Persistent Currents in Helical Structures

Recent discovery of mesoscopic electronic structures, in particular the carbon nanotubes, made necessary an investigation of what effect may helical symmetry of the conductor (metal or semiconductor) have on the persistent current oscillations. We investigate persistent currents in helical structures which are non-decaying in time, not requiring a voltage bias, dissipationless stationary flow of electrons in a normal-metallic or semiconducting cylinder or circular wire of mesoscopic dimension. In the presence of magnetic flux along the toroidal structure, helical symmetry couples circular and longitudinal currents to each other. Our calculations suggest that circular persistent currents in these structures have two components with periods $\Phi_0$ and $\Phi_0/s$ ($s$ is an integer specific to any geometry). However, resultant circular persistent current oscillations have $\Phi_0$ period. \pacs{PACS:}PACS:73.23.-b