We have fabricated and measured superconducting single-electron transistors with Al leads and Nb islands. At bias voltages below the gap of Nb we observe clear signatures of resonant tunneling of Cooper pairs, and of Coulomb blockade of the subgap currents due to linewidth broadening of the energy levels in the superconducting density of states of Nb. The experimental results are in good agreement with numerical simulations.The single-electron transistor 1 (SET) and its superconducting version is one of the most versatile tools in mesoscopic physics. It has been used for extremely sensitive charge measurements, 2 for the construction of Cooper pair pumps and other adiabatic devices with applications in metrology, 3 and more recently for building up superconducting quantum bits. 4 The IV characteristics of superconducting SETs present the usual features of quasiparticle tunneling (at voltages above 2∆ Nb + 2∆ Al ), Josephson-quasiparticle tunneling (at half of these values), and Josephson effect (around zero bias). These features have been thoroughly investigated by now by many groups and the physics of a charge transport at these bias voltages is well understood. However, at low bias voltages also other transport processes could become important and can alter the performance of Josephson-based devices. In this paper, we study two such processes appearing in our Nb-based SET: Resonant tunneling of Cooper pairs, and transport through states inside the gap of Nb (subgap currents).We have fabricated Al/AlO x /Nb/AlO x /Al single electron transistors using a lithographic technique described elsewhere. 5 Measurements were done using a small dilution refrigerator equipped with well-thermalized and electrically filtered measuring lines. The superconducting gaps obtained for Nb and Al (∆ Nb = 1.4 mV, ∆ Al = 0.2 meV), and also the measured critical temperatures for Nb (T C,Nb ≈ 8.0 − 8.5 K), show that the films are indeed of good quality.At voltages below the gap of Nb, a series of gatedependent resonance peaks appears in the IV characteristics of the SET (Fig. 1). We interpret this as resonant tunneling of Cooper pairs, a transport phenomenon first predicted theoretically and later observed in Al symmetrically-biased superconducting SETs. 6 Below we describe the same process for our Nb-island SETs under the asymmetric bias shown in Fig. 1. We consider a generic process in which a charge δq 1 tunnels through the left junction and a charge δq 2 tunnels through the second junction, both into the island. During the process, a charge δq = δq 1 + δq 2 is transferred into the island and a charge δQ = δq 1 − δq 2 is transferred through the external circuit in the forward direction. The change in the electrostatic free energy (including work done by the sources) associated with this process iswhere q 0 is the initial charge of the island, C 1 and C 2 are the capacitances of the left and right junctions, C g is the gate capacitance, and C Σ = C 1 + C 2 + C g . Resonant Cooper pair tunneling in superconducting SETs occurs when no en...

We present a method to measure the critical temperature of the island of a superconducting single electron transistor. The method is based on a sharp change in the slope of the zero-bias conductance as a function of temperature. We have used this method to determine the superconducting phase transition temperature of the Nb island of an superconducting single electron transistor with Al leads. We obtain T Nb c as high as 8.5 K and gap energies up to ∆ Nb ≃ 1.45 meV. By looking at the zero bias conductance as a function of magnetic field instead of temperature, also the critical field of the island can be determined. Using the orthodox theory, we have performed extensive numerical simulations of charge transport properties in the SET at temperatures comparable to the gap, which match very well the data, therefore providing a solid theoretical basis for our method.