Revised Calculation of $\bm \kappa_2(T)$ for s-wave Type-II Superconductors

TL;DR

This paper revises the calculation of the Maki parameters and pair potential in s-wave type-II superconductors near the upper critical field, highlighting the importance of Fermi surface details and correcting previous results.

Contribution

It provides corrected and more accurate calculations of $oldsymbol{}$ and $oldsymbol{}$ parameters, considering impurity effects and Fermi surface geometry.

Findings

Eilenberger's results on $$ are quantitatively incorrect and are corrected.

Differences between 2D and 3D systems are significant, emphasizing Fermi surface importance.

The coefficient of $({f r})$ near $H_{c2}$ is determined accurately.

Abstract

This paper presents revised calculations for the Maki parameters $\kappa_{1}$ and $\kappa_{2}$ and the pair potential $\Delta({\bf r})$ of s-wave type-II superconductors near the upper critical field $H_{c2}$ with arbitrary impurity concentration. It is found that Eilenberger's well-known results on $\kappa_{2}$ [Phys. Rev. {\bf 153}, 584 (1967)] are not correct quantitatively, which are modified appropriately. Calculations are also performed for a two-dimensional system with an isotropic Fermi surface. The results in the clean limit differ substantially from those in three dimensions with an spherical Fermi surface. This fact indicates the necessity of considering detailed Fermi-surface structures for a quantitative understanding of the parameters. The coefficient of $\Delta({\bf r})\propto(H_{c2}-B)^{1/2}$, which is basic to any theoretical evaluation of the thermodynamic and transport properties near $H_{c2}$, is obtained accurately.