Electronic Properties and Persistent Spin Currents of Nanospring under Static Magnetic Field

TL;DR

This study theoretically investigates the relativistic electronic properties of a nanospring under a static magnetic field, revealing mechanisms for persistent spin currents driven by spin-orbit interaction and curvature effects.

Contribution

It derives a spin-orbit-inclusive wave equation for nanosprings, introduces the helical momentum operator, and demonstrates two mechanisms for persistent spin current generation.

Findings

Persistent spin current occurs with nonzero spin-orbit interaction or magnetic field.

Two mechanisms for spin current generation: surface inversion asymmetry and curvature coupling.

Energy spectra and wave functions are numerically obtained and analyzed.

Abstract

Relativistic electronic properties of a nanospring under a static magnetic field are theoretically investigated in the present study. The wave equation accounting for the spin-orbit interaction is derived for the nanospring as a special case of the Pauli equation for a spin-1/2 particle confined to a curved surface under an electromagnetic field. We define the helical momentum operator and show that it commutes with the Hamiltonian owing to the helical geometry of the nanospring. The energy eigenstates are hence also the eigenstates of the helical momentum. We solve the equation numerically to obtain the surface wave functions and the energy spectra. The electronic properties are systematically examined by varying the parameters that characterize the system. It is demonstrated that either the nonzero spin-orbit interaction or the nonzero external magnetic field suffices for the occurrence of the persistent spin current on the nanospring. Two different mechanisms are shown to generate the persistent spin current. One employs the spin-orbit interaction coming from the local inversion asymmetry on the surface, while the other employs the curvature coupling with the external magnetic field.