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Dirac plasmons and beyond: the past, present, and future of plasmonics in 3D topological insulators

Published online by Cambridge University Press:  28 August 2018

T. Ginley ,
Y. Wang ,
Z. Wang  and
S. Law
T. Ginley
Affiliation:
Department of Materials Science and Engineering, University of Delaware, Newark DE 19716, USA
Y. Wang
Affiliation:
Department of Materials Science and Engineering, University of Delaware, Newark DE 19716, USA
Z. Wang
Affiliation:
Department of Materials Science and Engineering, University of Delaware, Newark DE 19716, USA
S. Law*
Affiliation:
Department of Materials Science and Engineering, University of Delaware, Newark DE 19716, USA
*
Address all correspondence to S. Law at [email protected]
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Abstract

We review progress studying unique plasmonics in topological insulators (TIs). First, we describe exfoliation and deposition synthesis approaches. TI materials have substantially improved: it is now possible to grow samples with few trivial electrons and controllable doping. We then describe the theory behind the unique behavior of the coupled, 2D Dirac plasmons. While reviewing experimental efforts, we note that Dirac plasmons have been conclusively demonstrated in TIs and they show remarkable properties including long lifetimes, large mode indices, and huge modulation depths. Finally, we describe the opportunities that are present now that high-quality materials can be obtained, including spin and nanoparticle plasmons.

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Prospective Articles
Information
MRS Communications , Volume 8 , Issue 3 , September 2018 , pp. 782 - 794
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Copyright © Materials Research Society 2018 

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References

1.Chen, Y.L., Analytis, J.G., Chu, J.-H., Liu, Z.K., Mo, S.-K., Qi, X.L., Zhang, H.J., Lu, D.H., Dai, X., Fang, Z., Zhang, S.C., Fisher, I.R., Hussain, Z., and Shen, Z.-X.: Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009).Google Scholar
2.Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y.S., Cava, R.J., and Hasan, M.Z.: Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398–402 (2009).Google Scholar
3.Bansil, A., Lin, H., and Das, T.: Colloquium: topological band theory. Rev. Mod. Phys. 88, 21004 (2016).Google Scholar
4.Pesin, D. and MacDonald, A.H.: Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409–416 (2012).Google Scholar
5.Tumelero, M.A., Faccio, R., and Pasa, A.A.: The role of interstitial native defects in the topological insulator Bi2Se3. J. Phys. Condens. Matter 28, 425801 (2016).Google Scholar
6.Ando, Y.: Topological insulator materials. J. Phys. Soc. Jpn. 82, 102001 (2013).Google Scholar
7.Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., and Firsov, A.A.: Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).Google Scholar
8.Novoselov, K.S., Jiang, D., Schedin, F., Booth, T.J., Khotkevich, V.V., Morozov, S.V., and Geim, A.K.: Two-dimensional atomic crystals. Proc. Natl. Acad. Sci. 102, 10451–10453 (2005).Google Scholar
