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Single electron tunneling into small superconducting islands is sensitive tothe gap energy of the excitations created in the process and, hence, depends onthe parity of the electron number in the island. We study these effects byanalyzing the kinetics of the system. Since the interplay of Coulomb blockadeand parity effects leads to a blocking of single electron tunneling, higherorder tunneling processes become important. This is well-established fortwo-electron tunneling. Here we study processes of third and fourth order. Weestimate the order of magnitude for these processes and discuss their relevancefor recent experiments.

Parity Effects and Higher Order Tunneling in Superconducting Set Transistors