Robustness of s-wave superconductivity against Coulomb interactions in Na$_x$CoO$_2$

TL;DR

This paper investigates how Coulomb interactions affect s-wave superconductivity in Na$_x$CoO$_2$, showing that certain phonon modes and orbital degrees of freedom help maintain a finite critical temperature despite Coulomb repulsion.

Contribution

It demonstrates that the Suhl-Kondo mechanism and orbital degrees of freedom stabilize s-wave superconductivity against Coulomb interactions in Na$_x$CoO$_2$.

Findings

T_c is enhanced by shear and breathing phonons via the SK mechanism.

T_c remains finite despite strong Coulomb interactions.

Orbital degrees of freedom are crucial for understanding superconductivity in this material.

Abstract

We study the depairing effect due to Coulomb interactions in Na$_x$CoO$_2$. We consider the electron-phonon coupling and the Coulomb interactions, and determine $T_c$ for s-wave superconductivity by solving the linearized Eliashberg equation. When we consider shear phonons as well as breathing phonons, $T_c$ is enhanced by Suhl-Kondo (SK) mechanism. Since SK mechanism is strong against Coulomb interactions, $T_c$ remains finite even if strong Coulomb interactions cancel out the attractive force due to breathing phonons. The orbital degree of freedom is important to understand the mechanism of superconductivity in Na$_x$CoO$_2$.