自旋—轨道耦合体系中自旋输运特性的理论研究
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摘要
自旋-轨道耦合效应在基础研究和实际应用方面都引起了人们极大的兴趣与关注。电子的自旋状态可以由自旋-轨道耦合作用来控制,不需要利用磁性材料或外加磁场,这使全电学方法控制的自旋器件成为可能,例如已经提出的Datta-Das自旋场效应晶体管(Spin-FET)就是一种全电学操纵的自旋器件。半导体二维电子气中存在几种典型自旋-轨道耦合作用:Rashba自旋-轨道耦合,Dresseslhaus自旋-轨道耦合,以及杂质引起的自旋-轨道耦合。前二者属于内禀(Intrinsic)自旋-轨道耦合,杂质引起的自旋-轨道耦合属于外禀(Extrinsic)自旋-轨道耦合。电子自旋输运在自旋-轨道耦合调控下呈现出丰富的物理效应,例如自旋霍尔效应、自旋流等。此外,半导体低维材料生长技术日益完善,已经能够制造出具有高迁移率的纳米尺度的微结构器件,为自旋-轨道耦合效应的研究提供了实验基础。
本文研究了自旋轨道耦合体系中电子自旋的输运特性。研究工作包含如下四方面的内容,其中前三方面是关于具有特殊自旋输运性质的自旋器件模型设计,最后一方面是关于自旋螺旋态寿命的研究。
1.飞行自旋比特逻辑门的模型设计
基于自旋电子学的迅速发展,我们提出了飞行自旋比特的固态量子计算模型。器件模型是两个半导体量子线:具有Rashba自旋-轨道耦合作用的量子线和具有Dresselhaus自旋-轨道耦合作用的量子线。在模型中,电子自旋极化态是比特信息的载体,自旋-轨道耦合是控制自旋比特的手段,二维电子气是自旋信息的传输通道。Rashba和Dresselhaus两类自旋-轨道耦合实现了对自旋的两类操纵方式,结合这两类操纵方式(串连两类量子线),我们实现了一套通用的单量子自旋比特逻辑门:Hadamard门,相位门π/8门。另外,我们还计算了电子自旋在器件模型中的透射系数,确保在一定条件下实现全透射,从而使信息在传递中没有损耗。
2.弹道电导双稳开关效应
弹道自旋场效应晶体管中,可以利用自旋-轨道耦合作用调控输出电流。我们研究了具有周期Rashba结构的自旋场效应晶体管中电子自旋的输运性质,并得到理想的开关效应。一定强度的周期Rashba自旋-轨道耦合会产生能隙,当入射电子的能量处在能隙内时,电子不能通过,电导为0,通道处于“断开”状态。减小Rashba自旋-轨道耦合强度至低于某临界值时,电子可以全透射,电导最大,通道处于“闭合”状态。因此,通过调节自旋-轨道耦合强度,我们实现了控制弹道电导的双稳开关效应。利用周期Rashba结构实现的是双稳的开关效应,比利用单个Rashba区实现的开关效应,性能要稳定很多。我们期望这个稳定的开关效应能在未来的纳电子器件中得到应用。
3.自旋过滤器的模型设计
自旋过滤器的功能是使无自旋极化流转变为自旋极化流。利用空间调制的弱磁场和自旋-轨道耦合,我们提出了两种自旋过滤器模型。模型(一)是对半导体量子线施加均一弱磁场和周期Rashba自旋-轨道耦合。周期的Rashba结构产生了一个电子无法通过的能隙,弱磁场破坏体系的时间反演对称性,使原本重合的上自旋能隙和下自旋能隙分离,我们在分离的能隙内分别得到上自旋极化流和下自旋极化流。模型(二)是对量子线施加周期弱磁场和均一自旋-轨道耦合。周期磁场产生分离的上自旋能隙和下自旋能隙,使上自旋极化流和下自旋极化流分布在不同能量区间,调节Rashba自旋-轨道耦合还可以实现上自旋极化流和下自旋极化流的灵活转变。
4自旋螺旋(Spin helix)态寿命的研究
利用自旋-轨道耦合作用控制自旋态时,通常也要考虑其引起的自旋弛豫效应。最近,Bernevig等人在两个特殊的自旋-轨道耦合体系中发现了寿命无限长的自旋螺旋态(Phys.Rev.Lett.97,236601(2006)),而且该自旋螺旋态的寿命不受非磁性杂质的影响。但是Bemevig等人在提出自旋寿命无限长时没有考虑杂质分布可能引起的外禀自旋-轨道耦合对自旋寿命的影响,这其实是一个非常重要的问题。我们运用格林函数运动方程的方法,深入研究了杂质引起的外禀自旋-轨道耦合对自旋螺旋态寿命的影响。结果表明考虑外禀自旋-轨道耦合作用后,自旋螺旋态的寿命不再是无穷大,且自旋螺旋态的寿命强烈的依赖于外禀自旋-轨道耦合强度和杂质密度。此外,研究还发现,内禀自旋-轨道耦合,因为外禀自旋-轨道耦合的存在,会对自旋寿命产生显著的影响。
Spin-orbit coupling (SOC) effect has generated great interest from both academic and practical perspectives. In particular, SOC allows for purely electric manipulation of the electron spin, i.e. magnetic material or external magnetic field is not required, which may result in the ail-electrically controlled spin device, such as the Datta-Das spin field-effect-transistor. In semiconductor two-dimensional electron gas system, there are several typical SOC mechanisms: Rashba SOC, Dresselhaus SOC, and the SOC induced by impurities. Both Rashba and Dresselhaus SOC belong to the intrinsic SOC, and the impurity-induced SOC belongs to the extrinsic SOC. Electronic systems with strong spin-orbit couplings exhibit exotic effects, such as the spin Hall effect, the spin current, etc. Also, the well developed techniques on the fabrication of nanostructures with high mobility have provided the necessary basis for the experimental investigation on the spin-orbit coupling effect.
