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Motivated by the recent observation of the shell effect in a nanoscale puresuperconductor by Bose {\em et al} [Nat. Mat. {\bf 9}, 550 (2010)], we explorethe possible shell-like effect in a strongly disordered superconductor as it isknown to produce nanosize superconducting puddles (SPs). We find a remarkablechange in the texture of the pairing amplitudes that is responsible for formingthe SP, upon monotonic tuning of the average electron density, $\langle n\rangle$, and keeping the disorder landscape unaltered. Both the spatiallyaveraged pairing amplitude and the quasiparticle excitation gap oscillate with$\langle n \rangle$. This oscillation is due to a rapid change in the low-lyingquasiparticle energy spectra and thereby a change in the shapes and positionsof the SPs. We establish a correlation between the formation of SPs and theshell-like effect. The experimental consequences of our theory are alsodiscussed.

physical review letters

Amplitude Fluctuations Driven by the Density of Electron Pairs within  Nanosize Granular Structuters inside Strongly Disordered Superconductors:  Evidence for a Shell-Like Effect