Abstract
Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. In addition, there is experimental evidence that whether an enhancement or a reduction is found depends on the strength of the electron-phonon interaction in the bulk. We reveal how the strength of the e-ph interaction interplays with the quantum-size effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data. We demonstrate that strong e-ph scattering smears the peak structure in the electronic density-of-states of a metallic grain and enhances the electron mass, and thereby limits the highest Tc achievable by quantum confinement.
Highlights
Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit
We reveal how the strength of the e-ph interaction interplays with the quantum-size effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data
We demonstrate that strong e-ph scattering smears the peak structure in the electronic density-of-states of a metallic grain and enhances the electron mass, and thereby limits the highest Tc achievable by quantum confinement
Summary
Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. A recent experiment by Bose et al.[1] revealed material-dependent quantum size effects in superconducting grains which led to reconsider an old but fundamental problem of superconductivity in confined systems. Subsequent experimental studies of superconducting confined systems showed either a decrease or an increase of Tc with sample size, depending on the material. A scanning tunneling microscope (STM) was used to detect the superconducting gap in a single physically isolated ultra-small Pb/Sn grain[1,43,44] These studies traced the size evolution of superconductivity in isolated nanoparticles that were grown on a substrate. Pb particles exhibited a decrease of the gap with decreasing particle www.nature.com/scientificreports/
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