Strongly enhanced superconductivity due to finite energy spin fluctuations induced by an incipient band : a FLEX study on the bilayer Hubbard model with vertical and diagonal interlayer hoppings

TL;DR

This study uses FLEX calculations to show that incipient bands in a bilayer Hubbard model significantly enhance spin-fluctuation-mediated superconductivity, especially when narrow and wide bands coexist.

Contribution

It demonstrates how finite energy spin fluctuations from incipient bands can strongly boost superconductivity in a bilayer Hubbard model with specific interlayer hoppings.

Findings

Superconductivity is strongly enhanced when a band is incipient.

Large spin fluctuation weight in an appropriate energy range boosts pairing.

Narrow and wide band coexistence broadens the optimal parameter regime.

Abstract

We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimized eigenvalue of the linearized Eliashberg equation, a measure for the strength of superconductivity, is not strongly affected by the bare width of the incipient band, but the parameter regime where superconductivity is optimized is wide when the incipient band is narrow, and in this sense, the coexistence of narrow and wide bands is favorable for superconductivity.