Effects of magnetic flux in a loop formed by an s-wave superconductor and an $\mathrm{s_{\pm}}$ superconductor

Identifying the correct order parameter structure of the iron based superconductors will provide insight into the pairing mechanism in these materials. Due to the multi-orbital band structure of these materials and the proximity of the superconducting phase to an anti-ferromagnetic phase, most theories favor magnetic fluctuations as the pairing mechanism and an order parameter with the so-called $\mathrm{s_{\pm}}$ symmetry. However, it is experimentally challenging to distinguish the $\mathrm{s_{\pm}}$ symmetry from conventional s-wave symmetry; thus, the $\mathrm{s_{\pm}}$ structure remains unconfirmed. In 2010, Chen \textit{et al} showed evidence of integer and half integer flux quantum transitions in an $\mathrm{Nb}$-$\mathrm{NdFeAsO_{0.88}F_{0.12}}$ loop excited by electromagnetic pulses [1]. We present a theoretical study of the effects of magnetic flux in a superconducting s/$\mathrm{s_{\pm}}$ loop inspired by these results. Our findings are in agreement with preliminary results of a phenomenological Ginzburg Landau model [2], and help clarify the relation between the transitions observed in the experiment and the $\mathrm{s_{\pm}}$ symmetry.\\[4pt] [1] C.-T. Chen \textit{et al}, Nature Physics 6, 260 (2010).\\[0pt] [2] Berg, Lindner, Pereg-Barnea, Phys. Rev. Lett. 106, 1470.