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 $T_c.$ 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 μm agrees well with the theoretical calculation of $T^{*}.$

• Received 26 June 1997

DOI:https://doi.org/10.1103/PhysRevB.57.120