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Relativistic electronic properties of a nanospring under a static magneticfield are theoretically investigated in the present study. The wave equationaccounting for the spin-orbit interaction is derived for the nanospring as aspecial case of the Pauli equation for a spin-1/2 particle confined to a curvedsurface under an electromagnetic field. We define the helical momentum operatorand show that it commutes with the Hamiltonian owing to the helical geometry ofthe nanospring. The energy eigenstates are hence also the eigenstates of thehelical momentum. We solve the equation numerically to obtain the surface wavefunctions and the energy spectra. The electronic properties are systematicallyexamined by varying the parameters that characterize the system. It isdemonstrated that either the nonzero spin-orbit interaction or the nonzeroexternal magnetic field suffices for the occurrence of the persistent spincurrent on the nanospring. Two different mechanisms are shown to generate thepersistent spin current. One employs the spin-orbit interaction coming from thelocal inversion asymmetry on the surface, while the other employs the curvaturecoupling with the external magnetic field.

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