Scientific article
Open access

BCS superconductivity near the band edge: Exact results for one and several bands

Published inPhysical review. B, vol. 94, no. 2, 024511
Publication date2016

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 SrTiO3 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 Tc at low density n is nonanalytic and faster than any power of n. In three dimensions, we also find that Tc 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.

Citation (ISO format)
VALENTINIS, Davide Filippo, VAN DER MAREL, Dirk, BERTHOD, Christophe. BCS superconductivity near the band edge: Exact results for one and several bands. In: Physical review. B, 2016, vol. 94, n° 2, p. 024511. doi: 10.1103/PhysRevB.94.024511
Main files (1)
Article (Published version)
ISSN of the journal2469-9950

Technical informations

Creation07/15/2016 3:57:00 PM
First validation07/15/2016 3:57:00 PM
Update time03/15/2023 12:34:08 AM
Status update03/15/2023 12:34:07 AM
Last indexation05/02/2024 5:36:45 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack