Active tuning hBN phonon polaritons and spontaneous emission rates based on VO<sub>2</sub> and graphene

Zhou Kun; Ma Hao-Yue; Sun Xi-Xian; Wu Xiao-Hu

doi:10.7498/aps.72.20222167

Abstract

Active tunability of phonon dispersion and spontaneous emission (SE) are still open problems due to their exciting potential applications. In view of the fact that polaritons are very sensitive to the dielectric environment, in this study, with the help of the differences in optical property between the phase change material vanadium dioxide (VO₂) during the phase transition from the insulating state to metallic state and the tunable surface plasmon polaritons (SPPs) in graphene, a heterostructure composed of hyperbolic material hexagonal boron nitride (hBN) and graphene and VO₂ is proposed to investigate the active tunability of hBN phonon polaritons (PhPs). In order to illustrate the underlying physical mechanism of the above heterostructures, the dispersion distributions of the above heterostructures are calculated and represented by the imaginary part of the p-polarized Fresnel reflection coefficient of the heterostructure, meanwhile the dispersion relation of the hBN/VO₂ heterostructure in hyperbolic region is verified by the quasi-static approximation method.Results indicate that the active tunability of hBN PhPs inside type-I and type-II hyperbolic bands can be achieved by controlling VO₂ phase transition in hBN/VO₂ heterostructure. The PhP dispersion change of the hBN/VO₂ heterostructure is mainly caused by the change of the VO₂ dielectric function when VO₂ substrate changes from the insulating state into metallic state, which affects the total Fresnel reflection coefficient of the heterostructure, finally resulting in the PhP dispersion change of hBN/VO₂ heterostructure. When graphene is introduced into the hBN/VO₂ heterostructure, coupled hyperbolic plasmon-phonon polaritons (HPPPs) are obtained within type-I and type-II hyperbolic band of hBN, while the surface plasmon-phonon polaritons (SPPPs) are generated outside its hyperbolic bands. Moreover, comparative analysis of SE rates is presented for a quantum emitter positioned with the hBN/VO₂ and graphene/hBN/VO₂ heterostructure, revealing that the SE rates of these heterostructures can be modulated by the passive means including changing the hBN thickness and distance between the dipole emitter and the proposed heterostructure, and also by the active means including tuning VO₂ phase states and graphene chemical potential without changing structural configurations. This study provides a theoretical guidance in realizing active tunability of both phonon dispersion and SE rate of the natural or artificial anisotropic optical materials by using functional materials including phase change materials and graphene.

Keywords:

Authors and contacts

1.
School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, China
2.
Shandong Institute of Advanced Technology, Jinan 250100, China

Corresponding author: Zhou Kun, zhoukun0209@163.com ; Wu Xiao-Hu, xiaohu.wu@iat.cn

Funds: Project supported by National Natural Science Foundation of China (Grant No. 52204258), the Fundamental Research Funds for the Central Universities (Grant No. 2022QN1017), the Xinjiang Key Research and Development Special Task, China (Grant No. 2022B03003-3), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2022YQ57).

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References

[1]	Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948 Google Scholar
[2]	Drachev V P, Podolskiy V A, Kildishev A V 2013 Opt. Express 21 15048 Google Scholar
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Cited By

图 1 (a) hBN/VO₂异质结构示意图, t代表hBN的厚度; (b) VO₂的折射系数n和消光系数k^[15]; (c) hBN介电常数张量分量的实部

Figure 1. (a) Schematic diagram of the hBN/VO₂ heterostructure, t represents the hBN thickness; (b) the refractive index n and extinction coefficient k of VO₂^[15]; (c) real parts of the permittivity tensor components of hBN.

