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

TL;DR

This paper investigates how electron density fluctuations in strongly disordered superconductors cause amplitude oscillations and shell-like effects, linked to the formation of nanoscale superconducting puddles, with implications for understanding disordered superconductivity.

Contribution

It demonstrates the presence of shell-like effects in disordered superconductors driven by electron density changes, revealing a new mechanism for amplitude fluctuations and puddle formation.

Findings

Pairing amplitude and gap oscillate with electron density.

Nanoscale superconducting puddles form and change shape with density.

Shell-like effects are correlated with puddle formation and spectral changes.

Abstract

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