Distinguishing between $s+id$ and $s+is$ pairing symmetries in multiband superconductors through spontaneous magnetization pattern induced by a defect

TL;DR

This paper proposes a method to differentiate between $s+is$ and $s+id$ pairing symmetries in multiband superconductors by analyzing the distinct spontaneous magnetization patterns induced by defects.

Contribution

It introduces a theoretical approach combining perturbation theory and numerical Ginzburg-Landau calculations to distinguish pairing symmetries via magnetization angular dependence.

Findings

Distinct angular magnetization patterns for $s+is$ and $s+id$ states.

Magnetization patterns depend on the symmetry of the order parameter.

Potential experimental method to identify pairing symmetry.

Abstract

The symmetry of the pairing state in iron pnictide superconductor $\mathrm{Ba_{1-x}K_xFe_2As_2}$ is still controversial. At optimal doping ($x \approx 0.4$), it is very likely $s$-wave, but for $x=1$ there are experimental and theoretical arguments for both $s$-wave and $d$-wave. Depending on the choice for $x=1$, intermediate $s+is$ and $s+id$ states have been proposed for intermediate doping $ 0.4 < x < 1$. In both states, the time reversal symmetry is broken and a spontaneous magnetization is allowed. In this work we study a spontaneous magnetization induced by a nonmagnetic defect in the $s+is$ and $s+id$ states by using a perturbation theory and numerical calculations for the Ginzburg-Landau free energy functional. We show that the angular dependence of the magnetization is distinct in these two states due to the difference in symmetry properties of the order parameters. Our results indicate a possible way to distinguish between the $s+is$ and $s+id$ pairing symmetries in multi-band superconductors.