Proximity-induced Cooper-pair in a very small normal-metal island

Abstract

We analyzed the electronic states in a very small normal-metal (N)/insulator (I)/superconductor (S) tunneling junction, taking into account the charging effect generated with the charge transfer through the insulator. This junction has the microscopic (quasiparticle) and the macroscopic (Cooper-pair) aspects at the same time even if the relevant energies (eV, k B T) are much lower than the superconducting gap energy in the S electrode. By using the expression with Andreev reflection and Cooperon for the proximity effect, both the aspects (micro/macro) can be treated consistently. The results show that if the charging energy E C is comparable to or smaller than the Thouless energy of the N region, a proximity-induced gap appears in the quasiparticle density of states and a Cooper-pair exists in the N region. However, the Cooper-pair does not oscillate between N and S regions. This behavior is quite different from the Cooper-pair in the single Cooper-pair box.