Colloquium : The unexpected properties of alkali metal iron selenide superconductors

Iron-based superconductors are an amazing class of layered materials where superconductivity and magnetism coexist, cooperate, and, sometimes, compete with each other. The complexity of these materials comes from the strong orbital nature of its electrons. In this Colloquium the latest developments and controversies regarding these materials are discussed with an eye on the future developments in this exciting field. The iron-based superconductors that contain FeAs layers as the fundamental building block in the crystal structures have been rationalized in the past using ideas based on the Fermi surface nesting of hole and electron pockets when in the presence of weak Hubbard U interactions. This approach seemed appropriate considering the small values of the magnetic moments in the parent compounds and the clear evidence based on photo-emission experiments of the required electron and hole pockets. The conceptual issues considered established for the alkali metal iron selenides, as well as several issues that still require further work, are discussed.