Superconducting correlations in ultra-small metallic grains

To describe the crossover from the bulk BCS superconductivity to a fluctuation-dominated regime in ultrasmall metallic grains, new order parameters and correlation functions, such as parity gap'' and pair-mixing correlation function’', have been recently introduced. In this paper, we discuss the small-grain behaviour of the Penrose-Onsager-Yang off-diagonal long-range order (ODLRO) parameter in a pseudo-spin representation. Relations between the ODLRO parameter and those mentioned above are established through analytical and numerical calculations.