Parity effect in superconducting islands with increasing lengths

We explore island length effects in single-electron transistors with superconducting islands and normal-metal leads. It had been shown experimentally that the current versus gate-induced charge characteristics change from $2e$ periodicity to e periodicity above a temperature T* far below Tc. According to the equilibrium model of this parity effect proposed by Tuominen et al., T* depends inversely on the logarithm of the island volume, so T* should be depressed as the island length is increased. Our high-current-sensitivity data show that the depression of T* with increasing island length from 2 to 10 {μ}m agrees well with the theoretical calculation of T*.