Unlike bulk superconductivity, where one energy scale, the energy gap, characterizes pairing correlations, we show that in small superconducting grains there exist two different such quantities. The first characterizes collective properties of the grain, such as the condensation energy, and the second single-particle properties. To describe these two energy scales, we define two corresponding pairing parameters, and show that although both reduce to the bulk gap for large grains, this occurs at different size scales.

• Received 13 October 2002

DOI:https://doi.org/10.1103/PhysRevB.67.064506