彎曲結構中的非線性自旋軌道耦合效應

The Nonlinear Spin-Orbit Coupling Effects in Curved Structures

張鑑源(Jian-Yuan Chang)

指導教授 ： 張慶瑞

國立臺灣大學/理學院/應用物理所/博士(2013年)

https://doi.org/10.6342/NTU.2013.01723

摘要

對於Rashba自旋軌道耦合與Dresselhaus自旋軌道耦合在一個具有任意形狀的曲面中，其精確的哈密頓函數被嚴謹地推導獲得。我們發現兩個正交的主曲率可以控制電子的自旋傳輸，而且在曲面正交方向的局限位勢的漸近行為則是可以忽略的。另外我們也發現高階的動量項在大曲率的曲面中發揮了重要的作用。曲面中的線性自旋軌道耦合只誘導產生額外的虛位勢項，然而曲面中的非線性自旋軌道耦合則會誘導產生額外的虛動能項、虛動量項以及虛位勢項。由於額外的曲率誘導項以及關聯虛磁場的作用，曲面中的自旋傳輸是不相同於在平面中的。我們也明確地推導獲得在柱面或球面中的自旋軌道耦合的哈密頓函數，而且在奈米圓環中的自旋進動以及關聯本徵態也被詳細地分析研究。因此我們推論曲率會顯著影響彎曲結構中的自旋軌道耦合與自旋傳輸。

關鍵字

自旋軌道耦合 ； 自旋傳輸 ； 非線性動量 ； 幾何位勢 ； 主曲率

並列摘要

The exact Hamiltonians for Rashba and Dresselhaus spin-orbit couplings on a curved surface with an arbitrary shape are rigorously derived. Two orthogonal principal curvatures dominate the electronic spin transport, and the asymptotic behavior of the normal confined potential on a curved surface is insignificant. For a curved surface with a large curvature, the higher order momentum terms play an important role in controlling spin transport. The linear spin-orbit coupling on a curved surface only induces the extra pseudo-potential term, and the cubic spin-orbit coupling on a curved surface can induce the extra pseudo-kinetic, pseudo-momentum, and pseudo-potential terms. Because of the extra curvature-induced terms and the associated pseudo-magnetic fields, spin transport on a curved surface is very different from that on a flat surface. The spin-orbit Hamiltonians on a cylindrical or spherical surface are explicitly derived here, and the spin precession and the associated eigenstates on a nanoring are analyzed in detail. We can conclude that the curvature has a significant influence on the spin-orbit coupling and spin transport in curved structures.

並列關鍵字

spin-orbit coupling ； spin transport ； nonlinear momentum ； geometric potential ； principal curvature

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