Even-odd electron number effects in a small superconducting island: Magnetic-field dependence

As a consequence of electron pairing, the free energy of a small superconducting island at low temperatures depends on whether it contains an even or odd number of electrons, i.e., on the parity of the total number of electrons. This produces a 2e periodicity in the tunneling current versus gate-induced charge characteristics of a superconducting single-electron tunneling transistor. Magnetic-field data show that the 2e to e periodicity crossover temperature decreases approximately as ${\mathit{H}}^2$, in good agreement with our statistical mechanical parity model extended to include magnetic-field pair-breaking effects.