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

D. Valentinis, D. van der Marel, and C. Berthod
Phys. Rev. B 94, 024511 – Published 14 July 2016

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 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.

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  • Received 18 January 2016

DOI:https://doi.org/10.1103/PhysRevB.94.024511

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Valentinis, D. van der Marel, and C. Berthod*

  • Department of Quantum Matter Physics (DQMP), University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland

  • *christophe.berthod@unige.ch

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Issue

Vol. 94, Iss. 2 — 1 July 2016

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