In this dissertation, we investigate the spin transport properties of electrons in systems with spin-orbit couplings. The main results of our investigation are listed as follows, which include four parts. The former three are related to the model design of spin devices with special spin transport properties, and the last is about the study of lifetime of the spin helix.
I. Model design of flying spin-qubit logic gate.
We propose a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Two simple device units are utilized: one-dimensional semiconductor wires with Dresselhaus SOC and Rashba SOC, separately. Qubit information coded by the electron spin can be manipulated effectively by the SOC when passing through the semiconductor wire. The different manipulative behaviors in Dresselhaus and Rashba wires enable us to make the diverse quantum logic gates. By connecting the Dresselhaus and Rashba units in series, we obtain a universal set of single qubit gates: Hadamard, phase, and 7r/8 gates, inferring that an arbitrary single qubit gate can be achieved in the semiconductor nanowires. We also discuss the conditions for the total transmission of the incident electrons, which ensures all the gates obtained are lossless.
II. Bistable switching effect for ballistic transport.
In the spin field-effect-transistor (spin-FET), the outgoing current can be tuned by the spin-orbit coupling. We investigate the spin transport properties in the spin-FET with spatially periodic Rashba structure, and obtain an ideal switching effect. When an appropriate magnitude of Rashba strength is provided, an energy gap can be formed due to the periodic Rashba potential. This causes the incident electrons with energies in the gap to be totally reflected. If the Rashba strength is tuned to be smaller than a critical value, all the incident electrons can be transmitted. Therefore, a stable 'rectangle-type' switching effect can be obtained by controlling the Rashba SOC. The switching effect realized through the periodic Rashba structure is found to be more stable than that realized through a single Rashba segment. The ideal switching effect might be applicable in future nanoelectronic devices.
III. Model design of the spin filter.
The spin filter can generate spin-polarized current out of an unpolarized source. We present two theoretical schemes for spin filters in one-dimensional semiconductor quantum wires with spatially modulated Rashba SOC and weak magnetic field. In the first scheme, the SOC is periodic and the weak magnetic field is applied uniformly along the wire. The periodic Rashba potential results in two coinciding energy gaps for spin-up and spin-down electrons, while the weak magnetic field can separate the two gaps by breaking the time reversal symmetry, and therefore full spin polarizations with opposite signs are obtained within the two separated energy intervals. In the second scheme, the weak magnetic field is periodic while the SOC is uniform. The periodic magnetic field induces two separated energy gaps, and we obtain the spin-up and spin-down current in the two energy intervals. An ideal negative/positive switching effect for spin polarization is realized by tuning the strength of SOC.
