechnol. 8(1), 13–24 (2013). [CrossRef]
34. C. Lu, Q. Lu, M. Gao, and Y. Lin, “Dynamic manipulation of THz waves enabled by phase-transition VO2 thin film,” Nanomater. 11(1), 114 (2021). [CrossRef]
