| Summary: | 博士 === 國立臺灣大學 === 應用物理所 === 101 === 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.
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