IV. Investigation on the lifetime of the spin helix.
Although strong spin-orbit interaction is useful for manipulating the electron spin, it also induces undesired effect of spin relaxation. Bernevig et al discovered a persistent spin helix (PSH) in two special SOC systems, and the lifetime of the spin helix is robust against the spin-independent impurities (Phys. Rev. Lett. 97, 236601 (2006)). However, influence of the impurity-induced SOC, which actually is a very important problem, was not considered in their proposal. In the present work, we investigate the influence of the impurity-induced spin-orbit scattering on the properties of the spin helix, using the method of equations of motion of Green's function. The results show that lifetime of the spin helix is not divergent, and it is closely dependent on the strength of the extrinsic SOC and the impurity density. The intrinsic SOC also has great influence on the lifetime of the spin helix, if the extrinsic SOC is present.
本文研究了自旋轨道耦合体系中电子自旋的输运特性。研究工作包含如下四方面的内容,其中前三方面是关于具有特殊自旋输运性质的自旋器件模型设计,最后一方面是关于自旋螺旋态寿命的研究。
1.飞行自旋比特逻辑门的模型设计
基于自旋电子学的迅速发展,我们提出了飞行自旋比特的固态量子计算模型。器件模型是两个半导体量子线:具有Rashba自旋-轨道耦合作用的量子线和具有Dresselhaus自旋-轨道耦合作用的量子线。在模型中,电子自旋极化态是比特信息的载体,自旋-轨道耦合是控制自旋比特的手段,二维电子气是自旋信息的传输通道。Rashba和Dresselhaus两类自旋-轨道耦合实现了对自旋的两类操纵方式,结合这两类操纵方式(串连两类量子线),我们实现了一套通用的单量子自旋比特逻辑门:Hadamard门,相位门π/8门。另外,我们还计算了电子自旋在器件模型中的透射系数,确保在一定条件下实现全透射,从而使信息在传递中没有损耗。
2.弹道电导双稳开关效应
弹道自旋场效应晶体管中,可以利用自旋-轨道耦合作用调控输出电流。我们研究了具有周期Rashba结构的自旋场效应晶体管中电子自旋的输运性质,并得到理想的开关效应。一定强度的周期Rashba自旋-轨道耦合会产生能隙,当入射电子的能量处在能隙内时,电子不能通过,电导为0,通道处于“断开”状态。减小Rashba自旋-轨道耦合强度至低于某临界值时,电子可以全透射,电导最大,通道处于“闭合”状态。因此,通过调节自旋-轨道耦合强度,我们实现了控制弹道电导的双稳开关效应。利用周期Rashba结构实现的是双稳的开关效应,比利用单个Rashba区实现的开关效应,性能要稳定很多。我们期望这个稳定的开关效应能在未来的纳电子器件中得到应用。
3.自旋过滤器的模型设计
自旋过滤器的功能是使无自旋极化流转变为自旋极化流。利用空间调制的弱磁场和自旋-轨道耦合,我们提出了两种自旋过滤器模型。模型(一)是对半导体量子线施加均一弱磁场和周期Rashba自旋-轨道耦合。周期的Rashba结构产生了一个电子无法通过的能隙,弱磁场破坏体系的时间反演对称性,使原本重合的上自旋能隙和下自旋能隙分离,我们在分离的能隙内分别得到上自旋极化流和下自旋极化流。模型(二)是对量子线施加周期弱磁场和均一自旋-轨道耦合。周期磁场产生分离的上自旋能隙和下自旋能隙,使上自旋极化流和下自旋极化流分布在不同能量区间,调节Rashba自旋-轨道耦合还可以实现上自旋极化流和下自旋极化流的灵活转变。
4自旋螺旋(Spin helix)态寿命的研究
利用自旋-轨道耦合作用控制自旋态时,通常也要考虑其引起的自旋弛豫效应。最近,Bernevig等人在两个特殊的自旋-轨道耦合体系中发现了寿命无限长的自旋螺旋态(Phys.Rev.Lett.97,236601(2006)),而且该自旋螺旋态的寿命不受非磁性杂质的影响。但是Bemevig等人在提出自旋寿命无限长时没有考虑杂质分布可能引起的外禀自旋-轨道耦合对自旋寿命的影响,这其实是一个非常重要的问题。我们运用格林函数运动方程的方法,深入研究了杂质引起的外禀自旋-轨道耦合对自旋螺旋态寿命的影响。结果表明考虑外禀自旋-轨道耦合作用后,自旋螺旋态的寿命不再是无穷大,且自旋螺旋态的寿命强烈的依赖于外禀自旋-轨道耦合强度和杂质密度。此外,研究还发现,内禀自旋-轨道耦合,因为外禀自旋-轨道耦合的存在,会对自旋寿命产生显著的影响。
Spin-orbit coupling (SOC) effect has generated great interest from both academic and practical perspectives. In particular, SOC allows for purely electric manipulation of the electron spin, i.e. magnetic material or external magnetic field is not required, which may result in the ail-electrically controlled spin device, such as the Datta-Das spin field-effect-transistor. In semiconductor two-dimensional electron gas system, there are several typical SOC mechanisms: Rashba SOC, Dresselhaus SOC, and the SOC induced by impurities. Both Rashba and Dresselhaus SOC belong to the intrinsic SOC, and the impurity-induced SOC belongs to the extrinsic SOC. Electronic systems with strong spin-orbit couplings exhibit exotic effects, such as the spin Hall effect, the spin current, etc. Also, the well developed techniques on the fabrication of nanostructures with high mobility have provided the necessary basis for the experimental investigation on the spin-orbit coupling effect.
