Abstract

The spin texture of the surface state for topological insulators can be manipulated by the polarization of light, which might play a potential role in the applications in spintronics. However, the study so far in this direction mainly focuses on the classical light-topological-insulators interactions; TIs coupled to quantized light remains barely explored. In this paper, we develop a formalism to deal with this issue of spin texture of the surface state for topological insulators (for example Bi2Se3 and SmB6) irradiated by a quantum field, and we find that the coupling between an electron and a single-mode quantum field modulates only the arrow length that represents the spin polarization of a topological surface state. Specifically, when the photon number of a single-mode quantum field is fixed, the azimuth angle between the quantum light and the material surface manipulates the spin textures along the constant energy contour rotating (clockwise or counterclockwise) around the high symmetry point, and the polar angle controls the magnitude of the spin polarization. These results are quite different from the situation where an external field is not applied to an electron in a crystal or where a classical external field is utilized to control the spin polarization of a photoemitted electron in a vacuum. Our results have potential applications in quantum optics and condensed-matter physics.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  35. D. Yudin, O. V. Kibis, and I. A. Shelykh, “Optically tunable spin transport on the surface of a topological insulator,” New J. Phys. 18, 103014 (2016).
    [Crossref]
  36. O. V. Kibis, “Metal-insulator transition in graphene induced by circularly polarized photons,” Phys. Rev. B 81, 165433 (2010).
    [Crossref]
  37. Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
    [Crossref]
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    [Crossref]

2016 (3)

R. Yu, H. M. Weng, Z. Fang, and X. Dai, “Pseudospin, real spin, and spin polarization of photoemitted electrons,” Phys. Rev. B 94, 085123 (2016).
[Crossref]

R. W. Bomantara, “Generating controllable type-II Weyl points via periodic driving,” Phys. Rev. B 94, 235447 (2016).
[Crossref]

D. Yudin, O. V. Kibis, and I. A. Shelykh, “Optically tunable spin transport on the surface of a topological insulator,” New J. Phys. 18, 103014 (2016).
[Crossref]

2015 (3)

B. Gulácsi and B. Dóra, “From Floquet to Dicke: quantum spin Hall insulator interacting with quantum light,” Phys. Rev. Lett. 115, 160402 (2015).
[Crossref] [PubMed]

R. Yu, H. M. Weng, X. Hu, Z. Fang, and X. Dai, “Model Hamiltonian for topological Kondo insulator SmB6,” New J. Phys. 17, 023012 (2015).
[Crossref]

J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, “Spin Hall effects,” Rev. Mod. Phys. 87, 1218–1220 (2015).
[Crossref]

2014 (3)

Z. H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S. Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron Spin-Polarization Control in the Topological Insulator Bi2Se3,” Phys. Rev. Lett. 112, 076802 (2014).
[Crossref]

S. Kim, S. Yoshizawa, Y. Ishida, K. Eto, K. Segawa, Y. Ando, S. Shin, and F. Komori, “Robust Protection from Backscattering in the Topological Insulator Bi1.5Sb0.5Te1.7Se1.3,” Phys. Rev. Lett. 112, 136802 (2014).
[Crossref]

B. Roy, J. D. Sau, M. Dzero, and V. Galitski, “Surface theory of a family of topological Kondo insulators,” Phys. Rev. B 90, 155314 (2014).
[Crossref]

2013 (4)

F. Lu, J. Z. Zhao, H. M. Weng, Z. Fang, and X. Dai, “Correlated Topological Insulators with Mixed Valence,” Phys. Rev. Lett. 110, 096401 (2013).
[Crossref] [PubMed]

H. J. Zhang, C. X. Liu, and S. C. Zhang, “Spin-Orbital Texture in Topological Insulators,” Phys. Rev. Lett. 111, 066801 (2013).
[Crossref] [PubMed]

Y. Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, and D. S. Dessau, “Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators,” Nat. Phys. 9, 499–504 (2013).
[Crossref]

Z. H. Zhu, C. N. Veenstra, G. Levy, A. Ubaldini, P. Syers, N.P. Butch, J. Paglione, M. W. Haverkort, I.S. Elfimov, and A. Damascelli, “Layer-By-Bayer Entangled Spin-Orbital Texture of the Topological Surface State in Bi2Se3,” Phys. Rev. Lett. 110, 216401 (2013).
[Crossref]

