Effect of quantum fluctuations on the critical supercurrent through a mesoscopic normal-metal island

We consider the transport properties of a single-electron transistor consisting of a diffusive normal-metal island and superconducting electrodes. We show that the interplay of a dissipative impedance of the gate electrode, a weak magnetic field, and a charging energy of the island causes a suppression of the critical supercurrent of the transistor. When the device is voltage biased, pumping of single electrons can be achieved by a periodic modulation of the gate voltage [1-3]. We derive the analytic expressions for the error rates and show that they are suppressed by the applied magnetic field [4].

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