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A substantial enhancement of the superconducting gap was recently reported inclean, large ~30nm, and close to hemispherical Sn grains. A satisfactoryexplanation of this behaviour is still missing as shell effects caused byfluctuations of the spectral density or surface phonons are negligible in thisregion. Here we show that this enhancement is caused by spatial inhomogeneitiesof the Cooper's pairs density of probability. In the mean field approach thatwe employ these inhomogeneities are closely related to the eigenstates of theone-body problem, namely, a particle in a hemispherical shaped potential. Theparameter free theoretical prediction agrees well with the experimentalresults. A similar enhancement is predicted for other weakly coupledsuperconductors.

Inhomogenous pairing and enhancement of superconductivity in large Sn nanograins