Abstract
We revisit the problem of a BCS superconductor in the regime where the Fermi energy is smaller than the Debye energy. This regime is relevant for low-density superconductors such as that are not in the BEC limit, as well as in the problem of “shape resonances” associated with the confinement of a three-dimensional superconductor. While the problem is not new, exact results were lacking in the low-density limit. In two dimensions, we find that the initial rise of the pairing temperature at low density is nonanalytic and faster than any power of . In three dimensions, we also find that is nonanalytic, but starts with zero slope at weak coupling and infinite slope at strong coupling. Self-consistent treatment of the chemical potential and energy dependence of the density of states are crucial ingredients to obtain these results. We also present exact results for multiband systems and confirm our analytical expressions by numerical simulations.
2 More- Received 18 January 2016
DOI:https://doi.org/10.1103/PhysRevB.94.024511
©2016 American Physical Society