Topological insulator: Spintronics and quantum computations

doi:10.1007/s11467-019-0893-4

Front. Phys.

2019, Vol. 14

Issue (4) : 43401 https://doi.org/10.1007/s11467-019-0893-4

Review article

Topological insulator: Spintronics and quantum computations

Mengyun He^1,², Huimin Sun^1,², Qing Lin He^1,²(

)

¹. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
². CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

Download: PDF(2060 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Topological insulators are emergent states of quantum matter that are gapped in the bulk with timereversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

Keywords topological insulator Majorana fermion topological spintronics topological superconductor

Corresponding Author(s): Qing Lin He

Issue Date: 25 April 2019

Cite this article:

Mengyun He,Huimin Sun,Qing Lin He. Topological insulator: Spintronics and quantum computations[J]. Front. Phys. , 2019, 14(4): 43401.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-019-0893-4
https://academic.hep.com.cn/fop/EN/Y2019/V14/I4/43401

1	M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010) https://doi.org/10.1103/RevModPhys.82.3045
2	X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011) https://doi.org/10.1103/RevModPhys.83.1057
3	C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016) https://doi.org/10.1103/RevModPhys.88.035005
4	P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Topological surface states protected from backscattering by chiral spin texture, Nature 460(7259), 1106 (2009) https://doi.org/10.1038/nature08308
5	T. Zhang, P. Cheng, X. Chen, J. F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q. K. Xue, Experimental demonstration of topological surface states protected by time-reversal symmetry, Phys. Rev. Lett. 103(26), 266803 (2009) https://doi.org/10.1103/PhysRevLett.103.266803
6	K. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980) https://doi.org/10.1103/PhysRevLett.45.494
7	D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a twodimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982) https://doi.org/10.1103/PhysRevLett.49.405
8	J. E. Moore, The birth of topological insulators, Nature 464(7286), 194 (2010) https://doi.org/10.1038/nature08916
9	B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314(5806), 1757 (2006) https://doi.org/10.1126/science.1133734
10	M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Quantum spin hall insulator state in HgTe quantum wells, Science 318(5851), 766 (2007) https://doi.org/10.1126/science.1148047
11	D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature 452(7190), 970 (2008) https://doi.org/10.1038/nature06843
12	Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5(6), 398 (2009) https://doi.org/10.1038/nphys1274
13	C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95(14), 146802 (2005) https://doi.org/10.1103/PhysRevLett.95.146802
14	L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98(10), 106803 (2007) https://doi.org/10.1103/PhysRevLett.98.106803
15	H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5(6), 438 (2009) https://doi.org/10.1038/nphys1270
16	N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018) https://doi.org/10.1103/RevModPhys.90.015001
17	D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of unconventional quantum spin textures in topological insulators, Science 323(5916), 919 (2009) https://doi.org/10.1126/science.1167733
18	Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S. K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Experimental realization of a three-dimensional topological insulator, Bi2Te3, Science 325(5937), 178 (2009) https://doi.org/10.1126/science.1173034
