# Finite energy spin fluctuation as a pairing glue in systems with coexisting electron and hole bands

## TL;DR

This paper investigates how finite energy spin fluctuations can mediate superconductivity in systems with coexisting electron and hole bands, revealing that optimal pairing occurs when Fermi surface nesting is partially degraded, unlike traditional models.

## Contribution

It demonstrates that in models with electron and hole bands, superconductivity is enhanced by finite energy spin fluctuations at degraded nesting, contrasting with conventional models where perfect nesting is ideal.

## Key findings

- Superconductivity peaks when Fermi surface nesting is slightly degraded.
- In models with electron and hole bands, the spin susceptibility maximum remains fixed despite nesting degradation.
- The bilayer Hubbard model may realize high T_c superconductivity in actual materials.

## Abstract

We study, within the fluctuation exchange approximation, the spin-fluctuation-mediated superconductivity in Hubbard-type models possessing electron and hole bands, and compare them with a model on a square lattice with a large Fermi surface. In the square lattice model, superconductivity is more enhanced for better nesting for a fixed band filling. By contrast, in the models with electron and hole bands, superconductivity is optimized when the Fermi surface nesting is degraded to some extent, where finite energy spin fluctuation around the nesting vector develops. The difference lies in the robustness of the nesting vector, namely, in models with electron and hole bands, the wave vector at which the spin susceptibility is maximized is fixed even when the nesting is degraded, whereas when the Fermi surface is large, the nesting vector varies with the deformation of the Fermi surface. We also discuss the possibility of realizing in actual materials the bilayer Hubbard model, which is a simple model with electron and hole bands, and is expected to have a very high T_c.