Revised Tolmachev-Morel-Anderson pseudopotential for layered conventional superconductors with nonlocal Coulomb interaction

TL;DR

This paper investigates how static nonlocal Coulomb interactions affect layered conventional superconductors, showing they suppress superconductivity and modify the pseudopotential, which can be effectively described by a revised local Coulomb pseudopotential.

Contribution

The authors derive a revised Coulomb pseudopotential accounting for nonlocal interactions, improving the modeling of superconductivity in layered materials.

Findings

Nonlocal Coulomb interactions suppress superconductivity and lower critical temperature.

Most properties can be described by a revised local Coulomb pseudopotential larger than traditional models.

The analysis provides an expression for the pseudopotential valid with nonlocal Coulomb interactions.

Abstract

We study the effects of static nonlocal Coulomb interactions in layered conventional superconductors and show that they generically suppress superconductivity and reduce the critical temperature. Although the nonlocal Coulomb interaction leads to a significant structure in the superconducting gap function, we find that most properties can be effectively described by means of an appropriately revised local Coulomb pseudopotential $\tilde{\mu}_C^*$, which is larger than the commonly adopted retarded Tolmachev-Morel-Anderson pseudopotential $\mu^*_C$. To understand this, we analyze the Bethe-Salpeter equation describing the screening of Coulomb interaction in the superconducting state and obtain an expression for $\tilde{\mu}_C^*$, which is valid in the presence of nonlocal Coulomb interactions. This analysis also reveals how the structure of the nonlocal Coulomb interaction weakens the screening effects from high-energy pair fluctuations and therefore yields larger values of the pseudopotential. Our findings are especially important for layered conventional superconductors with small Fermi energies and can be easily taken into account ab initio studies.