19	D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A tunable topological insulator in the spin helical Dirac transport regime,Nature 460(7259), 1101 (2009) https://doi.org/10.1038/nature08234
20	A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A. Vaezi, A. Manchon, E. A. Kim, N. Samarth, and D. C. Ralph, Spin-transfer torque generated by a topological insulator, Nature 511(7510), 449 (2014) https://doi.org/10.1038/nature13534
21	Y. Fan and K. L. Wang, Spintronics based on topological insulators, Spin 06(02), 1640001 (2016) https://doi.org/10.1142/S2010324716400014
22	R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science 329(5987), 61 (2010) https://doi.org/10.1126/science.1187485
23	J. Wu, J. Liu, and X. J. Liu, Topological spin texture in a quantum anomalous Hall insulator, Phys. Rev. Lett. 113(13), 136403 (2014) https://doi.org/10.1103/PhysRevLett.113.136403
24	L. Fu and C. L. Kane, Superconducting proximity effect and majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100(9), 096407 (2008) https://doi.org/10.1103/PhysRevLett.100.096407
25	J. Wang and S. C. Zhang, Topological states of condensed matter, Nat. Mater. 16(11), 1062 (2017) https://doi.org/10.1038/nmat5012
26	B. Lian, X. Q. Sun, A. Vaezi, X. L. Qi, and S. C. Zhang, Topological quantum computation based on chiral Majorana fermions, Proc. Natl. Acad. Sci. USA 115(43), 10938 (2018) https://doi.org/10.1073/pnas.1810003115
27	P. Deorani, J. Son, K. Banerjee, N. Koirala, M. Brahlek, S. Oh, and H. Yang, Observation of inverse spin Hall effect in bismuth selenide,Phys. Rev. B 90(9), 094403 (2014) https://doi.org/10.1103/PhysRevB.90.094403
28	H. C. Han, Y. S. Chen, M. D. Davydova, P. N. Petrov, P. N. Skirdkov, J. G. Lin, J. C. Wu, J. C. A. Huang, K. A. Zvezdin, and A. K. Zvezdin, Spin pumping and probe in permalloy dots-topological insulator bilayers, Appl. Phys. Lett. 111(18), 182411 (2017) https://doi.org/10.1063/1.5004097
29	A. A. Baker, A. I. Figueroa, L. J. Collins-McIntyre, G. van der Laan, and T. Hesjedal, Spin pumping in ferromagnet-topological insulator-ferromagnet heterostructures, Sci. Rep. 5(1), 7907 (2015) https://doi.org/10.1038/srep07907
30	J. C. Rojas-Sánchez, S. Oyarzun, Y. Fu, A. Marty, C. Vergnaud, S. Gambarelli, L. Vila, M. Jamet, Y. Ohtsubo, A. Taleb-Ibrahimi, P. Le Fevre, F. Bertran, N. Reyren, J. M. George, and A. Fert, Spin to charge conversion at room temperature by spin pumping into a new type of topological insulator: α-Sn films, Phys. Rev. Lett. 116(9), 096602 (2016) https://doi.org/10.1103/PhysRevLett.116.096602
31	C. N. Wu, Y. H. Lin, Y. T. Fanchiang, H. Y. Hung, H. Y. Lin, P. H. Lin, J. G. Lin, S. F. Lee, M. Hong, J. Kwo, Strongly enhanced spin current in topological insulator/ferromagnetic metal heterostructures by spin pumping, J. Appl. Phys. 117(17), 17D148(2015) https://doi.org/10.1063/1.4918631
32	Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L. T. Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R. N. Schwartz, Y. Tserkovnyak, and K. L. Wang, Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure, Nat. Mater. 13(7), 699 (2014) https://doi.org/10.1038/nmat3973
33	Y. Fan, X. Kou, P. Upadhyaya, Q. Shao, L. Pan,M. Lang, X. Che, J. Tang, M. Montazeri, K. Murata, L. T. Chang, M. Akyol, G. Yu, T. Nie, K. L. Wong, J. Liu, Y. Wang, Y. Tserkovnyak, and K. L. Wang, Electric-field control of spin–orbit torque in a magnetically doped topological insulator, Nat. Nanotechnol. 11(4), 352 (2016) https://doi.org/10.1038/nnano.2015.294
34	Z. Jiang, C. Z. Chang, M. R. Masir, C. Tang, Y. Xu, J. S. Moodera, A. H. MacDonald, and J. Shi, Enhanced spin Seebeck effect signal due to spin-momentum locked topological surface states, Nat. Commun. 7(1), 11458 (2016) https://doi.org/10.1038/ncomms11458