9.Teweldebrhan, D., Goyal, V., and Balandin, A.A.: Exfoliation and characterization of bismuth telluride atomic quintuples and quasi-two-dimensional crystals. Nano Lett. 10, 1209–1218 (2010).Google Scholar
10.Hossain, M.Z., Rumyantsev, S.L., Shahil, K.M.F., Teweldebrhan, D., Shur, M., and Balandin, A.A.: Low-frequency current fluctuations in “graphene-like” exfoliated thin-films of bismuth selenide topological insulators. ACS Nano 5, 2657–2663 (2011).Google Scholar
11.Teweldebrhan, D., Goyal, V., Rahman, M., and Balandin, A.A.: Atomically-thin crystalline films and ribbons of bismuth telluride. Appl. Phys. Lett. 96, 053107 (2010).Google Scholar
12.Shahil, K.M.F., Hossain, M.Z., Goyal, V., and Balandin, A.A.: Micro-Raman spectroscopy of mechanically exfoliated few-quintuple layers of Bi2Te3, Bi2Se3, and Sb2Te3 materials. J. Appl. Phys. 111, 054305 (2012).Google Scholar
13.Sun, L., Lin, Z., Peng, J., Weng, J., Huang, Y., and Luo, Z.: Preparation of few-layer bismuth selenide by liquid-phase-exfoliation and its optical absorption properties. Sci. Rep. 4, 4794 (2014).Google Scholar
14.Ren, L., Qi, X., Liu, Y., Hao, G., Huang, Z., Zou, X., Yang, L., Li, J., and Zhong, J.: Large-scale production of ultrathin topological insulator bismuth telluride nanosheets by a hydrothermal intercalation and exfoliation route. J. Mater. Chem. 22, 4921 (2012).Google Scholar
15.Sokolikova, M.S., Sherrell, P.C., Palczynski, P., Bemmer, V.L., and Mattevi, C.: Room-temperature growth of colloidal Bi2Te3 nanosheets. Chem. Commun. 53, 8026 (2017).Google Scholar
16.Kong, D., Dang, W., Cha, J.J., Li, H., Meister, S., Peng, H., Liu, Z., and Cui, Y.: Few-layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential. Nano Lett. 10, 2245–2250 (2010).Google Scholar
17.Cao, H., Venkatasubramanian, R., Liu, C., Pierce, J., Yang, H., Zahid Hasan, M., Wu, Y., and Chen, Y.P.: Topological insulator Bi2Te3 films synthesized by metal organic chemical vapor deposition. Appl. Phys. Lett. 101, 162104 (2012).Google Scholar
18.Guo, X., Xu, Z.J., Liu, H.J.C., Zhao, B., Dai, X.Q., He, H.T., Wang, J.N., Liu, H.J.C., Ho, W.K., and Xie, M.H.: Single domain Bi2Se3 films grown on InP(111)A by molecular-beam epitaxy. Appl. Phys. Lett. 102, 151604 (2013).Google Scholar
19.Ginley, T., Wang, Y., and Law, S.: Topological insulator film growth by molecular beam epitaxy: a review. Crystals 6, 154 (2016).Google Scholar
20.Koirala, N., Brahlek, M., Salehi, M., Wu, L., Dai, J., Waugh, J., Nummy, T., Han, M.G., Moon, J., Zhu, Y., Dessau, D., Wu, W., Armitage, N.P., and Oh, S.: Record surface state mobility and quantum hall effect in topological insulator thin films via interface engineering. Nano Lett. 15, 8245–8249 (2015).Google Scholar
21.Wang, Y., Ginley, T.P., and Law, S.: Growth of high-quality Bi2Se3 topological insulators using (Bi1−xInx)Se3 buffer layers. J. Vac. Sci. Technol., B 36, 02D101 (2018).Google Scholar
22.Ginley, T.P. and Law, S.: Growth of Bi2Se3 topological insulator films using a selenium cracker source. J. Vac. Sci. Technol., B 34, 02L105 (2016).Google Scholar
23.Li, H.D., Wang, Z.Y., Kan, X., Guo, X., He, H.T., Wang, Z.Y., Wang, J.N., Wong, T.L., Wang, N., and Xie, M.H.: The van der Waals epitaxy of Bi2Se3 on the vicinal Si(111) surface: an approach for preparing high-quality thin films of a topological insulator. New J. Phys. 12, 103038 (2010).Google Scholar
