受空间曲线约束的自旋轨道耦合电子的量子力学
Quantum mechanics of a spin-orbit coupled electron constrained to a space curve
摘要：
本文导出了电子在空间曲线上运动的有效一维薛定谔-泡利方程。电子被限制使用一个双薄壁量子化程序与绝热分离的快速和缓慢的量子自由度。这个过程是能够产生一个正确的埃尔米特一维薛定谔-泡利算子。我们发现，扭曲的空间曲线产生一个额外的量子几何势，添加到著名的曲率诱导的。最后，我们导出了纳米螺旋线中自旋轨道耦合电子的一维哈密顿量的解析形式。
英文摘要：
We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow quantum degrees of freedom. This procedure is capable of yielding a correct Hermitian one-dimensional Schrodinger-Pauli operator. We find that the torsion of the space curve generates an additional quantum geometric potential, adding to the well-known curvature-induced one. Finally, we derive an analytic form of the one-dimensional Hamiltonian for spin-orbit coupled electrons in a nanoscale helical wire.
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