35	Y. Q. Huang, Y. X. Song, S. M. Wang, I. A. Buyanova, and W. M. Chen, Spin injection and helicity control of surface spin photocurrent in a three dimensional topological insulator, Nat. Commun. 8, 15401 (2017) https://doi.org/10.1038/ncomms15401
36	L. Liu, A. Richardella, I. Garate, Y. Zhu, N. Samarth, and C. T. Chen, Spin-polarized tunneling study of spinmomentum locking in topological insulators, Phys. Rev. B 91(23), 235437 (2015) https://doi.org/10.1103/PhysRevB.91.235437
37	Y. Shiomi, K. Nomura, Y. Kajiwara, K. Eto, M. Novak, K. Segawa, Y. Ando, and E. Saitoh, Spin-electricity conversion induced by spin injection into topological insulators,Phys. Rev. Lett. 113(19), 196601 (2014) https://doi.org/10.1103/PhysRevLett.113.196601
38	Y. Lv, J. Kally, D. Zhang, J. S. Lee, M. Jamali, N. Samarth, and J. P. Wang, Unidirectional spin-Hall and Rashba–Edelstein magnetoresistance in topological insulator-ferromagnet layer heterostructures, Nat. Commun. 9(1), 111 (2018) https://doi.org/10.1038/s41467-017-02491-3
39	K. Yasuda, A. Tsukazaki, R. Yoshimi, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Large unidirectional magnetoresistance in a magnetic topological insulator, Phys. Rev. Lett. 117(12), 127202 (2016) https://doi.org/10.1103/PhysRevLett.117.127202
40	Q. L. He, X. Kou, A. J. Grutter, G. Yin, L. Pan, X. Che, Y. Liu, T. Nie, B. Zhang, S. M. Disseler, B. J. Kirby, W. II Ratcliff, Q. Shao, K. Murata, X. Zhu, G. Yu, Y. Fan, M. Montazeri, X. Han, J. A. Borchers, and K. L. Wang, Tailoring exchange couplings in magnetic topological-insulator/antiferromagnet heterostructures, Nat. Mater. 16(1), 94 (2017) https://doi.org/10.1038/nmat4783
41	Q. L. He, G. Yin, L. Yu, A. J. Grutter, L. Pan, C. Z. Chen, X. Che, G. Yu, B. Zhang, Q. Shao, A. L. Stern, B. Casas, J. Xia, X. Han, B. J. Kirby, R. K. Lake, K. T. Law, and K. L. Wang, Topological transitions induced by antiferromagnetism in a thin-film topological insulator, Phys. Rev. Lett. 121(9), 096802 (2018) https://doi.org/10.1103/PhysRevLett.121.096802
42	K. Yasuda, R. Wakatsuki, T. Morimoto, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, M. Ezawa, M. Kawasaki, N. Nagaosa, and Y. Tokura, Geometric Hall effects in topological insulator heterostructures, Nat. Phys. 12(6), 555 (2016) https://doi.org/10.1038/nphys3671
43	C. Liu, Y.Zang, W. Ruan, Y. Gong, K. He, X. Ma, Q. K. Xue, and Y. Wang, Dimensional crossover-induced topological Hall effect in a magnetic topological insulator, Phys. Rev. Lett. 119(17), 176809 (2017) https://doi.org/10.1103/PhysRevLett.119.176809
44	Q. L. He, G. Yin, A. J. Grutter, L. Pan, X. Che, G. Yu, D. A. Gilbert, S. M. Disseler, Y. Liu, P. Shafer, B. Zhang, Y. Wu, B. J. Kirby, E. Arenholz, R. K. Lake, X. Han, and K. L. Wang, Exchange-biasing topological charges by antiferromagnetism, Nat. Commun. 9(1), 2767 (2018) https://doi.org/10.1038/s41467-018-05166-9
45	F. Wilczek, Majorana returns, Nat. Phys. 5(9), 614 (2009) https://doi.org/10.1038/nphys1380
46	J. Nilsson, A. R. Akhmerov, and C. W. Beenakker, Splitting of a Cooper pair by a pair of Majorana bound states, Phys. Rev. Lett. 101(12), 120403 (2008) https://doi.org/10.1103/PhysRevLett.101.120403
47	M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80(7), 076501 (2017) https://doi.org/10.1088/1361-6633/aa6ac7
48	N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61(15), 10267 (2000) https://doi.org/10.1103/PhysRevB.61.10267
49	A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Uspekhi 44(10S), 131 (2001) https://doi.org/10.1070/1063-7869/44/10S/S29
50	J. C. Teo and C. L. Kane, Majorana fermions and non-Abelian statistics in three dimensions, Phys. Rev. Lett. 104(4), 046401 (2010) https://doi.org/10.1103/PhysRevLett.104.046401
