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arXiv · 1808.09959

Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface

Guo-Hua Liang·Yong-Long Wang·Meng-Yun Lai·Hui Liu·Hong-Shi Zong·Shi-Ning Zhu
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Abstract

By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the non-relativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic field and an effective spin-orbit interaction generated by the spin connection. Geometrically, the pseudo-magnetic field is proportional to the Gaussian curvature and the effective spin-orbit interaction is determined by the Weingarten curvature tensor. Particularly, we find that the pseudo-magnetic field and the effective spin-orbit interaction can be employed to separate the electrons with different spin orientations. All these results are demonstrated in two examples, a straight cylindrical surface and a bent one.

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Guo-Hua Liang, Yong-Long Wang, Meng-Yun Lai, Hui Liu, Hong-Shi Zong, Shi-Ning Zhu. 2018-08-29. Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface. https://doi.org/10.1103/physreva.98.062112

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