Progress of nematic superconductivity in iron-based superconductors

Despite more than ten years of extensive research, the superconducting mechanism of iron-based superconductors (FeSCs) is still an open question. Generally, the high-temperature superconductivity is often observed with suppression of magnetic ordering, spin-density-wave, or even the structure transition by carrier doping. Furthermore, an electronic state ordering is also observed at temperatures close to or even above these transitions. Due to its proximity to the superconducting state and disappearance near the optimal superconductivity, it has been also suggested to interplay with superconductivity on a phenomenological level. Nevertheless, there is still no direct evidence to bridge the superconductivity to these transitions. Recently, another nematic order was observed in the superconducting state of heavily hole-doped compound AFe$$_2$$As$$_2$$ (A = K, Rb, Cs), providing a possibility to explore the superconductivity gap symmetry nature. Here, by reviewing the recent experimental progresses on the nematic superconductivity in the FeSCs, we will introduce the progresses by various methods including the quasi-particle interference from scanning tunneling microscope, anisotropic gap magnitudes from angular resolved photoemission, the upper critical field and the superconducting transition temperatures from transport measurements. In addition, some recent reports and theoretical explanations for experimental results are followed