51	J. P. Xu, M. X. Wang, Z. L. Liu, J. F. Ge, X. Yang, C. Liu, Z. A. Xu, D. Guan, C. L. Gao, D. Qian, Y. Liu, Q. H. Wang, F. C. Zhang, Q. K. Xue, and J. F. Jia, Experimental detection of a Majorana mode in the core of a magnetic vortex inside a topological insulator-superconductor Bi2Te3/NbSe2 heterostructure, Phys. Rev. Lett. 114(1), 017001 (2015) https://doi.org/10.1103/PhysRevLett.114.017001
52	H. H. Sun, K. W. Zhang, L. H. Hu, C. Li, G. Y. Wang, H. Y. Ma, Z. A. Xu, C. L. Gao, D. D. Guan, Y. Y. Li, C. Liu, D. Qian, Y. Zhou, L.Fu, S. C. Li, F. C. Zhang, and J. F. Jia, Majorana zero mode detected with spin selective andreev reflection in the vortex of a topological superconductor, Phys. Rev. Lett. 116(25), 257003 (2016) https://doi.org/10.1103/PhysRevLett.116.257003
53	F. Yang, Y. Ding, F. Qu, J. Shen, J. Chen, Z. Wei, Z. Ji, G. Liu, J. Fan, C. Yang, T. Xiang, and L. Lu, Proximity effect at superconducting Sn-Bi2Se3 interface, Phys. Rev. B 85, 104508 (2012) https://doi.org/10.1103/PhysRevB.85.104508
54	G. Koren, T. Kirzhner, Y. Kalcheim, and O. Millo, Signature of proximity-induced px+ipy triplet pairing in the doped topological insulator Bi2Se3 by the s-wave superconductor NbN, Europhys. Lett. (EPL) 103(6), 67010 (2013) https://doi.org/10.1209/0295-5075/103/67010
55	J. Wang, C. Z. Chang, H. Li, K. He, D. Zhang, M. Singh, X.C. Ma, N. Samarth, M. Xie, Q.K. Xue, and M. H. W. Chan,Interplay between topological insulators and superconductors, Phys. Rev. B 85, 045415 (2012) https://doi.org/10.1103/PhysRevB.85.045415
56	S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, M. Sato, and Y. Ando, Topological Superconductivity in CuxBi2Se3, Phys. Rev. Lett. 107(21), 217001 (2011) https://doi.org/10.1103/PhysRevLett.107.217001
57	S. Sasaki, Z. Ren, A. A. Taskin, K. Segawa, L. Fu, and Y. Ando, Odd-parity pairing and topological superconductivity in a strongly spin–orbit coupled semiconductor, Phys. Rev. Lett. 109(21), 217004 (2012) https://doi.org/10.1103/PhysRevLett.109.217004
58	Q. L. He, H. Liu, M. He, Y. H. Lai, H. He, G. Wang, K. T. Law, R. Lortz, J. Wang, and I. K. Sou, Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure, Nat. Commun. 5(1), 4247 (2014) https://doi.org/10.1038/ncomms5247
59	P. Zareapour, A. Hayat, S. Y. Zhao, M. Kreshchuk, A. Jain, D. C. Kwok, N. Lee, S. W. Cheong, Z. Xu, A. Yang, G. D. Gu, S. Jia, R. J. Cava, and K. S. Burch, Proximityinduced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3, Nat. Commun. 3(1), 1056 (2012) https://doi.org/10.1038/ncomms2042
60	M. Veldhorst, M. Snelder, M. Hoek, T. Gang, V. K. Guduru, X. L. Wang, U. Zeitler, W. G. van der Wiel, A. A. Golubov, H. Hilgenkamp, and A. Brinkman, Josephson supercurrent through a topological insulator surface state, Nat. Mater. 11(5), 417 (2012) https://doi.org/10.1038/nmat3255
61	F. Qu, F. Yang, J. Shen, Y. Ding, J. Chen, Z. Ji, G. Liu, J. Fan, X. Jing, C. Yang, and L. Lu, Strong superconducting proximity effect in Pb-Bi2Te3 hybrid structures, Sci. Rep. 2(1), 339 (2012) https://doi.org/10.1038/srep00339
62	J. R. Williams, A. J. Bestwick, P. Gallagher, S. S. Hong, Y. Cui, A. S. Bleich, J. G. Analytis, I. R. Fisher, and D. Goldhaber-Gordon, Unconventional Josephson effect in hybrid superconductor–topological insulator devices, Phys. Rev. Lett. 109(5), 056803 (2012) https://doi.org/10.1103/PhysRevLett.109.056803
63	S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, H. Buhmann, L. W. Molenkamp, and A. Yacoby, Induced superconductivity in the quantum spin Hall edge, Nat. Phys. 10, 638 (2014) https://doi.org/10.1038/nphys3036