24.Liu, Y., Weinert, M., and Li, L.: Spiral growth without dislocations: molecular beam epitaxy of the topological insulator Bi2Se3 on epitaxial graphene/SiC(0001). Phys. Rev. Lett. 108, 115501 (2012).Google Scholar
25.Hor, Y.S., Checkelsky, J.G., Qu, D., Ong, N.P., and Cava, R.J.: Superconductivity and non-metallicity induced by doping the topological insulators Bi2Se3 and Bi2Te3. J. Phys. Chem. Solids 72, 572–576 (2011).Google Scholar
26.Choi, Y.H., Jo, N.H., Lee, K.J., Lee, H.W., Jo, Y.H., Kajino, J., Takabatake, T., Ko, K.T., Park, J.H., and Jung, M.H.: Simple tuning of carrier type in topological insulator Bi2Se3 by Mn doping. Appl. Phys. Lett. 101, 152103 (2012).Google Scholar
27.Hor, Y.S., Williams, A.J., Checkelsky, J.G., Roushan, P., Seo, J., Xu, Q., Zandbergen, H.W., Yazdani, A., Ong, N.P., and Cava, R.J.: Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator. Phys. Rev. Lett. 104, 057001 (2010).Google Scholar
28.Liu, Z., Yao, X., Shao, J., Zuo, M., Pi, L., Tan, S., Zhang, C., and Zhang, Y.: Superconductivity with topological surface state in SrxBi2Se3. J. Am. Chem. Soc. 137, 10512–10515 (2015).Google Scholar
29.Chang, C.-Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., Ou, Y., Wei, P., Wang, L.-L., Ji, Z.-Q., Feng, Y., Ji, S., Chen, X., Jia, J., Dai, X., Fang, Z., Zhang, S.-C., He, K., Wang, Y., Lu, L., Ma, X.-C., and Xue, Q.-K.: Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).Google Scholar
30.Chang, C.Z., Zhao, W., Kim, D.Y., Zhang, H., Assaf, B.A., Heiman, D., Zhang, S.C., Liu, C., Chan, M.H.W., and Moodera, J.S.: High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015).Google Scholar
31.Zhao, Y., Liu, H., Guo, X., Jiang, Y., Sun, Y., Wang, H., Wang, Y., Li, H.D., Xie, M.H., Xie, X.C., and Wang, J.: Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices. Nano Lett. 14, 5244–5249 (2014).Google Scholar
32.Wang, Z.Y., Guo, X., Li, H.D., Wong, T.L., Wang, N., and Xie, M.H.: Superlattices of Bi2Se3/In2Se3: Growth characteristics and structural properties. Appl. Phys. Lett. 99, 23112 (2011).Google Scholar
33.Chang, C.Z., Tang, P., Feng, X., Li, K., Ma, X.C., Duan, W., He, K., and Xue, Q.K.: Band engineering of Dirac surface states in topological-insulator-based van der Waals heterostructures. Phys. Rev. Lett. 115, 136801 (2015).Google Scholar
34.Chen, Z., Garcia, T.A., Hernandez-Mainet, L.C., Zhao, L., Deng, H., Krusin-Elbaum, L., and Tamargo, M.C.: Molecular beam epitaxial growth and characterization of Bi2Se3/II–VI semiconductor heterostructures. Appl. Phys. Lett. 105, 242105 (2014).Google Scholar
35.Stauber, T. and Gómez-Santos, G.: Plasmons in layered structures including graphene. New J. Phys. 14, 105018 (2012).Google Scholar
36.Stauber, T., Gómez-Santos, G., and Brey, L.: Spin-charge separation of plasmonic excitations in thin topological insulators. Phys. Rev. B 88, 205427 (2013).Google Scholar
37.Poyli, M.A., Hrtoň, M., Nechaev, I.A., Nikitin, A.Y., Echenique, P.M., Silkin, V.M., Aizpurua, J., and Esteban, R.: Controlling surface charge and spin density oscillations by Dirac plasmon interaction in thin topological insulators. Phys. Rev. B 97, 115420 (2018).Google Scholar