DownLoad: Full-Size Img PowerPoint

图 2 (a) hBN/VO₂(I)和 (b) hBN/VO₂(M)异质结构的PhPs色散分布, 其中白色圆圈代表利用(4)式计算得到的色散分支; hBN/VO₂异质结构在 (c) k_x/k₀ = 20和 (d) k_x/k₀ = 30的PhPs色散曲线

Figure 2. (a) Hybrid PhPs dispersion of hBN/VO₂(I) and (b) hBN/VO₂(M) heterostructures, the white circles represent the dispersion branches calculated by Eq. (4); Dispersion curves of hBN/VO₂ heterostructures at (c) k_x/k₀ = 20 and (d) k_x/k₀ = 30.

DownLoad: Full-Size Img PowerPoint

图 3 (a)—(c)/(e)—(g) 石墨烯/hBN/VO₂异质结构的耦合色散随石墨烯化学势μ_g的变化关系; (d) 石墨烯/hBN/VO₂(I)异质结构在k_x/k₀ =20的色散曲线随石墨烯化学势μ_g的变化规律; (h) 石墨烯/hBN/VO₂异质结构在k_x/k₀ = 20的色散曲线

Figure 3. (a)–(c)/(e)–(g) Coupling dispersions of graphene/hBN/VO₂ heterostructures as function of graphene chemical potentials μ_g; (d) dispersion curves of graphene/hBN/VO₂(I) heterostructures at k_x/k₀ = 20 as function of graphene chemical potential μ_g; (h) dispersion curves of graphene/hBN/VO₂ heterostructures at k_x/k₀ = 20.

DownLoad: Full-Size Img PowerPoint

图 4 hBN/VO₂异质结构在 (a) I和 (b) II型双曲线带内的SE率随hBN厚度t的变化规律

Figure 4. SE rates of hBN/VO₂ heterostructures within (a) type-I and (b) type-II hyperbolic bands as function of hBN thickness t.

DownLoad: Full-Size Img PowerPoint

图 5 石墨烯/hBN/VO₂异质结构在 (a) I和 (b) II双曲线带内的SE率随μ_g的变化规律. t = 90 nm

Figure 5. SE rates of graphene/hBN/VO₂ heterostructures within (a) type-I and (b) type-II hyperbolic bands as function of μ_g. t = 90 nm