64	E. Bocquillon, R. S. Deacon, J. Wiedenmann, P. Leubner, T. M. Klapwijk, C. Brune, K. Ishibashi, H. Buhmann, and L. W. Molenkamp, Gapless Andreev bound states in the quantum spin Hall insulator HgTe, Nat. Nanotechnol. 12(2), 137 (2016) https://doi.org/10.1038/nnano.2016.159
65	M. X. Wang, C. Liu, J. P. Xu, F. Yang, L. Miao, M. Y. Yao, C. L. Gao, C. Shen, X. Ma, X. Chen, Z. A. Xu, Y. Liu, S. C. Zhang, D. Qian, J. F. Jia, and Q. K. Xue, The coexistence of superconductivity and topological order in the Bi2Se3 thin films, Science 336(6077), 52 (2012) https://doi.org/10.1126/science.1216466
66	S. Y. Xu, N. Alidoust, I. Belopolski, A. Richardella, C. Liu, M. Neupane, G. Bian, S. H. Huang, R. Sankar, C. Fang, B. Dellabetta, W. Dai, Q. Li, M. J. Gilbert, F. Chou, N. Samarth, and M. Z. Hasan, Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor, Nat. Phys. 10(12), 943 (2014) https://doi.org/10.1038/nphys3139
67	E. Wang, H. Ding, A. V. Fedorov, W. Yao, Z. Li, Y. F. Lv, K. Zhao, L. G. Zhang, Z. Xu, J. Schneeloch, R. Zhong, S. H. Ji, L. Wang, K. He, X. Ma, G. Gu, H. Yao, Q. K. Xue, X. Chen, and S. Zhou, Fully gapped topological surface states in Bi2Se3 films induced by a dwave high-temperature superconductor, Nat. Phys. 9(10), 621 (2013) https://doi.org/10.1038/nphys2744
68	Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi, K. Murata, X. Kou, Z. Chen, T. Nie, Q. Shao, Y. Fan, S. C. Zhang, K. Liu, J. Xia, and K. L. Wang, Chiral Majorana fermion modes in a quantum anomalous Hall insulatorsuperconductor structure, Science 357(6348), 294 (2017) https://doi.org/10.1126/science.aag2792
69	C. F. Pai, Switching by topological insulators,Nat. Mater. 17(9), 755 (2018) https://doi.org/10.1038/s41563-018-0146-x
70	J. Han, A. Richardella, S. A. Siddiqui, J. Finley, N. Samarth, and L. Liu, Room-temperature spin–orbit torque switching induced by a topological insulator, Phys. Rev. Lett. 119(7), 077702 (2017) https://doi.org/10.1103/PhysRevLett.119.077702
71	Y. Wang, D. Zhu, Y. Wu, Y. Yang, J. Yu, R. Ramaswamy, R. Mishra, S. Shi, M. Elyasi, K. L. Teo, Y. Wu, and H. Yang, Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin–orbit torques, Nat. Commun. 8(1), 1364 (2017) https://doi.org/10.1038/s41467-017-01583-4
72	M. Dc, R. Grassi, J. Y. Chen, M. Jamali, D. Reifsnyder Hickey, D. Zhang, Z. Zhao, H. Li, P. Quarterman, Y. Lv, M. Li, A. Manchon, K. A. Mkhoyan, T. Low, and J. P. Wang, Room-temperature high spin–orbit torque due to quantum confinement in sputtered BixSe1-x films, Nat. Mater. 17(9), 800 (2018) https://doi.org/10.1038/s41563-018-0136-z
73	N. H. D. Khang, Y. Ueda, and P. N. Hai, A conductive topological insulator with large spin Hall effect for ultralow power spin–orbit torque switching, Nat. Mater. 17(9), 808 (2018) https://doi.org/10.1038/s41563-018-0137-y
74	D. A. Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett. 86(2), 268 (2001) https://doi.org/10.1103/PhysRevLett.86.268
75	J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nat. Phys. 7(5), 412 (2011) https://doi.org/10.1038/nphys1915
76	D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea, Milestones toward Majorana-based quantum computing, Phys. Rev. X 6 , 031016 (2016) https://doi.org/10.1103/PhysRevX.6.031016
77	T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes, Phys. Rev. B 95(23), 235305 (2017) https://doi.org/10.1103/PhysRevB.95.235305
78	J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75(7), 076501 (2012) https://doi.org/10.1088/0034-4885/75/7/076501
79	A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303(1), 2 (2003) https://doi.org/10.1016/S0003-4916(02)00018-0
80	S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, H. Buhmann, L. W. Molenkamp, and A. Yacoby, Induced superconductivity in the quantum spin Hall edge, Nat. Phys. 10(9), 638 (2014) https://doi.org/10.1038/nphys3036

