Abstract
The confinement of a superconductor in a thin film changes its Fermi-level density of states and is expected to change its critical temperature . Previous calculations have reported large discontinuities of when the chemical potential coincides with a subband edge. By solving the BCS gap equation exactly, we show that such discontinuities are artifacts and that is a continuous function of the film thickness. We also find that is reduced in thin films compared with the bulk if the confinement potential is lower than a critical value, while for stronger confinement increases with decreasing film thickness, reaches a maximum, and eventually drops to zero. Our numerical results are supported by several exact solutions. We finally interpret experimental data for ultrathin lead thin films in terms of a thickness-dependent effective mass.
2 More- Received 19 January 2016
- Revised 15 July 2016
DOI:https://doi.org/10.1103/PhysRevB.94.054516
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