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Although the pairing mechanism of the Fe-based superconductors (FeSCs) hasnot yet been settled with a consensus, as to the pairing symmetry and thesuperconducting (SC) gap function, the abundant majority of experiments aresupporting 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 uniquegap state {\it per se} and displays numerous unexpected novel SC propertiessuch as a strong reduction of the coherence peak, non-trivial impurity effects,nodal-gap-like nuclear magnetic resonance (NMR) signals, various Volovikeffects in the specific heat (SH) and thermal conductivity, and anomalousscaling 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 mistakenas evidence for a nodal gap state such as a d-wave gap. In this review, weprovide detailed explanations of theoretical principles for the variousnon-trivial SC properties of the $s^{\pm}$-wave pairing state, and thencritically compare the theoretical predictions with the experiments of theFeSCs. This will provide a pedagogical overview of how much we can coherentlyunderstand the wide range of different experiments of the FeSCs within the$s^{\pm}$-wave gap model.

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