Phonon Boost Effect on the $S^{\pm}$-wave Superconductor with Incipient Band

TL;DR

This paper demonstrates that all phonons, including local and forward-scattering types, can enhance the superconducting transition temperature in an $s^{ extrm{ iny{ extpm}}}$-wave superconductor with an incipient band, especially as the band sinks deeper.

Contribution

It reveals that both local and forward-scattering phonons contribute to boosting $T_c$ in the incipient band model, highlighting the importance of all phonons in interface and intrinsic systems.

Findings

All phonons contribute to $T_c$ enhancement.

Deeper incipient bands increase local phonon boost effect.

Interface phonons from SrTiO$_3$ substrate are significant.

Abstract

We showed that the all phonons -- not only forward-scattering phonon but also local (all-momentum-scattering) phonon -- contribute to boosting $T_c$ of the $s^{\pm}$-wave pairing state in the incipient band model. In particular, when the incipient band sinks deeper, the phonon boost effect of the local phonon increases and becomes as effective as the one of the forward-scattering phonon. Our finding implies that all interface phonons -- not only the 90 $meV$ Fuchs-Kliewer (F-K) phonon but also the 60 $meV$ F-K phonon -- from the SrTiO$_3$ substrate and all intrinsic phonons of the FeSe monolayer itself should contribute to increase $T_c$ of the FeSe/STO monolayer system.