Properties of boson-exchange superconductors

TLDR

Tc is the critical temperature and ω_ln is an average boson energy mediating the pairing potential in Eliashberg theory. The author reviews successes of Eliashberg theory in describing conventional superconductors and notes that a definitive application to oxides awaits better experimental results. The review examines strong‑coupling limits of Tc/ω_ln≈1 and the asymptotic limit Tc/ω_ln→∞, motivated by high‑Tc cuprate discovery. Functional‑derivative techniques and simple analytic correction formulas for the strong‑coupling parameter Tc/ω_ln clarify deviations from BCS laws, provide insight into the realistic strong‑coupling regime, and suggest that high‑energy boson‑exchange mechanisms—possibly with phonon contributions—operate in cuprate oxides.

Abstract

The author reviews some of the important successes achieved by Eliashberg theory in describing the observed superconducting properties of many conventional superconductors. Functional derivative techniques are found to help greatly in understanding the observed deviations from BCS laws. Approximate analytic formulas with simple correction factors for strong-coupling corrections embodied in the single parameter $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}$ are also found to be very helpful. Here ${T}_{c}$ is the critical temperature and ${\ensuremath{\omega}}_{\mathrm{ln}}$ is an average boson energy mediating the pairing potential in Eliashberg theory. In view of the discovery of high-${T}_{c}$ superconductivity in the copper oxides, results in the very strong coupling limit of $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}\ensuremath{\sim}1$ are also considered, as is the asymptotic limit when $\frac{{T}_{c}}{{\ensuremath{\omega}}_{\mathrm{ln}}}\ensuremath{\rightarrow}\ensuremath{\infty}$. This case is of theoretical interest only, but it is nevertheless important because simple analytic results apply that give insight into the more realistic strong-coupling regime. A discussion more specific to the oxides is included in which it is concluded that some high-energy boson-exchange mechanism must be operative, with, possibly, some important phonon contribution in some cases. A more definitive application of boson-exchange models to the oxides awaits better experimental results.