38.Stauber, T., Gómez-Santos, G., and Brey, L.: Plasmonics in topological insulators: spin-charge separation, the influence of the inversion layer, and phonon-plasmon coupling. ACS Photonics 4, 2978–2988 (2017).Google Scholar
39.Stauber, T.: Plasmonics in Dirac systems: from graphene to topological insulators. J. Phys. Condens. Matter 26, 123201 (2014).Google Scholar
40.Deshko, Y., Krusin-Elbaum, L., Menon, V., Khanikaev, A., and Trevino, J.: Surface plasmon polaritons in topological insulator nano-films and superlattices. Opt. Express 24, 7398–7410 (2016).Google Scholar
41.Wu, L., Tse, W.K., Brahlek, M., Morris, C.M., Aguilar, R.V., Koirala, N., Oh, S., and Armitage, N.P.: High-resolution Faraday rotation and electron-phonon coupling in surface states of the Bulk-insulating topological insulator Cu0.02Bi2Se3. Phys. Rev. Lett. 115, 217602 (2015).Google Scholar
42.Politano, A., Silkin, V.M., Nechaev, I.A., Vitiello, M.S., Viti, L., Aliev, Z.S., Babanly, M.B., Chiarello, G., Echenique, P.M., and Chulkov, E.V.: Interplay of surface and Dirac plasmons in topological insulators: the case of Bi2Se3. Phys. Rev. Lett. 115, 216802 (2015).Google Scholar
43.Sim, S., Jang, H., Koirala, N., Brahlek, M., Moon, J., Sung, J.H., Park, J., Cha, S., Oh, S., Jo, M.-H., Ahn, J.-H., and Choi, H.: Ultra-high modulation depth exceeding 2, 400% in optically controlled topological surface plasmons. Nat. Commun. 6, 8814 (2015).Google Scholar
44.Ginley, T.P. and Law, S.: Coupled Dirac plasmons in topological insulators. Adv. Opt. Mater. 6, 1800113 (2018).Google Scholar
45.Di Pietro, P., Ortolani, M., Limaj, O., Di Gaspare, A., Giliberti, V., Giorgianni, F., Brahlek, M., Bansal, N., Koirala, N., Oh, S., Calvani, P., and Lupi, S.: Observation of Dirac plasmons in a topological insulator. Nat. Nanotechnol. 8, 556–560 (2013).Google Scholar
46.Grigorenko, A.N., Polini, M., and Novoselov, K.S.: Graphene plasmonics. Nat. Photonics 6, 749–758 (2012).Google Scholar
47.Brar, V.W., Jang, M.S., Sherrott, M., Lopez, J.J., and Atwater, H.A.: Highly confined tunable mid-infrared plasmonics in graphene nanoresonators. Nano Lett. 13, 2541–2547 (2013).Google Scholar
48.Ju, L., Geng, B., Horng, J., Girit, C., Martin, M., Hao, Z., Bechtel, H.A., Liang, X., Zettl, A., Shen, Y.R., and Wang, F.: Graphene plasmonics for tunable terahertz metamaterials. Nat. Nanotechnol. 6, 630–634 (2011).Google Scholar
49.Fei, Z., Gregory, O., Andreev, O., Bao, O.W., Zhang, L.M., Mcleod, A.S., Wang, C., Stewart, M.K., Zhao, Z., Dominguez, G., Thiemens, M., Fogler, M.M., Tauber, M.J., Castro-Neto, A.H., Lau, C.N., Keilmann, F., and Basov, D.N.: Infrared nanoscopy of Dirac plasmons at the graphene-SiO2 interface. Nano Lett. 11, 4701–4705 (2011).Google Scholar
50.Schiefele, J., Pedrós, J., Sols, F., Calle, F., and Guinea, F.: Coupling light into graphene plasmons through surface acoustic waves. Phys. Rev. Lett. 111, 237405 (2013).Google Scholar
51.Zhan, T.R., Zhao, F.Y., Hu, X.H., Liu, X.H., and Zi, J.: Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies. Phys. Rev. B 86, 165416 (2012).Google Scholar
52.Vicarelli, L., Vitiello, M.S., Coquillat, D., Lombardo, A., Ferrari, A.C., Knap, W., Polini, M., Pellegrini, V., and Tredicucci, A.: Graphene field-effect transistors as room-temperature terahertz detectors. Nat. Mater. 11, 865–871 (2012).Google Scholar
