Inhomogenous pairing and enhancement of superconductivity in large Sn nanograins

A substantial enhancement of the superconducting gap was recently reported in clean, large ~30nm, and close to hemispherical Sn grains. A satisfactory explanation of this behaviour is still missing as shell effects caused by fluctuations of the spectral density or surface phonons are negligible in this region. Here we show that this enhancement is caused by spatial inhomogeneities of the Cooper's pairs density of probability. In the mean field approach that we employ these inhomogeneities are closely related to the eigenstates of the one-body problem, namely, a particle in a hemispherical shaped potential. The parameter free theoretical prediction agrees well with the experimental results. A similar enhancement is predicted for other weakly coupled superconductors.