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The spin-orbit interaction and spin Hall effect have drawn special attention. Not only theoretical predictions have been made, but also the generation of spin currents has been achieved in experiment. In this paper, we study the spin current and the spin Hall conductivity under the influence of rotation in the curved space-time. Our work shows that the nontrivial geometries could modify the spin-orbital interaction. By using the extended Drude model, we calculate the spin-dependent force and obtain a correction to this force by non-mediocre geometry. When considering the rotation effect, the general Dirac equation is given. The Hamiltonian under the non-relativistic approximation is obtained by the Foldy-Wouthuysen transform. According to this, we calculate the spin current and spin Hall conductance. The polarization vector is deformed due to the effect of the rotation in the curved space-time. The magnitude and direction of the spin current are changed because of the correction to rotation, and the spin Hall conductivity. The nontrivial space-time geometry leads to the anisotropic nature of the spin current. Our work uses a general method that does not depend on the model, so the result can be used to analyze the electromagnetic dynamics of charged spin particles in quantum Hall systems, and it also helps to theoretically study the defects in crystals. Our results can also be extended to the optical subsystem. Considering the spin effect of photons, based on the spin-orbit coupling of photon, a light splitting phenomenon emerges in an inhomogeneous medium, which is the spin hall effect of photon. Our discussion has a certain reference value for studying the behavior of the photonic spin Hall effect in the static gravitational field. At the same time, using the optical chips to simulate curved space-time, photon manipulation and precision measurement can give some theoretical support.
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Keywords:
- spin Hall effect /
- curved space-time /
- cosmic string
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[1] Hirsch J E 1999 Phys. Rev. Lett. 83 1834
Google Scholar
[2] Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213
Google Scholar
[3] Culcer D, Sinova J, Sinitsyn N A, Jungwirth T, MacDonald A H, Niu Q 2004 Phys. Rev. Lett. 93 046602
Google Scholar
[4] Qi X L, Zhang S C 2010 Phys. Today 63 33
Google Scholar
[5] Nir S, Sergey N, Vladimir K, Erez H 2012 Nano Lett. 12 1620
Google Scholar
[6] Zhang S C, Bernevig B A, Hughes T 2006 Science 314 1757
Google Scholar
[7] Chowdhury D, Basu B 2014 Physical B 448 155
Google Scholar
[8] Chowdhury D, Basu B 2013 Ann. Phys. 329 166
Google Scholar
[9] Dyakonov M I, Perel V I 1971 JETP Lett. 13 467
[10] Dyakonov M I, Perel V I 1971 Phys. Lett. A 35 459
Google Scholar
[11] Martin G, Dmitry V F, Peter Z, Ingrid M 2010 Phys. Rev. Lett. 104 186403
Google Scholar
[12] Chazalviel J N 1975 Phys. Rev. B 11 3918
Google Scholar
[13] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004 Science 306 1910
Google Scholar
[14] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004 Phys. Rev. Lett. 93 176601
Google Scholar
[15] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Phys. Rev. Lett. 106 076601
Google Scholar
[16] Eugene M C 2007 Phys. Rev. Lett. 99 206601
Google Scholar
[17] Vilenkin A 1985 Phys. Rep. 121 263
Google Scholar
[18] Dayi O F, Elbistan M 2009 Phys. Lett. A 373 1314
Google Scholar
[19] Knut B, Claudio F, Nascimento J R 2009 Eur. Phys. J. C 60 501
Google Scholar
[20] Matsuo M, Ieda J, Harii K, Saitoh E, Maekawa S 2013 Phys. Rev. B 87 180402(R)
Google Scholar
[21] Matsuo M, Ieda J, Maekawa S, Saitoh E 2013 J. Korean Phys. Soc. 62 1404
Google Scholar
[22] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Appl. Phys. Lett. 98 242501
Google Scholar
[23] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Phys. Rev. B 84 104410
Google Scholar
[24] Matsuo M, Ohnuma Y, Kato T, Maekawa S 2018 Phys. Rev. Lett. 120 037201
Google Scholar
[25] Kobayashi D, Yoshikawa T, Matsuo M, Iguchi R, Maekawa S, Saitoh E, Nozaki Y 2017 Phys. Rev. Lett. 119 077202
Google Scholar
[26] Foldy L L, Wouthuysen S A 1950 Phys. Rev. 78 29
Google Scholar
[27] Tani S 1951 Prog. Theor. Phys. 6 267
Google Scholar
[28] Ma K, Dulat S 2011 Phys. Rev. A 84 012104
Google Scholar
[29] Bakke K 2013 Gen. Relat. Gravit. 45 1847
Google Scholar
[30] Kountouriotis K, Barreda J L, Keiper T D, Zhang M, Xiong P 2018 Nano Lett. 18 4386
Google Scholar
[31] Albrecht J D, Smith D L 2003 Phys. Rev. B 68 035340
Google Scholar
[32] Vutukuri S, Chshiev M, Butler W H 2006 J. Appl. Phys. 99 08K302
Google Scholar
[33] Schliemann J, Loss D 2004 Phys. Rev. B 69 165315
Google Scholar
[34] Slachter A, Bakker F L, van Wees B J 2011 Phys. Rev. B 84 174408
Google Scholar
[35] Ralph D C, Stiles M D 2008 J. Magn. Magn. Mater. 320 1190
Google Scholar
[36] Ling X, Zhou X, Huang K, Liu Y, Qiu C, Luo H, Wen S 2017 Rep. Prog. Phys. 80 066401
Google Scholar
[37] Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901
Google Scholar
[38] Hosten O, Kwiat P 2008 Science 319 787
Google Scholar
[39] Resch K J 2008 Science 319 733
Google Scholar
[40] Zhou X, Luo H, Wen S 2014 Appl. Phys. Lett. 104 051130
Google Scholar
[41] Luo H, Wen S, Shu W, Tang Z, Zou Y, Fan D 2009 Phys. Rev. A 80 043810
Google Scholar
[42] Luo H, Ling X, Zhou X, Shu W, Wen S, Fan D 2011 Phys. Rev. A 84 033801
Google Scholar
[43] Bliokh K Y, Bliokh K P 2006 Phys. Rev. Lett. 96 073903
Google Scholar
[44] Xiao S, Zhong F, Liu H, Zhu S, Li J 2015 Nature Commun. 6 8360
Google Scholar
[45] Zhong F, Li J, Liu H, Zhu S 2018 Phys. Rev. Lett. 120 243901
Google Scholar
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