53.Iorsh, I.V., Mukhin, I.S., Shadrivov, I.V., Belov, P.A., and Kivshar, Y.S.: Hyperbolic metamaterials based on multilayer graphene structures. Phys. Rev. B 87, 75416 (2013).Google Scholar
54.Zeng, S., Baillargeat, D., Ho, H.-P., and Yong, K.-T.: Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications. Chem. Soc. Rev. 43, 3426 (2014).Google Scholar
55.Liu, Y., Cheng, R., Liao, L., Zhou, H., Bai, J., Liu, G., Liu, L., Huang, Y., and Duan, X.: Plasmon resonance enhanced multicolour photodetection by graphene. Nat. Commun. 2, 579 (2011).Google Scholar
56.Giannini, V., Francescato, Y., Amrania, H., Phillips, C.C., and Maier, S.A.: Fano resonances in nanoscale plasmonic systems: a parameter-free modeling approach. Nano Lett. 11, 2835–2840 (2011).Google Scholar
57.Autore, M., Engelkamp, H., D'Apuzzo, F., Di Gaspare, A., Di Pietro, P., Lo Vecchio, I., Brahlek, M., Koirala, N., Oh, S., and Lupi, S.: Observation of magnetoplasmons in Bi2Se3 topological insulator. ACS Photonics 2, 1231–1235 (2015).Google Scholar
58.Ou, J.-Y., So, J.-K., Adamo, G., Sulaev, A., Wang, L., and Zheludev, N.I.: Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2. Nat. Commun. 5, 5139 (2014).Google Scholar
59.In, C., Sim, S., Kim, B., Bae, H., Jung, H., Jang, W., Son, M., Moon, J., Salehi, M., Seo, S.Y., Soon, A., Ham, M.H., Lee, H., Oh, S., Kim, D., Jo, M.H., and Choi, H.: Control over electron-phonon interaction by Dirac plasmon engineering in the Bi2Se3 topological insulator. Nano Lett. 18, 734–739 (2018).Google Scholar
60.Aguilar, R.V., Stier, A. V., Liu, W., Bilbro, L.S., George, D.K., Bansal, N., Wu, L., Cerne, J., Markelz, A.G., Oh, S., and Armitage, N.P.: Terahertz response and colossal kerr rotation from the surface states of the topological insulator Bi2Se3. Phys. Rev. Lett.. 108, 087403 (2012).Google Scholar
61.Autore, M., D'Apuzzo, F., Di Gaspare, A., Giliberti, V., Limaj, O., Roy, P., Brahlek, M., Koirala, N., Oh, S., García de Abajo, F.J., and Lupi, S.: Plasmon-phonon interactions in topological insulator microrings. Adv. Opt. Mater. 3, 1257–1263 (2015).Google Scholar
62.Egerton, R.F.: Electron energy-loss spectroscopy in the TEM. Rep. Prog. Phys. 72, 016502 (2009).Google Scholar
63.Liou, S.C., Chu, M.-W., Sankar, R., Huang, F.-T., Shu, G.J., Chou, F.C., and Chen, C.H.: Plasmons dispersion and nonvertical interband transitions in single crystal Bi2Se3 investigated by electron energy-loss spectroscopy. Phys. Rev. B 87, 85126 (2013).Google Scholar
64.Nechaev, I.A., Aguilera, I., De Renzi, V., di Bona, A., Lodi Rizzini, A., Mio, A.M., Nicotra, G., Politano, A., Scalese, S., Aliev, Z.S., Babanly, M.B., Friedrich, C., Blügel, S., and Chulkov, E.V.: Quasiparticle spectrum and plasmonic excitations in the topological insulator Sb2Te3. Phys. Rev. B 91, 245123 (2015).Google Scholar
65.Kogar, A., Vig, S., Thaler, A., Wong, M.H., Xiao, Y., Reig-i-Plessis, D., Cho, G.Y., Valla, T., Pan, Z., Schneeloch, J., Zhong, R., Gu, G.D., Hughes, T.L., MacDougall, G.J., Chiang, T.-C., and Abbamonte, P.: Surface collective modes in the topological insulators Bi2Se3 and Bi0.5Sb1.5Te3−xSex. Phys. Rev. Lett. 115, 257402 (2015).Google Scholar
