我們研究了在ballistic尺度下，電子自旋在奈米線裡受到Rashba自旋軌道效應影響下的的極化現象。解析上，我們計算了奈米線內被允許的電子特徵波函數及其對應之垂直平面自旋分量分佈。在這些特徵態的垂直平面自旋分量分佈中，我們發現了其相鄰態的對偶性。此外，我們亦由對稱性的分析，說明此垂直平面的自旋分量在橫切面上必為反對稱；並且，其值只有在時間反向對稱被破壞時才不為零。我們並且使用Open Boundary Supercell Stack Method 對此系統作了數值分析。數值結果顯示，此自旋堆積現象在考慮微弱的晶格點隨機位能時，依然保持原型；但若隨機位能太強，則會被抑制。而通道內的固定雜質亦造成自旋堆積的改變。當通道兩側邊界有粗糙表面時，此粗糙的程度會將自旋堆積往通道內推擠，並且會減低自旋極化堆積的程度。

We study the the spin polarization in nano-wire in presence of Rashba spin orbit interaction in ballistic regime. Analytically, we calculate the allowed eigenstates in the wire and their corresponding out-of-plane component of spin distribution. Among the out-of-plane component of spin for the eigenstates, we find the parity effect between every other states. From the symmetry arguments, we show that the out-of-plane component of spin must be anti-symmetric in the lateral direction, and that it is non-zero only when the time-reversal symmetry property of the system is broken. We also study the system numerically with
Open-boundary Planar Supercell Stack Method. The numerical results show that the spin accumulation remains in the presence of weak disorder potential but is diminished
when the disorder potential is large. With the existence of impurity in the system, we show that it does excite out-of-plane spin component unlike the prediction of the general
scattering analysis. In the presence of surface roughness, the spin accumulation is pushed away from the edges and the amplitude of the accumulation decrease as the roughness
becomes strong.

[1] S. Datta and B. Das, Appl. Phys. Lett., 56, 665 (1990).
[2] M. I. D'yakonov and V. I. Perel', JEPT Lett., 13,467, (1971).
[3] L.-J. Cui et al., App. Phys. Lett., 80, 3132 (2002).
[4] J. E. Hirsch, Phys. Rev. Lett., 83, 1834 (1999).
[5] S. Zhang, Phys. Rev. Lett., 85, 393 (2000).
[6] J. Sinova et al., Phys. Rev. Lett., 92, 126603 (2004).
[7] Y.K. Kato et al., Science, 306, 1910 (2004).
[8] B. Jusserand et al., Phys. Rev. B, 51, 4707 (1995).
[9] J. Nitta et al., Phys. Rev. Lett.,78, 1335 (1997).
[10] J. Sinova et al., cond-mat/0412595 (2004).
[11] Kirby, S. K.,Ting, D. Z.-T. McGill, T. C. J. Vac. Sci. Technol. B,, 11, 1738 (1993).
[12] D. Z.-Y. Ting, S. K. Kirby, and T. C. McGill,J. Vac. Sci. Technol. B,, 11, 1738(1994).
[13] H. Imamura et al., Phys. Rev. B,69, 121303(R) (2004).