Ginzburg-Landau theory of dirty two band $s_{\pm}$ superconductors

TL;DR

This paper derives a Ginzburg-Landau theory for dirty two-band s± superconductors, revealing two regimes based on impurity scattering that significantly affect their superconducting behavior.

Contribution

It introduces a Ginzburg-Landau framework for dirty two-band s± superconductors and characterizes their behavior under different impurity scattering regimes.

Findings

Strong impurity scattering makes the superconductor behave as a single-band dirty superconductor.

Weak impurity scattering leads to a network of frustrated grains connected by Josephson junctions.

Most pnictide superconductors are in the weak scattering regime.

Abstract

In this paper we study the effect of non-magnetic impurities on two-band $s_{\pm}$ superconductors by deriving the corresponding Ginzburg-Landau (GL) equation. Depending on the strength of (impurity-induced) inter-band scattering we find that there are two distinctive regions where the superconductors behave very differently. In the strong impurity induced inter-band scattering regime $T_c<<\tau^{-1}_t$, where $\tau_t\sim$ mean-life time an electron stays in one band the two-band superconductor behaves as an effective one-band dirty superconductor. In the other limit $T_c\geq\tau^{-1}_t$, the dirty two-band superconductor is described by a network of frustrated two-band superconductor grains connected by Josepshon tunnelling junctions. We argue that most pnictide superconductors are in the later regime.