In this dissertation, we investigate the spin transport properties of electrons in systems with spin-orbit couplings. The main results of our investigation are listed as follows, which include four parts. The former three are related to the model design of spin devices with special spin transport properties, and the last is about the study of lifetime of the spin helix.
I. Model design of flying spin-qubit logic gate.
We propose a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Two simple device units are utilized: one-dimensional semiconductor wires with Dresselhaus SOC and Rashba SOC, separately. Qubit information coded by the electron spin can be manipulated effectively by the SOC when passing through the semiconductor wire. The different manipulative behaviors in Dresselhaus and Rashba wires enable us to make the diverse quantum logic gates. By connecting the Dresselhaus and Rashba units in series, we obtain a universal set of single qubit gates: Hadamard, phase, and 7r/8 gates, inferring that an arbitrary single qubit gate can be achieved in the semiconductor nanowires. We also discuss the conditions for the total transmission of the incident electrons, which ensures all the gates obtained are lossless.
II. Bistable switching effect for ballistic transport.
In the spin field-effect-transistor (spin-FET), the outgoing current can be tuned by the spin-orbit coupling. We investigate the spin transport properties in the spin-FET with spatially periodic Rashba structure, and obtain an ideal switching effect. When an appropriate magnitude of Rashba strength is provided, an energy gap can be formed due to the periodic Rashba potential. This causes the incident electrons with energies in the gap to be totally reflected. If the Rashba strength is tuned to be smaller than a critical value, all the incident electrons can be transmitted. Therefore, a stable 'rectangle-type' switching effect can be obtained by controlling the Rashba SOC. The switching effect realized through the periodic Rashba structure is found to be more stable than that realized through a single Rashba segment. The ideal switching effect might be applicable in future nanoelectronic devices.
III. Model design of the spin filter.
The spin filter can generate spin-polarized current out of an unpolarized source. We present two theoretical schemes for spin filters in one-dimensional semiconductor quantum wires with spatially modulated Rashba SOC and weak magnetic field. In the first scheme, the SOC is periodic and the weak magnetic field is applied uniformly along the wire. The periodic Rashba potential results in two coinciding energy gaps for spin-up and spin-down electrons, while the weak magnetic field can separate the two gaps by breaking the time reversal symmetry, and therefore full spin polarizations with opposite signs are obtained within the two separated energy intervals. In the second scheme, the weak magnetic field is periodic while the SOC is uniform. The periodic magnetic field induces two separated energy gaps, and we obtain the spin-up and spin-down current in the two energy intervals. An ideal negative/positive switching effect for spin polarization is realized by tuning the strength of SOC.
IV. Investigation on the lifetime of the spin helix.
Although strong spin-orbit interaction is useful for manipulating the electron spin, it also induces undesired effect of spin relaxation. Bernevig et al discovered a persistent spin helix (PSH) in two special SOC systems, and the lifetime of the spin helix is robust against the spin-independent impurities (Phys. Rev. Lett. 97, 236601 (2006)). However, influence of the impurity-induced SOC, which actually is a very important problem, was not considered in their proposal. In the present work, we investigate the influence of the impurity-induced spin-orbit scattering on the properties of the spin helix, using the method of equations of motion of Green's function. The results show that lifetime of the spin helix is not divergent, and it is closely dependent on the strength of the extrinsic SOC and the impurity density. The intrinsic SOC also has great influence on the lifetime of the spin helix, if the extrinsic SOC is present.
引文
[1] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[2] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109 (1960)].
