Spin transport and spin Hall effect in an electron waveguide in the presence of an in-plane magnetic field and spin-orbit interaction
Spin transport and spin Hall effect in an electron waveguide in the presence of an in-plane magnetic field and spin-orbit interaction
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存在面内磁场和自旋轨道相互作用的电子波导中的自旋输运和自旋霍尔效应
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发表时间：
2007
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通讯作者：
Hongqi Xu
中科院分区：
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作者：
P. Brusheim;Hongqi Xu
我们研究了存在Rashba自旋轨道相互作用(SOI)和均匀面内磁场的量子波导中的电子自旋输运和自旋霍尔效应，以及相应无限大系统中电子态的能量色散关系和自旋极化性质。在没有自旋简并引线的假设下，导出了任意极化注入源产生的出射磁通的自旋极化的一般表达式。通过对系统对称性的分析，进一步推导出系统自旋分辨传输系数的约束条件。这些约束将对依赖于自旋的电导以及出射磁通的自旋极化施加限制。对于平行于波导的平面内磁场，当塞曼能量超过拉什巴能量时，由于与外加磁场的自旋对齐，电导振荡随SOI强度的变化而减小。此外，计算得到的SOI波导区的自旋几率分布和电荷几率分布分别表现为自旋霍尔型和齐特贝维型。对于外加横向面内磁场，SOI感生有效磁场与外加磁场平行或反平行。系统的电导主要由自旋守恒的输运过程决定，而自旋翻转输运过程只能通过通道间散射发生，因此受到极大的抑制。此外，当电子从具有自旋极化的铅沿外加的面内横场方向注入时，在SOI区没有发现电荷密度分布中的Zitterbewegung图案。然而，在SOI区，自旋极化概率分布仍然可以表现为自旋霍尔图案，并且可以通过调节外加磁场强度来反转自旋霍尔图案中的自旋极化符号。对于具有均匀SOI和面内磁场的无限大波导系统，我们证明了外加的面内磁场和SOI诱导的有效磁场之间的相互作用，以及子带杂化，将产生具有丰富特征的与波矢相关的Bloch态的自旋极化，这些特征不能用简单的一维模型来捕捉。
We study electron spin transport and the spin Hall effect in a quantum waveguide in the presence of Rashba spin-orbit interaction (SOI) and a homogeneous in-plane magnetic field, as well as the energy dispersion relation and spin polarization properties of the electron states in the corresponding infinite system. A general expression for the spin polarization of the outgoing flux, resulting from an arbitrarily polarized injection source, is derived for the quantum waveguide without the assumption of spin-degenerate leads. We further derive constraints on the spin-resolved transmission coefficients by analyzing the symmetries of the system. These constraints will impose restrictions on the spin-dependent conductances as well as the spin polarization of the outgoing flux. For an applied in-plane magnetic field parallel to the waveguide, conductance oscillations as a function of the SOI strength are diminished when the Zeeman energy exceeds the Rashba energy, due to spin alignment with the applied magnetic field. Furthermore, the calculated spin and charge probability distributions in the SOI waveguide region show spin Hall patterns and zitterbewegung patterns, respectively. For an applied transverse in-plane magnetic field, the SOI induced effective magnetic field is parallel or antiparallel with the applied field. The conductance of the system is then dominantly determined by spin-conserved transport processes, and spin-flipped transport processes can occur only through interchannel scattering and are therefore greatly suppressed. Furthermore, no zitterbewegung pattern in the charge density distribution can be found in the SOI region when the electrons are injected from a lead with spin polarization along the applied in-plane transverse field direction. However, the spin polarization probability distribution can still show a spin Hall pattern in the SOI region and the sign of the spin polarization in the spin Hall pattern can be reversed by tuning the applied magnetic field strength. For the corresponding infinite waveguide systems with uniform SOI and in-plane magnetic field, we show that the interplay between the applied in-plane magnetic field and the SOI induced effective magnetic field, together with subband hybridizations, will create a wave-vector-dependent spin polarization of the Bloch states with rich features and that these features cannot be captured by employing a simple one-dimensional model.