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

Abstract

By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the nonrelativistic 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. In particular, 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.