2012 (5)

S. R. Park, J. Han, C. Kim, Y. Y. Koh, C. Kim, H. Lee, H. J. Choi, J. H. Han, K. D. Lee, N. J. Hur, M. Arita, K. Shimada, H. Namatame, and M. Taniguchi, “Chiral Orbital-Angular Momentum in the Surface States of Bi2Se3,” Phys. Rev. Lett. 108, 046805 (2012).
[Crossref]

M. H. Liu, J. Zhang, C. Z. Chang, Z. C Zhang, X. Feng, K. Li, K. He, L. L Wang, X. Chen, X. Dai, Z. Fang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Crossover between Weak Antilocalization and Weak Localization in a Magnetically Doped Topological Insulator,” Phys. Rev. Lett. 108, 036805 (2012).
[Crossref] [PubMed]

M. Trif and Y. Tserkovnyak, “Resonantly tunablemajorana polariton in a microwave cavity,” Phys. Rev. Lett. 109, 257002 (2012).
[Crossref]

C. H. Park and S. G. Louie, “Spin polarization of photoelectrons from topological insulators,” Phys. Rev. Lett. 109, 097601 (2012).
[Crossref] [PubMed]

M. Dzero, K. Sun, P. Coleman, and V. Galitski, “Theory of topological Kondo insulators,” Phys. Rev. B 85, 045130 (2012).
[Crossref]

2011 (9)

Y. H. Wang, D. Hsieh, D. Pilon, L. Fu, D. R. Gardner, Y. S. Lee, and N. Gedik, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
[Crossref]

S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, “Direct Measurement of the Out-of-Plane Spin Texture in the Dirac-Cone Surface State of a Topological Insulator,” Phys. Rev. Lett. 106, 216803 (2011).
[Crossref] [PubMed]

Z. H. Pan, E. Vescovo, A. V. Fedorov, D. Gardner, Y. S. Lee, S. Chu, G. D. Gu, and T. Valla, “Electronic Structure of the Topological Insulator Bi2Se3 Using Angle-Resolved Photoemission Spectroscopy: Evidence for a Nearly Full Surface Spin Polarization,” Phys. Rev. Lett. 106, 257004 (2011).
[Crossref]

R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
[Crossref]

P. Hosur, “Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response,” Phys. Rev. B 83, 035309 (2011).
[Crossref]

M. H. Liu, C. Z. Chang, Z. C. Zhang, Y. Zhang, W. Ruan, K. He, L. L. Wang, X. Chen, J. F. Jia, S. C. Zhang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit,” Phys. Rev. B 83, 165440 (2011).
[Crossref]

S. Basak, H. Lin, L. A. Wray, S. Y. Xu, L. Fu, M. Z. Hasan, and A. Bansil, “Spin texture on the warped Dirac-cone surface states in topological insulators,” Phys. Rev. B 84, 121401 (2011).
[Crossref]

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1074–1075 (2011).
[Crossref]

T. Misawa, T. Yokoyama, and S. Murakami, “Electromagnetic spin polarization on the surface of topological insulator,” Phys. Rev. B 84, 165407 (2011).
[Crossref]

2010 (6)

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys. 82, 3057–3059 (2010).
[Crossref]

X. L. Qi and S. C. Zhang, “The quantum spin Hall effect and topological insulators,” Phys. Today 63, 33 (2010).
[Crossref]

H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, “Massive Dirac fermions and spin physics in an ultrathin film of topological insulator,” Phys. Rev. B 81, 115407 (2010).
[Crossref]

C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Z. Fang, and S. C. Zhang, “Model Hamiltonian for topological insulators,” Phys. Rev. B 82, 045122 (2010).
[Crossref]

O. V. Kibis, “Metal-insulator transition in graphene induced by circularly polarized photons,” Phys. Rev. B 81, 165433 (2010).
[Crossref]

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

2009 (4)

D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett 103, 146401 (2009).
[Crossref]

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, 1106–1109 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and Marin Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature. 461, 772–775 (2009).
[Crossref] [PubMed]

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, 1101–1105 (2009).
[Crossref] [PubMed]

2007 (1)

L. Fu, C. L. Kane, and E. J. Mele, “Topological Insulators in Three Dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[Crossref] [PubMed]

2004 (1)

A. Carollo, I. F. Guridi, M. F. Santos, and V. Vedral, “Stationary two-level atomic inversion in a quantized cavity field,” Phys. Rev. Lett. 92, 020402 (2004).
[Crossref]

2000 (1)

T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, “Magnetic Vortex Core Observation in Circular Dots of Permalloy,” Science. 289, 930–932 (2000).
[Crossref]

1988 (1)

C. M. Savage, “Spin-1/2 geometric phase driven by becohering quantum fields,” Phys. Rev. Lett. 60, 1828 (1988).
[Crossref] [PubMed]

Aguilar, R. V.

