弯曲时空中转动对自旋流的影响
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摘要
自旋轨道相互作用和自旋霍尔效应一直受到广泛关注,不仅在理论上进行了预测,而且也在实验中实现了自旋电流的产生.本文研究弯曲时空中转动对自旋流和自旋霍尔电导率的影响.非平庸几何可以改变自旋和轨道之间的相互作用,利用推广的Drude模型,计算了自旋依赖的作用力,并得到了非平庸几何对该力的修正.当计入转动效应时,给出了一般性的Dirac方程,并利用Foldy-Wouthuysen变换得到了非相对论近似下的哈密顿量.在此基础上,计算了自旋流和自旋霍尔电导率.在弯曲时空中由于转动的效应而导致偏振矢量的变形,自旋流的大小和方向都会因为转动而发生改变,因而自旋霍尔电导率也会随之得到修正.时空几何的非平庸性导致了自旋流有各向异性的特点.研究结论可以用于分析量子霍尔系统中带电旋量粒子的电磁动力学问题,也可以对晶体中的缺陷问题提供重要的理论帮助.对于光子系统来说,研究结果对于研究光子自旋霍尔效应在静态引力场中的行为具有一定的参考价值,对于实验上利用光子自旋霍尔效应来实现弯曲时空提供一定的理论支持.
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 nonmediocre 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.
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 nonmediocre 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.
引文
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[44] Xiao S, Zhong F, Liu H, Zhu S, Li J 2015 Nature Commun. 68360
[45] Zhong F, Li J, Liu H, Zhu S 2018 Phys. Rev. Lett. 120 243901
[2] Sinova J, Valenzuela S O, Wunderlich J, Back C H,Jungwirth T 2015 Rev. Mod. Phys. 87 1213
[3] Culcer D, Sinova J, Sinitsyn N A, Jungwirth T, MacDonald A H, Niu Q 2004 Phys. Rev. Lett. 93 046602
[4] Qi X L, Zhang S C 2010 Phys. Today 63 33
[5] Nir S, Sergey N, Vladimir K, Erez H 2012 Nano Lett. 12 1620
[6] Zhang S C, Bernevig B A, Hughes T 2006 Science 314 1757
[7] Chowdhury D, Basu B 2014 Physical B 448 155
[8] Chowdhury D, Basu B 2013 Ann. Phys. 329 166
[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
[11] Martin G, Dmitry V F, Peter Z, Ingrid M 2010 Phys. Rev.Lett. 104 186403
[12] Chazalviel J N 1975 Phys. Rev. B 11 3918
[13] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004Science 306 1910
[14] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004Phys. Rev. Lett. 93 176601
[15] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Phys. Rev.Lett. 106 076601
[16] Eugene M C 2007 Phys. Rev. Lett. 99 206601
[17] Vilenkin A 1985 Phys. Rep. 121 263
[18] Dayi O F, Elbistan M 2009 Phys. Lett. A 373 1314
[19] Knut B, Claudio F, Nascimento J R 2009 Eur. Phys. J. C 60501
[20] Matsuo M, Ieda J, Harii K, Saitoh E, Maekawa S 2013 Phys.Rev. B87 180402(R)
[21] Matsuo M, Ieda J, Maekawa S, Saitoh E 2013 J. Korean Phys. Soc. 62 1404
[22] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Appl. Phys.Lett. 98 242501
[23] Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Phys. Rev. B84 104410
[24] Matsuo M, Ohnuma Y, Kato T, Maekawa S 2018 Phys. Rev.Lett. 120 037201
[25] Kobayashi D, Yoshikawa T, Matsuo M, Iguchi R, Maekawa S, Saitoh E, Nozaki Y 2017 Phys. Rev. Lett. 119 077202
[26] Foldy L L, Wouthuysen S A 1950 Phys. Rev. 78 29
[27] Tani S 1951 Prog. Theor. Phys. 6 267
[28] Ma K, Dulat S 2011 Phys. Rev. A 84 012104
[29] Bakke K 2013 Gen. Relat. Gravit. 45 1847
[30] Kountouriotis K, Barreda J L, Keiper T D, Zhang M, Xiong P 2018 Nano Lett. 18 4386
[31] Albrecht J D, Smith D L 2003 Phys. Rev. B 68 035340
[32] Vutukuri S, Chshiev M, Butler W H 2006 J. Appl. Phys. 9908K302
[33] Schliemann J, Loss D 2004 Phys. Rev. B 69 165315
[34] Slachter A, Bakker F L, van Wees B J 2011 Phys. Rev. B 84174408
[35] Ralph D C, Stiles M D 2008 J. Magn. Magn. Mater. 320 1190
[36] Ling X, Zhou X, Huang K, Liu Y, Qiu C, Luo H, Wen S 2017Rep. Prog. Phys. 80 066401
[37] Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93083901
[38] Hosten O, Kwiat P 2008 Science 319 787
[39] Resch K J 2008 Science 319 733
[40] Zhou X, Luo H, Wen S 2014 Appl. Phys. Lett. 104 051130
[41] Luo H, Wen S, Shu W, Tang Z, Zou Y, Fan D 2009 Phys.Rev. A 80 043810
[42] Luo H, Ling X, Zhou X, Shu W, Wen S, Fan D 2011 Phys.Rev. A 84 033801
[43] Bliokh K Y, Bliokh K P 2006 Phys. Rev. Lett. 96 073903
[44] Xiao S, Zhong F, Liu H, Zhu S, Li J 2015 Nature Commun. 68360
[45] Zhong F, Li J, Liu H, Zhu S 2018 Phys. Rev. Lett. 120 243901