Interband superconductivity: contrasts between BCS and Eliashberg theory

TL;DR

This paper analyzes interband superconductivity, revealing unique effects and differences between BCS and Eliashberg theories, especially regarding gap ratios and density-of-states, with implications for pairing mechanisms in iron pnictides.

Contribution

It demonstrates that interband-only pairing leads to distinct properties and differences between BCS and Eliashberg theories, challenging conventional assumptions about pairing mechanisms.

Findings

Different density-of-states lead to unusual gap ratio behavior.

Weak-coupling limits of BCS and Eliashberg theories predict different dependencies.

Maximal gap ratio in interband pairing is proportional to the square root of the density-of-states ratio.

Abstract

The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density-of-states on the two bands lead to several unusual properties, including a gap ratio which behaves inversely to the ratio of density-of-states; the weak-coupling limit of the Eliashberg and the BCS theory, commonly taken as equivalent, in fact predict qualitatively different dependence of the $\Delta_{1}/\Delta_{2}$ and $\Delta/T_{c}$ ratios on coupling constants. We show analytically that these effects follow directly from the interband character of superconductivity. Our results show that in the interband-only pairing model the maximal gap ratio is $\sqrt{N_{2}/N_{1}}$ as strong-coupling effects act only to reduce this ratio. This suggests that if the large experimentally reported gap ratios (up to a factor 2) are correct, the pairing mechanism must include more intraband interaction than is usually assumed.