首页 » 文章 » 文章详细信息
Advanced Science Volume 6 ,Issue 7 ,2019-02-06
Anderson Localized Plasmon in Graphene with Random Tensile‐Strain Distribution
Communications
Jiahua Duan 1 , 2 , 3 Sanshui Xiao 3 Jianing Chen 1 , 2 , 4 , 5
Show affiliations
DOI:10.1002/advs.201801974
Received 2018-11-02,
PDF
摘要

Abstract Anderson localization, the unusual phenomenon discovered in a disordered medium, describes the phase transition from the extended to localized state. Owing to the interference in multiple elastic scattering, this concept is firstly demonstrated in an electron system, then to photon and matter waves. However, Anderson localization has not been observed for polaritonic waves with its unique features of strong field confinement and tunability. Here, Anderson localization of plasmon polaritons is experimentally reported in a flat graphene sheet simultaneously with homogenous charge carrier and random tensile‐strain distributions. By selectively choosing different disordered levels, the transition from quasi‐expansion to weak localization, and finally Anderson localization are observed. Relying on the infrared nanoimaging technique, the spatial dependence of the localization is further studied, and finally the transition window from weak to Anderson localization of graphene plasmon polaritons is identified with the aid of the scaling theory. The experimental approach paves a new way to study Anderson localization in other polaritonic systems such as phonon, exciton, magnon polaritons, etc.

关键词

strong localization;strains;graphene plasmons;disorder

授权许可

© 2019 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

图表

a,b) Schematic diagrams of graphene plasmon in ordered and disordered graphene. The different colors in (b) represent the carbon atoms with different strains, indicating the disorder caused by randomly distributed strains. c–e) Raman maps of tensile‐strain distribution in ordered, weak disordered, and strong disordered graphene systems. f–h) Spatial distribution of charge carrier shows similarly homogeneous in ordered, weak disordered, and strong disordered systems. Meanwhile, the doping levels in three conditions are similar, as ≈5 × 1012 cm−3. Graphene edge is marked with the red dashed line.

a–c) The near‐field images of three transport patterns (at the incident frequency of ω0 = 901 cm−1) including quasi‐expansion, weak localization, and Anderson localization. The blue‐dashed lines guide for the plasmonic fringes. d–f) The average intensity along the X‐direction, see the black dots, for these three conditions in linear coordinates. In the right panels of (e) and (f), we represent the results in semi‐log coordinates. The blue lines in (e) are obtained by Gaussian fitting to the intensity distribution. The red lines in the left panel of (f) are associated with exponential fits to the wings, and the right panel for linear fitting. Scale bars, 300 nm.

a–c) The average intensity along the Y‐direction for quasi‐expanded, weak localized and Anderson localized status. The red arrows denote the wavelength of graphene plasmons. d) The dispersion relation of graphene plasmon for these three states. The scattered points show the extracted experimental values and the background color shows the imaginary part of the Fresnel reflection coefficient, indicating that the Anderson transition has little influence on dispersion of graphene plasmon. e) Extracted field confinement factor. The X‐confinement factor increases during Anderson transition while keeping same for the Y‐confinement.

a) The localization length as a function of incident frequency for the weak and Anderson localized states. The error bars are statistical standard deviations with multiple measurements. b) Localization length versus kpl* for weak and strong localization regions. The kp and l* represent the wavevector and mean free path of graphene plasmons, respectively. The l* is calculated by the scaling theory (inset in Figure 4b).

通讯作者

1. Sanshui Xiao.DTU Fotonik, Department of Photonics Engineering and Center for Nanostructured Graphene, Technical University of Denmark, DK2800, Kgs. Lyngby, Denmark.saxi@fotonik.dtu.dk
2. Jianing Chen.Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China;School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China;Beijing National Laboratory for Condensed Matter Physics, 100190, Beijing, China;Songshan Lake Materials Laboratory, Dongguan, 523808, Guangdong, China.saxi@fotonik.dtu.dk

推荐引用方式

Jiahua Duan,Sanshui Xiao,Jianing Chen. Anderson Localized Plasmon in Graphene with Random Tensile‐Strain Distribution. Advanced Science ,Vol.6, Issue 7(2019)

您觉得这篇文章对您有帮助吗?
分享和收藏
0

是否收藏?

参考文献
[1] T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature 2007, 446, 52.
[2] Y. V. Bludov, A. Ferreira, N. M. R. Peres, M. I. Vasilevskiy, Int. J. Mod. Phys. B 2013, 27, 1341001.
[3] J. Liao, Y. Ou, X. Feng, S. Yang, C. Lin, W. Yang, K. Wu, K. He, X. Ma, Q. K. Xue, Y. Li, Phys. Rev. Lett. 2015, 114, 216601.
[4] D. N. Basov, M. M. Fogler, F. J. G. De Abajo, Science 2016, 354, aag1992.
[5] S. Dai, Z. Fei, Q. Ma, A. Rodin, M. Wagner, A. McLeod, M. Liu, W. Gannett, W. Regan, K. Watanabe, Science 2014, 343, 1125.
[6] M. Mascheck, S. Schmidt, M. Silies, T. Yatsui, K. Kitamura, M. Ohtsu, D. Leipold, E. Runge, C. Lienau, Nat. Photonics 2012, 6, 293.
[7] J. Duan, R. Chen, J. Li, K. Jin, Z. Sun, J. Chen, Adv. Mater. 2017, 29, 1702494.
[8] P. Hsieh, C. K. Chung, J. F. Mcmillan, M. Tsai, M. Lu, N. C. Panoiu, C. W. Wong, Nat. Phys. 2015, 11, 268.
[9] J. Duan, R. Chen, J. Chen, Chin. Phys. B 2017, 26, 117802.
[10] J. E. Lee, G. Ahn, J. Shim, Y. S. Lee, S. Ryu, Nat. Commun. 2012, 3, 1024.
[11] A. J. Chaves, N. M. R. Peres, F. A. Pinheiro, Phys. Rev. B 2015, 92, 195425.
[12] M. Leonetti, S. Karbasi, A. Mafi, C. Conti, Nat. Commun. 2014, 5, 4534.
[13] J. Chen, M. Badioli, P. Alonso‐González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, Nature 2012, 487, 77.
[14] Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. Mcleod, M. Wagner, L. Zhang, Z. Zhao, M. H. Thiemens, G. Dominguez, Nature 2012, 487, 82.
[15] T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin‐Moreno, F. Koppens, Nat. Mater. 2017, 16, 182.
[16] M. Segev, Y. Silberberg, D. N. Christodoulides, Nat. Photonics 2013, 7, 197.
[17] T. Sperling, W. Buhrer, C. M. Aegerter, G. Maret, Nat. Photonics 2013, 7, 48.
[18] P. W. Anderson, Phys. Rev. 1958, 109, 1492.
[19] D. S. Wiersma, Nat. Photonics 2013, 7, 188.
[20] M. Aeschlimann, T. Brixner, D. Differt, U. Heinzmann, M. Hensen, C. Kramer, F. Lükermann, P. Melchior, W. Pfeiffer, M. Piecuch, Nat. Photonics 2015, 9, 663.
[21] S. Xiao, X. Zhu, B. Li, N. A. Mortensen, Front. Phys. 2016, 11, 117801.
[22] S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, Phys. Rev. Lett. 1999, 82, 4520.
[23] A. Ioffe, A. Regel, Prog. Semicond. 1960, 4, 237.
[24] D. S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Nature 1997, 390, 671.
[25] A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonsogonzalez, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, Nat. Mater. 2015, 14, 421.
[26] A. K. Geim, K. S. Novoselov, Nat. Mater. 2007, 6, 183.
[27] E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan, Phys. Rev. Lett. 1979, 42, 673.
[28] P. A. D. Goncalves, E. J. C. Dias, S. Xiao, M. Vasilevskiy, N. A. Mortensen, N. M. R. Peres, ACS Photonics 2016, 3, 2176.
[29] A. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov, A. K. Geim, Rev. Mod. Phys. 2009, 81, 109.
[30] L. Novotny, B. Hecht, Physics Today 2007, 60, 62.
[31] G. Ni, H. Wang, J. Wu, Z. Fei, M. Goldflam, F. Keilmann, B. Özyilmaz, A. C. Neto, X. Xie, M. Fogler, Nat. Mater. 2015, 14, 1217.
[32] Z. Shi, X. Hong, H. A. Bechtel, B. Zeng, M. C. Martin, K. Watanabe, T. Taniguchi, Y.‐R. Shen, F. Wang, Nat. Photonics 2015, 9, 515.
[33] J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez‐Palencia, P. Bouyer, A. Aspect, Nature 2008, 453, 891.
[34] H. Zhang, J. Lu, W. Shi, Z. Wang, T. Zhang, M. Sun, Y. Zheng, Q. Chen, N. Wang, J.‐J. Lin, P. Sheng, Phys. Rev. Lett. 2013, 110, 066805.
[35] G. Roati, C. D'Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 2008, 453, 895.
[36] A. Lagendijk, B. v. Tiggelen, D. S. Wiersma, Physics Today 2009, 62, 24.