PARITY EFFECT AND THERMODYNAMICS OF CANONICAL SUPERCONDUCTING ENSEMBLES

The thermodynamic properties of a small isolated superconducting island depend on the parity of the electron number N. This parity effect is investigated by means of a path integral technique. For both even and odd N the temperature dependence of the specific heat and other thermodynamic quantities is governed by the factor exp(-2 Delta/T) in contrast to the standard BCS dependence exp(-Delta/T). For a wide region of parameters, fluctuations of the order parameter do not cause significant deviations from the mean field results. In d-wave superconductors the parity effect is suppressed by a factor similar to N-S(1/2) N-S being the effective number of superconducting electrons in the island.