Magnetoresistance in a Superconducting Single-Electron Transistor with a Multiply Connected Coulomb Island

Abstract

The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.