Abstract
Superconductivity develops in bulk doped and at the / interface with a dome-shaped density dependence of the critical temperature , despite different dimensionalities and geometries. We propose that the dome of / is a shape resonance due to quantum confinement of superconducting bulk . We substantiate this interpretation by comparing the exact solutions of a three-dimensional and quasi-two-dimensional two-band BCS gap equation. This comparison highlights the role of heavy bands for in both geometries. For bulk , we extract the density dependence of the pairing interaction from the fit to experimental data. We apply quantum confinement in a square potential well of finite depth and calculate in the confined configuration. We compare the calculated to transport experiments and provide an explanation as to why the optimal 's are so close to each other in two-dimensional interfaces and the three-dimensional bulk material.
- Received 22 November 2016
DOI:https://doi.org/10.1103/PhysRevB.96.094518
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