R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
[Crossref]

Ai, Q.

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
[Crossref]

Ando, Y.

S. Kim, S. Yoshizawa, Y. Ishida, K. Eto, K. Segawa, Y. Ando, S. Shin, and F. Komori, “Robust Protection from Backscattering in the Topological Insulator Bi1.5Sb0.5Te1.7Se1.3,” Phys. Rev. Lett. 112, 136802 (2014).
[Crossref]

S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, “Direct Measurement of the Out-of-Plane Spin Texture in the Dirac-Cone Surface State of a Topological Insulator,” Phys. Rev. Lett. 106, 216803 (2011).
[Crossref] [PubMed]

Arita, M.

S. R. Park, J. Han, C. Kim, Y. Y. Koh, C. Kim, H. Lee, H. J. Choi, J. H. Han, K. D. Lee, N. J. Hur, M. Arita, K. Shimada, H. Namatame, and M. Taniguchi, “Chiral Orbital-Angular Momentum in the Surface States of Bi2Se3,” Phys. Rev. Lett. 108, 046805 (2012).
[Crossref]

Armitage, N. P.

R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
[Crossref]

Back, C. H.

J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, “Spin Hall effects,” Rev. Mod. Phys. 87, 1218–1220 (2015).
[Crossref]

Bansal, N.

Y. Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, and D. S. Dessau, “Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators,” Nat. Phys. 9, 499–504 (2013).
[Crossref]

R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
[Crossref]

Bansil, A.

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C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Z. Fang, and S. C. Zhang, “Model Hamiltonian for topological insulators,” Phys. Rev. B 82, 045122 (2010).
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X. L. Qi and S. C. Zhang, “The quantum spin Hall effect and topological insulators,” Phys. Today 63, 33 (2010).
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Zhang, X. W.

Y. Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, and D. S. Dessau, “Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators,” Nat. Phys. 9, 499–504 (2013).
[Crossref]

Zhang, Y.

M. H. Liu, C. Z. Chang, Z. C. Zhang, Y. Zhang, W. Ruan, K. He, L. L. Wang, X. Chen, J. F. Jia, S. C. Zhang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit,” Phys. Rev. B 83, 165440 (2011).
[Crossref]

Zhang, Z. C

M. H. Liu, J. Zhang, C. Z. Chang, Z. C Zhang, X. Feng, K. Li, K. He, L. L Wang, X. Chen, X. Dai, Z. Fang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Crossover between Weak Antilocalization and Weak Localization in a Magnetically Doped Topological Insulator,” Phys. Rev. Lett. 108, 036805 (2012).
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Zhang, Z. C.

M. H. Liu, C. Z. Chang, Z. C. Zhang, Y. Zhang, W. Ruan, K. He, L. L. Wang, X. Chen, J. F. Jia, S. C. Zhang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit,” Phys. Rev. B 83, 165440 (2011).
[Crossref]

Zhao, J. Z.

F. Lu, J. Z. Zhao, H. M. Weng, Z. Fang, and X. Dai, “Correlated Topological Insulators with Mixed Valence,” Phys. Rev. Lett. 110, 096401 (2013).
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Zhdanovich, S.

Z. H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S. Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron Spin-Polarization Control in the Topological Insulator Bi2Se3,” Phys. Rev. Lett. 112, 076802 (2014).
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Zheng, H.

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
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Zhu, S. Y.

Z. H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S. Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron Spin-Polarization Control in the Topological Insulator Bi2Se3,” Phys. Rev. Lett. 112, 076802 (2014).
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Zhu, Z. H.