[3] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[4] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
[5] L. Hu, Z. Huang, and S. Hu, Phys. Rev. B 73, 235314 (2006).
[6] W. K. Tse and S. D. Sarma, Phys. Rev. Lett. 96, 056601 (2006); Phys. Rev. B 74, 245309 (2006).
[7] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306,1910 (2004).
[8] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).
[9] T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Phys. Rev. Lett. 98, 156601 (2007).
[10] N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and D. D. Awschalom, Phys. Rev. Lett. 97, 126603 (2006).
[11] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[12] J. Schliemann, J.C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).
[13] Q. F. Sun, X. C. Xie, and J. Wang, Phys. Rev. B 77, 035327 (2008).
[14] S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003).
[15] A. Wong, J. A. Maytorena, C. Lopez-Bastidas, and F. Mireles Phys. Rev. B 77, 035304 (2008).
[16] L. Jian and S. Q. Shen, Phys. Rev. B 76, 153302 (2007).
[17] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[18] A. E. Popescu and R. Ionicioiu, Phys. Rev. B 69, 245422 (2004).
[19] J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Phys. Rev. Lett. 78 1335 (1997).
[20] J. Schliemann, D. Loss, Phys. Rev. B 68,165311 (2003).
[21] S. Bandyopadhyay, M. Cahay, Appl. Phys. Lett. 85, 1814 (2004).
[22] L. Jiang and M.W. Wu, Phys. Rev. B 72, 033311 (2005).
[23] B. A. Bernevig, J. Orenstein, and S. C Zhang, Phys. Rev. Lett. 97,236601 (2006).
[24] D. Stepanenko and N. E. Bonesteel, Phys. Rev. Lett. 93,140501 (2004).
[25] Y. K. Kato, R. C. Myers, A. C. Gossard and D. D. Awschalom, Science, 306,1910 (2004).
[26] M. I. Dyakonov and V. I. Perel, Sov. Phys. JETP 33,467 (1971);
[1] D. K. Ferry and S. M. Goodnick, 1997 Transport in Nanostructures (New York: Cambridge University Press)
[2] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[3] J. B. Xia, Phys. Rev. B 45, 3593 (1992).
[4] J. Yao and Z. Q. Yang, Phys. Rev. B 73, 033314 (2006).
[5] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[6] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109 (1960)].
[1] B.E. Kane, Nature 393, 133 (1998).
[2] M. D. Bowdrey and J. A. Jones, Phys. Rev. A 74 052324 (2006).
[3] D. Loss and P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[4] S. Bandyopadhyay, Phys. Rev. B 61, 13813 (2000).
[5] D. Stepanenko and N. E. Bonesteel, Phys. Rev. Lett. 93, 140501 (2004).
[6] A. E. Popescu and R. Ionicioiu, Phys. Rev. B 69, 245422 (2004).
[7] J. M. Kikkawa and D. D. Awschalom, Nature (London) 397,139 (1999).
[8] Y. Kato, C. Myers, A. C. Gossard and D. D. Awschalom, Nature 427, 50 (2004).
[9] P. Foldi, B. Molnar, M. G. Benedict, and F. M. Peeters, Phys. Rev. B 71, 033309 (2005).
[10] T. Matsuyama, C.-M. Hu, D. Grundler, G. Meier, U. Merkt, Phys. Rev. B 65, 155322 (2002).
[11] C.-M. Hu and T. Matsuyama, Phys. Rev. Lett. 87,066803 (2001).
[12] J. Yao and Z. Q. Yang, Phys. Rev. B 73, 033314 (2006).
[13] Y. T. Zhang, Y. Guo, and Y C. Li, Phys. Rev. B, 72, 125334 (2005).
[14] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[1] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[2] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109(1960)].
[3] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[4] K. M. Jiang, Z. M. Zheng, Baigeng Wang, and D. Y. Xing, Appl. Phys. Lett. 89, 012105 (2006).
[5] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[6] T. Matsuyama, C.-M. Hu, D. Grundler, G. Meier, U. Merkt, Phys. Rev. B 65, 155322 (2002).
[7] C.-M. Hu, T. Matsuyama, Phys. Rev. Lett. 87,066803 (2001).
[8] J. Yao and Z.Q. Yang, Phys. Rev. B 73,033314 (2006).
[9] Y. T. Zhang, Y. Guo, and Y. C. Li, Phys. Rev. B, 72, 125334 (2005).
