A superconductor in the external pair potential. Accounting of the Coulomb pseudopotential

TL;DR

This paper extends a superconductivity model with an external pair potential to include Coulomb repulsion, deriving new equations and showing the potential's effectiveness in nonadiabatic superconductors with small Tolmachev logarithm.

Contribution

It generalizes the external pair potential model to account for Coulomb interactions and derives analogous Ginzburg-Landau equations for this extended framework.

Findings

Superconducting critical temperature depends on Coulomb interaction within Cooper pairs.

External pair potential is effective in nonadiabatic superconductors with small Tolmachev logarithm.

Derived free energy functional similar to Ginzburg-Landau equations.

Abstract

Formulated in [Low Temperature Physics/Fizika Nizkikh Temperatur, 41, 482 (2015)] model of hypothetical superconductivity with the source term (external pair potential) in BCS hamiltonian is generalized for a case if electrons interacts via both BCS model attraction and screened Coulomb repulsion. Unlike the previous work the superconductor has critical temperature which determined with the Coulomb interaction within a Cooper pair. It has been shown the external pair potential is effective for superconductors where Tolmachev logarithm is small (nonadiabatic case). A free energy functional and equations similar to Ginzburg-Landau equations have been found for such a model.