66.Jia, X., Zhang, S., Sankar, R., Chou, F.-C., Wang, W., Kempa, K., Plummer, E.W., Zhang, J., Zhu, X., and Guo, J.: Anomalous acoustic plasmon mode from topologically protected states. Phys. Rev. Lett. 119, 136805 (2017).Google Scholar
67.Glinka, Y.D., Babakiray, S., and Lederman, D.: Plasmon-enhanced electron-phonon coupling in Dirac surface states of the thin-film topological insulator Bi2Se3. J. Appl. Phys. 118, 135713 (2015).Google Scholar
68.Glinka, Y.D., Babakiray, S., Johnson, T.A., Holcomb, M.B., Lederman, D., and Merlin, R.: Nonlinear optical observation of coherent acoustic Dirac plasmons in thin-film topological insulators. Nat. Commun. 7, 13054 (2016).Google Scholar
69.Checkelsky, J.G., Hor, Y.S., Cava, R.J., and Ong, N.P.: Bulk band gap and surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3. Phys. Rev. Lett. 106, 196801 (2011).Google Scholar
70.King, P.D.C., Hatch, R.C., Bianchi, M., Ovsyannikov, R., Lupulescu, C., Landolt, G., Slomski, B., Dil, J.H., Guan, D., Mi, J.L., Rienks, E.D.L., Fink, J., Lindblad, A., Svensson, S., Bao, S., Balakrishnan, G., Iversen, B.B., Osterwalder, J., Eberhardt, W., Baumberger, F., and Hofmann, P.: Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3. Phys. Rev. Lett. 107, 096802 (2011).Google Scholar
71.Xiong, J., Khoo, Y., Jia, S., Cava, R.J., and Ong, N.P.: Tuning the quantum oscillations of surface Dirac electrons in the topological insulator Bi2Te2Se by liquid gating. Phys. Rev. B 88, 035128 (2013).Google Scholar
72.Fei, Z., Rodin, A.S., Andreev, G.O., Bao, W., McLeod, A.S., Wagner, M., Zhang, L.M., Zhao, Z., Thiemens, M., Dominguez, G., Fogler, M.M., Castro Neto, A.H., Lau, C.N., Keilmann, F., and Basov, D.N.: Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).Google Scholar
73.Gao, W., Shi, G., Jin, Z., Shu, J., Zhang, Q., Vajtai, R., Ajayan, P.M., Kono, J., and Xu, Q.: Excitation and active control of propagating surface plasmon polaritons in graphene. Nano Lett. 13, 3698–3702 (2013).Google Scholar
74.Chen, J., Badioli, M., Alonso-González, P., Thongrattanasiri, S., Huth, F., Osmond, J., Spasenovi, M., Centeno, A., Pesquera, A., Godignon, P., Elorza, A.Z., Camara, N., Javier García De Abajo, F., Hillenbrand, R., and Koppens, F.H.L.: Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).Google Scholar
75.Ullrich, C.A. and Flatte, M.E.: Intersubband spin-density excitations in quantum wells with Rashba spin splitting. Phys. Rev. B 66, 205305 (2011).Google Scholar
76.Magarill, L.I., Chaplik, A.V., and Éntin, M.V.: Spin response of 2D electrons to a lateral electric field. Semiconductors 35, 1081–1087 (2001).Google Scholar
77.Magarill, L.I., Chaplik, A.V., and Éntin, M.V.: Spin-plasmon oscillations of the two-dimensional electron gas. J. Exp. Theor. Phys. 92, 153–158 (2001).Google Scholar
78.Ullrich, C.A. and Flatte, M.E.: Anisotropic splitting of intersubband spin plasmons in quantum wells with bulk and structural inversion asymmetry. Phys. Rev. B 68, 235310 (2003).Google Scholar
79.Raghu, S., Chung, S.B., Qi, X., and Zhang, S.: Collective modes of a helical liquid. Phys. Rev. Lett. 104, 116401 (2010).Google Scholar
80.Efimkin, D.K., Lozovik, Y.E., and Sokolik, A.A.: Collective excitations on a surface of topological insulator. Nanoscale Res. Lett. 7, 163 (2012).Google Scholar