[10] S Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[1] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[2] A. T. Filip, B. H. Hoving, F.J. Jedema, B.J. van Wees, B. Dutta, S. Borghs, Phys. Rev. B 62, 9996 (2000).
[3] G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, B. J. van Wees, Phys. Rev. B 62, R4790 (2000).
[4] J. C. Egues, C. Gould, G. Richter, and L. W Molenkamp, Phys. Rev. B 64,195319 (2001).
[5] Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, D.D. Awschalom, Nature (London) 402, 787 (1999).
[6] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, Nature (London) 402, 790 (1999).
[7] F. Zhai and H. Q. Xu, Appl. Phys. Lett. 88, 032502 (2006); F. Zhai and H. Q. Xu, PHYSICAL REVIEW B 72, 085314 (2005)
[8] Q. W Shi, J. Zhou, and M. W. Wu, Appl. Phys. Lett. 85, 2547 (2004).
[9] M. W. Lu and X. H. Yan, Phys. Lett. A 358,478 (2006).
[10] Y. Huai, M. Pakala, Z. Diao, and Y. Ding, Appl. Phys. Lett. 87, 222510 (2005).
[11] G. Papp and F. M. Peeters, Appl. Phys. Lett. 78, 2184 (2001).
[12] P. Streda and P. seba, Phys. Rev. Lett. 90, 256601 (2003).
[13] I. A. Shelykh, N. G. Galkin, and N. T. Bagraev, Phys. Rev. B 72, 235316 (2005).
[14] A. W. Cummings, R. Akis, and D. K. Ferry, Appl. Phys. Lett. 89, 172115 (2006).
[15] A. A. Kiseleva and K. W. Kim, Appl. Phys. Lett. 78, 775 (2001).
[16] S. Pramanik, S. Bandyopadhyay, and M. Cahay, IEEE Trans. Nanotechnol. 4, 2 (2005).
[17]T.Matsuyama,C.-M.Hu,D.Grundler,G.Meier,and U.Merkt,Phys.Rev.B 65,155322(2002).
[18]U.Zulicke and C.Schroll,Phys.Rev.Lett.88,029701(2002).
[19]Q.F.Sun and X.C.Xie,Phys.Rev.B,71,155321(2005).
[20]L.G.Wang and K.Chang,Solid State Commun.137,260(2006).
[1] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).
[2] Y. K. Kato, R. C. Myers, A. C. Grossard, and D. D. Awschalom, Science 306, 1910 (2004).
[3] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[4] J. Schliemann, J.C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).
[5] Q. F. Sun, X. C. Xie, and J. Wang, Phys. Rev. B 77, 035327 (2008).
[6] S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003).
[7] B. K. Nikolic, and S. Souma, Phys. Rev. B 71, 195328 (2005).
[8] Y. V. Pershin, V. Privman, Phys. Rev. B 69, 073310 (2004).
[9] P. H. Song, K. W. Kim, Phys. Rev. B 66, 035207 (2002).
[10] J. S. Sandhu, A. P. Heberle, J. J. Baumberg, J. R. A. Cleaver, Phys. Rev. Lett. 86, 2150(2001).
[11] A. Tackeuchi and O. Wada, Appl. Phys. Lett. 70, 1033 (1991).
[12] M. I. D'yakonov and V. I. Perel', Sov. Phys. Solid State 13, 3023 (1972).
[13] B. A. Bernevig, J. Orenstein, and S. C Zhang, Phys. Rev. Lett. 97,236601 (2006).
[14] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[15] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960) [Solid State Ion. 2,1109 (1960)].
[16] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[17] C. P. Weber,l J. Orenstein, B.A. Bernevig, S. C Zhang, J. Stephens, and D. D. Awschalom. Phys. Rev. Lett. 98, 076604 (2007)
[18] M. H. Liu, K. W. Chen, S. H. Chen, and C. R. Chang, Phys. Rev. B 74, 235322 (2006).
[19] M. Ohno and K. Yoh, Phys. Rev. B 75, 241308(R)(2007).
[20] A. R. Cameron, P. Riblet, and A. Miller, Phys. Rev. Lett. 76,4793 (1996).
[21] C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, D. D. Awschalom, Nature 437, 1330(2005).
[22] W. K. Tse and S. D. Sarma, Phys. Rev. Lett. 96, 056601 (2006). Phys. Rev. B 74, 245309 (2006).
[2] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109 (1960)].
[3] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[4] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
[5] L. Hu, Z. Huang, and S. Hu, Phys. Rev. B 73, 235314 (2006).
