Topological defects in superconducting open nanotubes under gradual and abrupt switch-on of the transport current and magnetic field*

Dynamics of the order parameter in superconducting membranes of a complex geometry under a strong transport current in an external homogeneous magnetic field becomes intricate. The normal component of the external magnetic field becomes inhomogeneous. This can be used to control the superconducting behavior. We analyze a thin superconducting Nb open nanotube using the time-dependent Ginzburg-Landau equation coupled with the electric scalar potential. Near the critical transport current, the dissipation processes are driven by the vortex and phase-slip dynamics. The transition between the vortex and phase-slip regimes is found to depend on the external magnetic field only weakly if the magnetic field and/or the transport current are switched on gradually. In the case of an abrupt switch-on of the magnetic field or transport current, the system can be triggered to the stable phase-slip regime, within a certain window of parameters. As a result, a hysteresis effect in the current-voltage characteristics is predicted in the superconducting open nanotubes. Generally, the system state in open nanotubes near the critical transport current depends on the way, in which the final external parameters (transport current and magnetic field) are achieved, constituting the memory effect.