81.Stauber, T., Gómez-Santos, G., and Brey, L.: Plasmonics in topological insulators: spin-charge separation, the influence of the inversion layer, and phonon–plasmon coupling. ACS Photonics 4, 2978–2988 (2017).Google Scholar
82.Efimkin, D.K., Lozovik, Y.E., and Sokolik, A.A.: Spin-plasmons in topological insulator. J. Magn. Magn. Mater. 324, 3610–3612 (2012).Google Scholar
83.Appelbaum, I., Drew, H.D., Fuhrer, M.S., Appelbaum, I., Drew, H.D., and Fuhrer, M.S.: Proposal for a topological plasmon spin rectifier. Appl. Phys. Lett. 98, 23103 (2011).Google Scholar
84.Kondo, T., Nakashima, Y., Ota, Y., Ishida, Y., Malaeb, W., Okazaki, K., Shin, S., Kriener, M., Sasaki, S., Segawa, K., and Ando, Y.: Anomalous dressing of Dirac fermions in the topological surface state of Bi2Se3, Bi2Te3, and Cu-doped Bi2Se3. Phys. Rev. Lett. 110, 217601 (2013).Google Scholar
85.Cameron, A., Riblet, P., and Miller, A.: Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors. Phys. Rev. Lett. 76, 4793–4796 (1996).Google Scholar
86.Koralek, J.D., Weber, C.P., Orenstein, J., Bernevig, B.A., Zhang, S., Mack, S., and Awschalom, D.D.: Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009).Google Scholar
87.Weng, M.Q., Wu, M.W., and Cui, H.L.: Spin relaxation in n-type GaAs quantum wells with transient spin grating. J. Appl. Phys. 103, 063714 (2008).Google Scholar
88.Lai, Y.-P., Lin, I.-T., Wu, K.-H., and Liu, J.-M.: Plasmonics in topological insulators. Nanomater. Nanotechnol. 4, 13 (2014).Google Scholar
89.McIver, J.W., Hsieh, D., Steinberg, H., Jarillo-Herrero, P., and Gedik, N.: Control over topological insulator photocurrents with light polarization. Nat. Nanotechnol. 7, 96–100 (2012).Google Scholar
90.Lu, H.Z., Shan, W.Y., Yao, W., Niu, Q., and Shen, S.Q.: Massive Dirac fermions and spin physics in an ultrathin film of topological insulator. Phys. Rev. B 81, 115407 (2010).Google Scholar
91.Hosur, P.: Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response. Phys. Rev. B 83, 035309 (2011).Google Scholar
92.Imura, K.-I., Yoshimura, Y., Takane, Y., and Fukui, T.: Spherical topological insulator. Phys. Rev. B 86, 235119 (2012).Google Scholar
93.Durst, A.C.: Disorder-induced density of states on the surface of a spherical topological insulator. Phys. Rev. B 93, 245424 (2016).Google Scholar
94.Kundu, A., Zazunov, A., Yeyati, A.L., Martin, T., and Egger, R.: Energy spectrum and broken spin-surface locking in topological insulator quantum dots. Phys. Rev. B 83, 125429 (2011).Google Scholar
95.Siroki, G., Haynes, P.D., Lee, D.K.K., and Giannini, V.: Protection of surface states in topological nanoparticles. Phys. Rev. Mater. 1, 24201 (2017).Google Scholar
96.Siroki, G., Lee, D.K.K., Haynes, P.D., and Giannini, V.: Single-electron induced surface plasmons on a topological nanoparticle. Nat. Commun. 7, 12375 (2016).Google Scholar
97.Bonaccorso, F., Lombardo, A., Hasan, T., Sun, Z., Colombo, L., and Ferrari, A.C.: Production and processing of graphene and 2d crystals. Mater. Today 15, 564–589 (2012).Google Scholar
98.Nicolosi, V., Chhowalla, M., Kanatzidis, M.G., Strano, M.S., and Coleman, J.N.: Liquid exfoliation of layered materials. Science 340, 1226419–1226419 (2013).Google Scholar