[6] W. K. Tse and S. D. Sarma, Phys. Rev. Lett. 96, 056601 (2006); Phys. Rev. B 74, 245309 (2006).
[7] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306,1910 (2004).
[8] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).
[9] T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Phys. Rev. Lett. 98, 156601 (2007).
[10] N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and D. D. Awschalom, Phys. Rev. Lett. 97, 126603 (2006).
[11] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[12] J. Schliemann, J.C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).
[13] Q. F. Sun, X. C. Xie, and J. Wang, Phys. Rev. B 77, 035327 (2008).
[14] S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003).
[15] A. Wong, J. A. Maytorena, C. Lopez-Bastidas, and F. Mireles Phys. Rev. B 77, 035304 (2008).
[16] L. Jian and S. Q. Shen, Phys. Rev. B 76, 153302 (2007).
[17] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[18] A. E. Popescu and R. Ionicioiu, Phys. Rev. B 69, 245422 (2004).
[19] J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Phys. Rev. Lett. 78 1335 (1997).
[20] J. Schliemann, D. Loss, Phys. Rev. B 68,165311 (2003).
[21] S. Bandyopadhyay, M. Cahay, Appl. Phys. Lett. 85, 1814 (2004).
[22] L. Jiang and M.W. Wu, Phys. Rev. B 72, 033311 (2005).
[23] B. A. Bernevig, J. Orenstein, and S. C Zhang, Phys. Rev. Lett. 97,236601 (2006).
[24] D. Stepanenko and N. E. Bonesteel, Phys. Rev. Lett. 93,140501 (2004).
[25] Y. K. Kato, R. C. Myers, A. C. Gossard and D. D. Awschalom, Science, 306,1910 (2004).
[26] M. I. Dyakonov and V. I. Perel, Sov. Phys. JETP 33,467 (1971);
[1] D. K. Ferry and S. M. Goodnick, 1997 Transport in Nanostructures (New York: Cambridge University Press)
[2] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[3] J. B. Xia, Phys. Rev. B 45, 3593 (1992).
[4] J. Yao and Z. Q. Yang, Phys. Rev. B 73, 033314 (2006).
[5] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[6] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109 (1960)].
[1] B.E. Kane, Nature 393, 133 (1998).
[2] M. D. Bowdrey and J. A. Jones, Phys. Rev. A 74 052324 (2006).
[3] D. Loss and P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[4] S. Bandyopadhyay, Phys. Rev. B 61, 13813 (2000).
[5] D. Stepanenko and N. E. Bonesteel, Phys. Rev. Lett. 93, 140501 (2004).
[6] A. E. Popescu and R. Ionicioiu, Phys. Rev. B 69, 245422 (2004).
[7] J. M. Kikkawa and D. D. Awschalom, Nature (London) 397,139 (1999).
[8] Y. Kato, C. Myers, A. C. Gossard and D. D. Awschalom, Nature 427, 50 (2004).
[9] P. Foldi, B. Molnar, M. G. Benedict, and F. M. Peeters, Phys. Rev. B 71, 033309 (2005).
[10] T. Matsuyama, C.-M. Hu, D. Grundler, G. Meier, U. Merkt, Phys. Rev. B 65, 155322 (2002).
[11] C.-M. Hu and T. Matsuyama, Phys. Rev. Lett. 87,066803 (2001).
[12] J. Yao and Z. Q. Yang, Phys. Rev. B 73, 033314 (2006).
[13] Y. T. Zhang, Y. Guo, and Y C. Li, Phys. Rev. B, 72, 125334 (2005).
[14] S. Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[1] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[2] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2,1224 (1960) [Solid State Ion. 2,1109(1960)].
[3] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[4] K. M. Jiang, Z. M. Zheng, Baigeng Wang, and D. Y. Xing, Appl. Phys. Lett. 89, 012105 (2006).
[5] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[6] T. Matsuyama, C.-M. Hu, D. Grundler, G. Meier, U. Merkt, Phys. Rev. B 65, 155322 (2002).
[7] C.-M. Hu, T. Matsuyama, Phys. Rev. Lett. 87,066803 (2001).
[8] J. Yao and Z.Q. Yang, Phys. Rev. B 73,033314 (2006).
[9] Y. T. Zhang, Y. Guo, and Y. C. Li, Phys. Rev. B, 72, 125334 (2005).
[10] S Datta, Electronic Transport in Mesoscopic System (New York: Cambridge University Press), 1995.
