Superconducting Properties of the $s^{\pm}$-wave state: Fe-based superconductors

Although the pairing mechanism of the Fe-based superconductors (FeSCs) has not yet been settled with a consensus, as to the pairing symmetry and the superconducting (SC) gap function, the abundant majority of experiments are supporting for the spin-singlet sign-changing s-wave SC gaps on multibands ($s^{\pm}$-wave state). This multiband $s^{\pm}$-wave state is a very unique gap state {\it per se} and displays numerous unexpected novel SC properties such as a strong reduction of the coherence peak, non-trivial impurity effects, nodal-gap-like nuclear magnetic resonance (NMR) signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with the SH jump and the condensation energy vs. $T_c$, etc. In particular, many of these non-trivial SC properties can be easily mistaken as evidence for a nodal gap state such as a d-wave gap. In this review, we provide detailed explanations of theoretical principles for the various non-trivial SC properties of the $s^{\pm}$-wave pairing state, and then critically compare the theoretical predictions with the experiments of the FeSCs. This will provide a pedagogical overview of how much we can coherently understand the wide range of different experiments of the FeSCs within the $s^{\pm}$-wave gap model.