Relative phase between $s_{\pm}$ superconducting order parameter components in a two-band model with impurities

Abstract

We obtain solutions for Eliashberg equations within the Nambu representation for a two-band model of iron-based superconductors with nonmagnetic impurities. Two cases of a transition between $s_{\pm}$ and $s_{++}$ states are considered: (i) the transition is accompanied by the abrupt change of the order parameter sign within one of the bands and (ii) the change is smooth. For both cases, we studied the role of a gauge defined by the coefficients preceding the Pauli matrices $\hat\tau_1$ and $\hat\tau_2$ in a self-energy expansion, which correspond to the components of the order parameter. We show that the absolute value of the order parameter is conserved for solutions in the clean and in the Born limits. In an intermediate case, between the Born and unitary limits, result depends on the solution for the clean limit. We show that a common gauge for the Eliashberg equations in which one of the order parameter components vanishes is essential for adequate description of the multiband superconducting systems.