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arXiv 0907.1819cond-mat.mes-hallcond-mat.dis-nn
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Rashba自旋轨道耦合量子线中弱局域化修正和自旋弛豫的维数依赖性

Dimensional Dependence of Weak Localization Corrections and Spin Relaxation in Quantum Wires with Rashba Spin-Orbit Coupling

P. Wenk, S. Kettemann

摘要:

得到了具有线性Rashba自旋轨道耦合的无序量子线电导率的量子修正。对于具有自旋守恒边界条件的量子线,我们发现了从弱反到弱局域化的交叉,因为使用Cooperon方程的精确对角化减少了线宽W。这种交叉是由于传导电子的自旋弛豫速率的尺寸依赖性,当线宽度小于体自旋进动长度$L_{SO}$时,传导电子的自旋弛豫速率减小。因此,我们确认了先前对于小线宽$W/L_{SO}<= 1$ [PRL 98,176808(2007)]的结果,其中仅考虑了Cooperon方程的横向0-模式。我们发现,自旋螺旋的解决方案变得稳定的任意比例的线性Rashba和Dresselhaus耦合在狭窄的电线。对于较宽的线,自旋弛豫率被发现是不单调的线宽度的函数:它成为第一个增强的W上的顺序的散装$L_{SO}$之前,它成为减小较小的线宽度。此外,我们发现,自旋弛豫是最小的线的边缘宽的电线。研究了塞曼耦合对垂直于二维电子系统的磁场的影响,发现它使交叉从弱反到弱局域转移到更大的线宽$W_c$。当量子线的横向限制势是平滑的(绝热的)时,自旋弛豫速率被发现随着W的减小而增强。我们发现,只有一个自旋极化态保持有限的自旋弛豫率在这样的窄线。因此,我们得出结论,极化自旋注入到双量子线应该是有利的线与光滑的限制势。最后,在与横向周期性边界条件对应的管状导线中,我们发现自旋弛豫率没有降低。

英文摘要:

The quantum correction to the conductivity in disordered quantum wires with linear Rashba spin-orbit coupling is obtained. For quantum wires with spin-conserving boundary conditions, we find a crossover from weak anti- to weak localization as the wire width W is reduced using exact diagonalization of the Cooperon equation. This crossover is due to the dimensional dependence of the spin relaxation rate of conduction electrons, which becomes diminished, when the wire width is smaller than the bulk spin precession length $L_{SO}$. We thus confirm previous results for small wire width, $W/L_{SO}<= 1$ [PRL98,176808(2007)], where only the transverse 0-modes of the Cooperon equation had been taken into account. We find that spin helix solutions become stable for arbitrary ratios of linear Rashba and Dresselhaus coupling in narrow wires. For wider wires, the spin relaxation rate is found to be not monotonous as function of wire width: it becomes first enhanced for W on the order of the bulk $L_{SO}$ before it becomes diminished for smaller wire widths. In addition, we find that the spin relaxation is smallest at the edge of the wire for wide wires. The effect of the Zeeman coupling to the magnetic field perpendicular to the 2D electron system is studied and found that it shifts the crossover from weak anti- to weak localization to larger wire widths $W_c$. When the transverse confinement potential of the quantum wire is smooth (adiabatic), the spin relaxation rate is found to be enhanced as W is reduced. We find that only a spin polarized state retains a finite spin relaxation rate in such narrow wires. Thus, we conclude that the injection of polarized spins into nonmagnetic quantum wires should be favorable in wires with smooth confinement potential. Finally, in wires with tubular shape, corresponding to transverse periodic boundary conditions, we find no reduction of the spin relaxation rate.

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