Shell structure and strengthening of superconducting pair correlation in nanoclusters

The existence of shell structure and the accompanying high degeneracy of electronic levels leads to the possibility of strong superconducting pairing in metallic nanoclusters with $N\sim {10}^2–{10}^3$ delocalized electrons. The most favorable cases correspond to (a) “magic” clusters with strongly degenerate highest occupied and lowest unoccupied shells and a relatively small energy spacing between them as well as to (b) clusters with slightly incomplete shells and small Jahn-Teller splitting. It is shown that realistic sets of parameters lead to very high values of $T_c$ as well as to a strong alteration of the energy spectrum. The impact of fluctuations is analyzed. Spectroscopic experiments aimed at detecting the presence of pair correlations are proposed. The pairing should also manifest itself via odd-even effects in cluster spectra, similar to the case in nuclei.