[1]	Chen-Xiao Zhao (赵晨晓), Jin-Feng Jia (贾金锋). Stanene: A good platform for topological insulator and topological superconductor[J]. Front. Phys. , 2020, 15(5): 53201-.
[2]	Chang-Yong Zhu, Shi-Han Zheng, Hou-Jian Duan, Ming-Xun Deng, Rui-Qiang Wang. Double Andreev reflections at surface states of the topological insulators with hexagonal warping[J]. Front. Phys. , 2020, 15(2): 23602-.
[3]	Y. X. Zhao. Equivariant PT-symmetric real Chern insulators[J]. Front. Phys. , 2020, 15(1): 13603-.
[4]	Junjie Qi, Haiwen Liu, Hua Jiang, X. C. Xie. Dephasing effects in topological insulators[J]. Front. Phys. , 2019, 14(4): 43403-.
[5]	Hai-Peng Sun, Hai-Zhou Lu. Quantum transport in topological semimetals under magnetic fields (II)[J]. Front. Phys. , 2019, 14(3): 33405-.
[6]	Jia Liu, Chun Fai Chan, Ming Gong. Majorana fermions in semiconducting nanowire and Fulde–Ferrell superconductor hybrid structures[J]. Front. Phys. , 2019, 14(1): 13609-.
[7]	Dingping Li, Baruch Rosenstein, B. Ya. Shapiro, I. Shapiro. Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator[J]. Front. Phys. , 2015, 10(3): 107402-.
[8]	Ming Yang, Xiao-Long Zhang, Wu-Ming Liu. Tunable topological quantum states in three- and two-dimensional materials[J]. Front. Phys. , 2015, 10(2): 108102-.
[9]	Yi-Bin Hu, Yong-Hong Zhao, Xue-Feng Wang. A computational investigation of topological insulator Bi₂Se₃ film[J]. Front. Phys. , 2014, 9(6): 760-767.
[10]	Ying Xing (邢颖), Yi Sun (孙祎), Meenakshi Singh, Yan-Fei Zhao (赵弇斐), Moses H. W. Chan, Jian Wang (王健). Electronic transport properties of topological insulator films and low dimensional superconductors[J]. Front. Phys. , 2013, 8(5): 491-508.
[11]	Hui Li (李辉), Hailin Peng (彭海琳), Wenhui Dang (党文辉), Lili Yu (余力立), Zhongfan Liu (刘忠范). Topological insulator nanostructures: Materials synthesis, Raman spectroscopy, and transport properties[J]. Front. Phys. , 2012, 7(2): 208-217.
[12]	Ivan Knez, Rui-Rui Du. Quantum spin Hall effect in inverted InAs/GaSb quantum wells[J]. Front. Phys. , 2012, 7(2): 200-207.
[13]	Jun-liang Zhang, Si-jia Zhang, Hong-ming Weng, Wei Zhang, Liu-xiang Yang, Qing-qing Liu, Pan-pan Kong, Jie Zhu, Shao-min Feng, Xian-cheng Wang, Ri-cheng Yu, Lie-zhao Cao, Shoucheng Zhang, Xi Dai, Zhong Fang, Chang-qing Jin. Superconductivity of topological matters induced via pressure[J]. Front. Phys. , 2012, 7(2): 193-199.
[14]	Yulin Chen. Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy[J]. Front. Phys. , 2012, 7(2): 175-192.
[15]	Yong-qing Li, Ke-hui Wu, Jun-ren Shi, Xin-cheng Xie. Electron transport properties of three-dimensional topological insulators[J]. Front. Phys. , 2012, 7(2): 165-174.

Viewed

Full text

Abstract

Cited

Shared

Discussed