Ginzburg-Landau Expansion and Physical Properties of Odd-Gap Superconductors

TL;DR

This paper derives a Ginzburg-Landau theory for odd-gap superconductors, revealing unique dependencies of physical properties on pairing interactions and impurity effects, notably affecting the upper critical field behavior.

Contribution

It introduces a Ginzburg-Landau expansion tailored for odd-gap superconductors, highlighting the distinct influence of impurities and coupling constants on their physical properties.

Findings

Ginzburg-Landau coefficients depend on pairing coupling constant in odd-gap superconductors.

Impurities significantly alter the odd-gap pairing mechanism, unlike in conventional superconductors.

Complete temperature dependence of the upper critical field H_{c2} is derived for odd-gap cases.

Abstract

Ginzburg-Landau expansion is derived for superconductors with the gap-function odd over $k-k_{F}$. It is shown that in this odd-gap case Ginzburg-Landau coefficients possess an additional dependence on the pairing coupling constant which leads to the appropriate dependence of the physical properties. Non-magnetic impurities influence the odd-gap pairing in a significant way and the mechanism of this influence is quite different from that predicted by the usual theory of "dirty" superconductors. In particular this is reflected in an anomalous behavior of the upper critical field $H_{c2}$ slope close to $T_{c}$. We also derive the complete temperature dependence of $H_{c2}$ for the odd-gap case.