Z. H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S. Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron Spin-Polarization Control in the Topological Insulator Bi2Se3,” Phys. Rev. Lett. 112, 076802 (2014).
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Z. H. Zhu, C. N. Veenstra, G. Levy, A. Ubaldini, P. Syers, N.P. Butch, J. Paglione, M. W. Haverkort, I.S. Elfimov, and A. Damascelli, “Layer-By-Bayer Entangled Spin-Orbital Texture of the Topological Surface State in Bi2Se3,” Phys. Rev. Lett. 110, 216401 (2013).
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Zunger, A.

Y. Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, and D. S. Dessau, “Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators,” Nat. Phys. 9, 499–504 (2013).
[Crossref]

Nat. Phys. (1)

Y. Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, and D. S. Dessau, “Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators,” Nat. Phys. 9, 499–504 (2013).
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Nature (1)

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, 1101–1105 (2009).
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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, 1106–1109 (2009).
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Z. Wang, Y. D. Chong, J. D. Joannopoulos, and Marin Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature. 461, 772–775 (2009).
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R. Yu, H. M. Weng, X. Hu, Z. Fang, and X. Dai, “Model Hamiltonian for topological Kondo insulator SmB6,” New J. Phys. 17, 023012 (2015).
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D. Yudin, O. V. Kibis, and I. A. Shelykh, “Optically tunable spin transport on the surface of a topological insulator,” New J. Phys. 18, 103014 (2016).
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Phys. Rev. A (1)

Q. Ai, Y. Li, H. Zheng, and C. P. Sun, “Quantum anti-Zeno effect without rotating wave approximation,” Phys. Rev. A 81, 042116 (2010).
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Phys. Rev. B (11)

M. Dzero, K. Sun, P. Coleman, and V. Galitski, “Theory of topological Kondo insulators,” Phys. Rev. B 85, 045130 (2012).
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M. H. Liu, C. Z. Chang, Z. C. Zhang, Y. Zhang, W. Ruan, K. He, L. L. Wang, X. Chen, J. F. Jia, S. C. Zhang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, “Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit,” Phys. Rev. B 83, 165440 (2011).
[Crossref]

C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Z. Fang, and S. C. Zhang, “Model Hamiltonian for topological insulators,” Phys. Rev. B 82, 045122 (2010).
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R. W. Bomantara, “Generating controllable type-II Weyl points via periodic driving,” Phys. Rev. B 94, 235447 (2016).
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H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, “Massive Dirac fermions and spin physics in an ultrathin film of topological insulator,” Phys. Rev. B 81, 115407 (2010).
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P. Hosur, “Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response,” Phys. Rev. B 83, 035309 (2011).
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R. Yu, H. M. Weng, Z. Fang, and X. Dai, “Pseudospin, real spin, and spin polarization of photoemitted electrons,” Phys. Rev. B 94, 085123 (2016).
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T. Misawa, T. Yokoyama, and S. Murakami, “Electromagnetic spin polarization on the surface of topological insulator,” Phys. Rev. B 84, 165407 (2011).
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S. Basak, H. Lin, L. A. Wray, S. Y. Xu, L. Fu, M. Z. Hasan, and A. Bansil, “Spin texture on the warped Dirac-cone surface states in topological insulators,” Phys. Rev. B 84, 121401 (2011).
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Phys. Rev. Lett (1)

D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3,” Phys. Rev. Lett 103, 146401 (2009).
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Phys. Rev. Lett. (17)

H. J. Zhang, C. X. Liu, and S. C. Zhang, “Spin-Orbital Texture in Topological Insulators,” Phys. Rev. Lett. 111, 066801 (2013).
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R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Observation of a Warped Helical Spin Texture in Bi2Se3 from Circular Dichroism Angle-Resolved Photoemission Spectroscopy,” Phys. Rev. Lett. 107, 207602 (2011).
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[Crossref]

Z. H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S. Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron Spin-Polarization Control in the Topological Insulator Bi2Se3,” Phys. Rev. Lett. 112, 076802 (2014).
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Figures (10)

