Parity Effects on Electron Tunnelling Through Small Superconducting Islands

Single-electron tunnelling into small superconducting islands is sensitive to the gap energy of the excitations created in the process and, hence, depends on the electron number parity. At low temperatures, a 2 e -periodic, even-odd asymmetric dependence on the applied gate voltage has been observed, turning into an e -periodic behaviour at higher temperature. We explain the crossover and derive I-V characteristics of such systems by studying the dynamics. The rate of tunnelling of a single electron, the odd one, turns out to be crucial. It dominates at low temperature since in this process the excitation energy can be regained, while the competing many-electron processes are exponentially suppressed. Parity effects on single-electron and Cooper-pair tunnelling and the Andreev reflection in superconducting transistors yield rich structures in the I-V characteristics, which compare well with recent experimental findings.