Mesoscopic cross-film cryotrons: Vortex trapping and dc-Josephson-like oscillations of the critical current

We investigate theoretically and experimentally the transport properties of a plain Al superconducting strip in the presence of a single straight current-carrying wire, oriented perpendicular to the superconducting strip. It is well known that the critical current of the superconducting strip, Ic, in such cryotron--like system can be tuned by changing the current in the control wire, Iw. We demonstrated that the discrete change in the number of the pinned vortices/antivortices inside the narrow and long strip nearby the current-carrying wire results in a peculiar oscillatory dependence of Ic on Iw.