We investigate how the interplay of quantum confinement and particle number-parity fluctuations affects superconducting correlations in ultra-small metallic grains. Using the number-parity projected BCS formalism we calculate the critical temperature and the excitation gap as a function of the grain size for grains with even and odd number of confined carriers. We show that the experimentally observed anomalous increase of the coupling ratio ${\Delta }_E/k_B{T}_c$ with decreasing superconducting grain size can be attributed to an enhancement of the number-parity fluctuations in ultra-small grains.

• Received 20 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.214518