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Parity Effects and Higher Order Tunneling in Superconducting SET Transistors

Single electron tunneling into small superconducting islands is sensitive to the gap energy of the excitations created in the process and, hence, depends on the parity of the electron number in the island. We study these effects by analyzing the kinetics of the system. Since the interplay of Coulomb blockade and parity effects leads to a blocking of single electron tunneling, higher order tunneling processes become important. This is well-established for two-electron tunneling. Here we study processes of third and fourth order. We estimate the order of magnitude for these processes and discuss their relevance for recent experiments.