Fig. 1
Fig. 1 (a) Diagram of the experimental geometry. Linear polarization (σ-polarized and π-polarized) and circular polarization (righ tand left circular polarized) of photons can be continuously rotated by the θ and α angles. (b) The two-dimensional Brillouin zone for (111) surface with hihg-symmetry points Γ = (0, 0). (c) Corresponding two-dimensional Brillouin zone ofor the (001) surface with its hihg-symmetry points Γ ¯ = ( 0 , 0 ) , X ¯ = ( π , 0 ) , Y ¯ = ( 0 , π ) . Circles and ellipses around these hihg-symmetry points represent constant energy contour.
Fig. 2
Fig. 2 The real spin textures of surface states coupled to quantized σ-polarized light. Arrow indicates direction and relative length of the real spin in xy plane with different azimuth α.
Fig. 3
Fig. 3 The spin polarization of TSS in the xy plane of Bi2Se3 coupled to the quantized π-polarized light with different {α, θ}. The first and second rows indicate the spin textures on the upper and lower Dirac cone, respectively.
Fig. 4
Fig. 4 The real spin of Bi2Se3 irradiated by quantized circular polarized light. Arrow indicates direction and relative length of the real spin in the xy plane with different {α, θ}. The first and second rows indicate the spin textures on the upper and lower Dirac cone, respectively.
Fig. 5
Fig. 5 The real spin textures with the quantized σ-polarized light in the vicinity of Γ ¯ point. Arrows indicate the spin directions in the xy plane with different {α}.
Fig. 6
Fig. 6 The spin polarization with the quantized π-polarized light in the vicinity of Γ ¯ point. Arrows indicate the spin directions in the xy plane with different {α, θ}. The first and second rows indicate the textures on the upper and lower Dirac cone, respectively.
Fig. 7
Fig. 7 The real spin with quantized circular polarized light in the vicinity of Γ ¯ point. Arrows indicate the spin directions in the xy plane with different {α, θ}. The first row indicates the textures on the upper Dirac cone and the second row on the lower one.
Fig. 8
Fig. 8 The real spin for the system irradiated by the quantized σ-polarized light in the vicinity of Y ¯ point. Arrows indicate the spin directions in the xy plane with different α.
Fig. 9
Fig. 9 The spin polarization for the system irradiated by π-polarized light in the vicinity of Y ¯ point with different {α, θ}. The first and second rows indicate the textures on the upper and lower Dirac cone, reapectively.
Fig. 10
Fig. 10 The real spin in the vicinity of Y ¯ point for the upper Dirac cone under quantized circular polarized light with different {α, θ}. Arrows indicate the spin directions in the xy plane.