DownLoad: Full-Size Img PowerPoint

map

[1]	Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948 Google Scholar
[2]	Drachev V P, Podolskiy V A, Kildishev A V 2013 Opt. Express 21 15048 Google Scholar
[3]	Wu X, McEleney C A, González-Jiménez M, Macêdo R 2019 Optica 6 1478 Google Scholar
[4]	Zhou K, Lu L, Li B, Cheng Q 2021 J. Appl. Phys. 130 093102 Google Scholar
[5]	Zhou C L, Zhang Y, Torbatian Z, Novko D, Antezza M 2022 Phys. Rev. Mater. 6 075201 Google Scholar
[6]	刘伟, 黄勇, 吴会海 2017 工程热 38 2665 Liu W, Huang Y, Wu H H 2017 J. Eng. Thermophys. 38 2665
[7]	Jiang H, Choudhury S, Kudyshev Z A, Wang D 2019 Photonics Res. 7 815 Google Scholar
[8]	Zhang Q, Hu G, Ma W, Li P, Krasnok A, Hillenbrand R, Alù A 2021 Nature 597 187 Google Scholar
[9]	Dai S, Zhang J, Ma Q, Kittiwatanakul S, McLeod A, Chen, X 2019 Adv. Mater. 31 1900251 Google Scholar
[10]	Fei Z, Rodin A, Andreev G O 2012 Nature 487 82 Google Scholar
[11]	Ju L, Geng B, Horng J 2011 Nat. Nanotechnol. 6 630 Google Scholar
[12]	Zhou K, Cheng Q, Lu L 2020 Appl. Opt. 59 595 Google Scholar
[13]	杨冲, 韩伟华, 陈俊东, 张晓迪, 郭仰岩 2020 微纳电子技术 57 341 Google Scholar Yang C, Han W H, Chen J D, Zhang X D, Guo Y Y 2020 Micro-Nano Electron. Technol. 57 341 Google Scholar
[14]	罗明海, 徐马记, 黄其伟, 李派, 何云斌 2016 65 047201 Google Scholar Luo M H, Xu M J, Huang Q W, Li P, He Y B 2016 Acta Phys. Sin. 65 047201 Google Scholar
[15]	Benkahoul M, Chaker M, Margot J 2011 Sol. Energy Mater. Sol. Cells. 95 3504 Google Scholar
[16]	赵海鹏, 章新源, 何云斌, 豆书亮, 李垚, 李孝峰, 詹耀辉 2021 光学学报 41 1523001 Zhao H P, Z X Y, He Y B, Dou S L, Li Y, Li X F, Zhan Y H 2021 Acta Opt. Sin. 41 1523001 (in Chinese)
[17]	Soltani M, Chaker M, Haddad E 2004 Appl. Phys. Lett. 85 1958 Google Scholar
[18]	Lee S, Hippalgaonkar K, Yang F 2017 Science 355 371 Google Scholar
[19]	Tang K, Dong K, Li J 2021 Science 374 1504 Google Scholar
[20]	黄雅琴, 李毅, 李政鹏, 裴江恒, 田蓉, 刘进, 周建忠, 方宝英, 王晓华, 肖寒 2019 光学学报 39 0316001 Google Scholar Huang Y Q, Li Y, Li Z P, Pei J H, Tian R, Liu J, Zhou J Z, Fang B Y, Wang X H, Xiao H 2019 Acta Optics Sinica 39 0316001 Google Scholar
[21]	Mlyuka N, Niklasson G A, Granqvist C-G 2009 Sol. Energy Mater. Sol. Cells. 93 1685 Google Scholar
[22]	Kumar A, Low T, Fung K H 2015 Nano Lett. 15 3172 Google Scholar
[23]	Zhou K, Cheng Q, Lu L 2020 Opt. Express 28 1647 Google Scholar
[24]	Zhou K, Cheng Q, Song J 2019 Opt. Lett. 44 3430 Google Scholar
[25]	Dai S, Ma Q, Andersen T, Mcleod A S, Fei Z, Liu M K, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Commun. 6 6963 Google Scholar
[26]	Debu D T, Ladani F T, French D 2019 npj 2D Mater. Appl. 3 1 Google Scholar
[27]	Álvarez‐Pérez G, Folland T G, Errea I 2020 Adv. Mater. 32 1908176 Google Scholar
[28]	Zhao B, Guizal B, Zhang Z M 2017 Phys. Rev. B 95 246437 Google Scholar
[29]	Purcell E M, Torrey H C, Pound R V 1946 Phys. Rev. 69 37 Google Scholar
[30]	赵永生, 宋俊峰, 韩伟华, 李雪梅, 杜国同, 高鼎三 1999 光学学报 19 452 Google Scholar Zhao Y S, Song J F, Han W H, Li X M, Du G T, Gao D S 1999 Acta Optics Sinica. 19 452 Google Scholar
[31]	Cortes C, Newman W, Molesky S 2012 J. Opt. 14 063001 Google Scholar
[32]	Krishnamoorthy H N, Jacob Z, Narimanov E 2012 Science 336 205 Google Scholar
[33]	Zhou K, Zhong X, Cheng Q, Wu X 2022 Opt. Mater. 131 112623 Google Scholar

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Active tuning hBN phonon polaritons and spontaneous emission rates based on VO₂ and graphene

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Corresponding author: Zhou Kun, zhoukun0209@163.com ; Wu Xiao-Hu, xiaohu.wu@iat.cn

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Active tuning hBN phonon polaritons and spontaneous emission rates based on VO2 and graphene

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Corresponding author: Zhou Kun, zhoukun0209@163.com ; Wu Xiao-Hu, xiaohu.wu@iat.cn

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Active tuning hBN phonon polaritons and spontaneous emission rates based on VO₂ and graphene