[1] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[2] A. T. Filip, B. H. Hoving, F.J. Jedema, B.J. van Wees, B. Dutta, S. Borghs, Phys. Rev. B 62, 9996 (2000).
[3] G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, B. J. van Wees, Phys. Rev. B 62, R4790 (2000).
[4] J. C. Egues, C. Gould, G. Richter, and L. W Molenkamp, Phys. Rev. B 64,195319 (2001).
[5] Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, D.D. Awschalom, Nature (London) 402, 787 (1999).
[6] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, Nature (London) 402, 790 (1999).
[7] F. Zhai and H. Q. Xu, Appl. Phys. Lett. 88, 032502 (2006); F. Zhai and H. Q. Xu, PHYSICAL REVIEW B 72, 085314 (2005)
[8] Q. W Shi, J. Zhou, and M. W. Wu, Appl. Phys. Lett. 85, 2547 (2004).
[9] M. W. Lu and X. H. Yan, Phys. Lett. A 358,478 (2006).
[10] Y. Huai, M. Pakala, Z. Diao, and Y. Ding, Appl. Phys. Lett. 87, 222510 (2005).
[11] G. Papp and F. M. Peeters, Appl. Phys. Lett. 78, 2184 (2001).
[12] P. Streda and P. seba, Phys. Rev. Lett. 90, 256601 (2003).
[13] I. A. Shelykh, N. G. Galkin, and N. T. Bagraev, Phys. Rev. B 72, 235316 (2005).
[14] A. W. Cummings, R. Akis, and D. K. Ferry, Appl. Phys. Lett. 89, 172115 (2006).
[15] A. A. Kiseleva and K. W. Kim, Appl. Phys. Lett. 78, 775 (2001).
[16] S. Pramanik, S. Bandyopadhyay, and M. Cahay, IEEE Trans. Nanotechnol. 4, 2 (2005).
[17]T.Matsuyama,C.-M.Hu,D.Grundler,G.Meier,and U.Merkt,Phys.Rev.B 65,155322(2002).
[18]U.Zulicke and C.Schroll,Phys.Rev.Lett.88,029701(2002).
[19]Q.F.Sun and X.C.Xie,Phys.Rev.B,71,155321(2005).
[20]L.G.Wang and K.Chang,Solid State Commun.137,260(2006).
[1] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).
[2] Y. K. Kato, R. C. Myers, A. C. Grossard, and D. D. Awschalom, Science 306, 1910 (2004).
[3] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[4] J. Schliemann, J.C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).
[5] Q. F. Sun, X. C. Xie, and J. Wang, Phys. Rev. B 77, 035327 (2008).
[6] S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003).
[7] B. K. Nikolic, and S. Souma, Phys. Rev. B 71, 195328 (2005).
[8] Y. V. Pershin, V. Privman, Phys. Rev. B 69, 073310 (2004).
[9] P. H. Song, K. W. Kim, Phys. Rev. B 66, 035207 (2002).
[10] J. S. Sandhu, A. P. Heberle, J. J. Baumberg, J. R. A. Cleaver, Phys. Rev. Lett. 86, 2150(2001).
[11] A. Tackeuchi and O. Wada, Appl. Phys. Lett. 70, 1033 (1991).
[12] M. I. D'yakonov and V. I. Perel', Sov. Phys. Solid State 13, 3023 (1972).
[13] B. A. Bernevig, J. Orenstein, and S. C Zhang, Phys. Rev. Lett. 97,236601 (2006).
[14] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[15] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960) [Solid State Ion. 2,1109 (1960)].
[16] G. Dresslehaus, Phys. Rev. 100, 580 (1955).
[17] C. P. Weber,l J. Orenstein, B.A. Bernevig, S. C Zhang, J. Stephens, and D. D. Awschalom. Phys. Rev. Lett. 98, 076604 (2007)
[18] M. H. Liu, K. W. Chen, S. H. Chen, and C. R. Chang, Phys. Rev. B 74, 235322 (2006).
[19] M. Ohno and K. Yoh, Phys. Rev. B 75, 241308(R)(2007).
[20] A. R. Cameron, P. Riblet, and A. Miller, Phys. Rev. Lett. 76,4793 (1996).
[21] C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, D. D. Awschalom, Nature 437, 1330(2005).
[22] W. K. Tse and S. D. Sarma, Phys. Rev. Lett. 96, 056601 (2006). Phys. Rev. B 74, 245309 (2006).
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