Singularity-matching peaks in superconducting single-electron transistor

We report the experimental observation of the recently predicted peaks on the I-V curve of the superconducting single-electron transistor at relatively high temperatures. The peaks are due to the matching of singularities in the quasiparticle density of states in two electrodes of a tunnel junction. The energy shift due to Coulomb blockade provides the matching at finite voltage. 73.40.Gk, 73.40.Rw, 74.50.+r Typeset using REVTEX 1 Single-electron effects in superconducting structures have several additional features in comparison with that in normal metals or semiconductors. The main differences are due to the specific role of the parity of the electron number on a small island, the effects of the Josephson coupling,1,2,5–8 and the specific shape of the quasiparticle density of states (QDS). The last topic received relatively small attention so far in both theoretical and experimental single-electronics, although QDS leads to various interesting effects. Besides the well-known shift of the Coulomb blockade threshold by 4∆/e in SSS single-electron transistor (SET) (by 2∆/e in NSN or SNS cases), let us mention the direct reproduction of the QDS on the I-V curve of the SET with discrete energy spectrum of the central electrode and in the case of odd-parity current, singularity-matching (SM) peaks at finite temperatures, the limitation of the differential conductance by quantum resistance and the conductance jump at V = 4∆/e due to cotunneling. In this paper we discuss the theory of SM peaks in more detail and report their experimental observation in the SSS SET. Somewhat similar experimental results will be presented soon by another group. The origin of SM peaks can be easily understood from the “orthodox” theory of the SET. Let us neglect the effects due to Josephson coupling and consider only the quasiparticle tunneling. The dc current I through the SET consisting of two tunnel junctions in series can be calculated from the equations