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

H ^ o = σ × d ( k e c A ) z + ω a ^ a ^ ,
^ d = v 0 [ σ × ( k e c A ) ] z + ω a ^ a ^ ,
^ N = ( v 0 k e v 0 c A y sin β e v 0 c A x cos β ) τ z + ω a ^ a ^ + e v 0 c ( A y cos β A x sin β ) τ y ,
H ^ = v 0 k τ z + ω a ^ a ^ + e v 0 c ( A y cos β A x sin β ) τ y .
A = 2 π c 2 ω V ( a ^ + a ^ ) ( s i n α , c o s α , 0 ) ,
H ^ σ = v 0 k τ z + ω a ^ a ^ + i G cos ( β α ) ( τ τ + ) ( a ^ + a ^ ) ,
H ^ e f f = H ^ 0 + H ^ I + [ s ^ , H ^ 0 ] + [ s ^ , H ^ I ] + 1 2 [ s ^ , [ s ^ , H ^ 0 ] ] .
[ s ^ , H ^ 0 ] = [ s ^ , v 0 k τ z ] + [ s ^ , ω a ^ a ^ ] = y ( 2 v 0 k + ω ) τ + a ^ + x ( 2 v 0 k + ω ) τ a ^ .
x = y = i G ( 2 v 0 k + ω ) cos ( β α ) .
[ s ^ , [ s ^ , H ^ 0 ] ] = 2 2 v 0 k + ω [ G cos ( β α ) ] 2 τ z , [ s ^ , H ^ I ] = [ s ^ , i G cos ( β α ) ( τ a ^ τ + a ^ + τ a ^ τ + a ^ ) ] = 2 n 2 v 0 k + ω [ G cos ( β α ) ] 2 τ z ,
Ω σ = v 0 k + n 2 v 0 k + ω [ G cos ( β α ) ] 2 ,
H ^ e f f = Ω σ τ z + ω a ^ a ^ + i G cos ( β α ) ( τ a ^ τ + a ^ ) .
| a | 2 = ( n + 1 ) cos ( β α ) 2 G 2 ( n + 1 ) cos ( β α ) 2 G 2 + ( Ω σ + n ω E ) 2 , | b | 2 = ( Ω σ + n ω E ) 2 ( n + 1 ) cos ( β α ) 2 G 2 + ( Ω σ + n ω E ) 2 .
| ψ σ = e s ^ | ϕ ( 1 s ^ + 1 2 s ^ 2 ) | ϕ = a | e , n + b | g , n + 1 + i m cos ( β α ) [ n + 2 b | e , n + 2 + n a | g , n 1 ] 1 2 m 2 cos 2 ( β α ) [ n 2 a | e , n + n + 2 2 b | g , n + 1 ] ,
σ z φ , σ = σ ψ | τ x | ψ σ , σ x φ , σ = σ ψ | sin β τ z cos β τ y | ψ σ , σ y φ , σ = σ ψ | cos β τ z sin β τ y | ψ σ .
  σ ψ | τ y | ψ σ = σ ψ | τ x | ψ σ = 0 ,   σ ψ | τ z | ψ σ = | a | 2 ( [ 1 1 2 m 2 cos 2 ( β α ) n 2 ] 2 m 2 cos 2 ( β α ) n 2 ) | b | 2 ( [ 1 1 2 m 2 cos 2 ( β α ) n + 2 2 ] 2 m 2 cos 2 ( β α ) n + 2 2 ) .
S σ ψ | τ z | ψ σ ( g x x s i n β , g y y c o s β , 0 ) ,
A π = 2 π c 2 ω V ( a ^ + a ^ ) ( cos θ cos α , cos θ sin α , sin α ) .
H ^ π = v 0 k τ z + ω a ^ a ^ i G cos θ sin ( β α ) ( τ τ + ) ( a ^ + a ) .
A η = π c 2 ω V [ ( cos θ cos α ( a ^ + a ^ ) i η sin α ( a ^ a ^ ) ) e x + ( cos θ sin α ( a ^ + a ^ ) + i η cos α ( a ^ a ^ ) ) e y sin θ ( a ^ + a ^ ) e z ] ,
H ^ η = Ω η τ z + ω a ^ a ^ + i G / 2 ( κ a ^ τ κ * τ + a ^ ) ,
τ z = ( 1 0.5 n m κ κ * ) ( n + 1 ) G 2 κ κ * / 2 ( Ω η + ω n E η ) 2 ( n + 1 ) G 2 κ κ * / 2 ( 1 0.5 ( n + 2 ) m κ κ * ) ( Ω η + ω n E η ) 2 ( Ω η + ω n E η ) 2 + ( n + 1 ) G 2 κ κ * / 2 .
H Γ ¯ = v 0 [ σ x ( k y e c A y ) + σ y ( k x e c A x ) ] + ω a ^ a ^ .
H ^ Γ ¯ = v 0 k τ z I + ω a ^ a ^ + e v o c ( A y cos β + A x sin β ) τ y I ,
H ^ σ = v 0 k τ z I + ω a ^ a ^ + i G cos ( β + α ) ( τ I τ + I ) ( a ^ + a ^ ) .
H ^ π = v 0 k τ z I + ω a ^ a ^ + i G cos θ sin ( β + α ) ( τ I τ + I ) ( a ^ + a ^ ) .
H ^ η = v 0 k τ z I + ω a ^ a ^ + i G / 2 ( μ a ^ + μ * a ^ ) ( τ I τ + I ) ,
H ^ = υ y σ y ( k x e c A x ) υ x σ x ( k y e c A y ) + ω a ^ a ^ .
H ^ Y ¯ = D ( k ) τ z I I + ω a ^ a ^ + e v x c ( v y v x cos ϕ A x sin ϕ A y ) τ y I I ,
H ^ σ = D ( k ) τ z I I + ω a ^ a ^ i f ( ϕ ) ( τ I I τ + I I ) ( a ^ + a ^ ) ,
H ^ π = D ( k ) τ z I I + ω a ^ a ^ + i F ( ϕ ) ( τ I I τ + I I ) ( a ^ + a ^ ) ,
H ^ = D ( k ) τ z II + ω a ^ a ^ + ie υ x c π c 2 ω V ( ζ a ^ + ζ a ^ ) τ y II ,

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