  We propose a theoretical description of the phase diagram and physical
properties in A2Fe4Se5-type (A=K, Tl) compounds based on a coexistent local
moment and itinerant electron picture. Using neutron scattering and ARPES
measurements to fix the general structure of the local moment and itinerant
Fermi pockets, we find a superconducting (SC) regime with s-wave pairing at the
M pockets and an incipient sign-change s-wave near the Gamma point, which is
adjacent to an insulating state at low doping and a charge-density-wave (CDW)
state at high doping. The uniform susceptibility and resistivity are found to
be consistent with the experiment. The main distinction with iron pnictide
superconductors is also discussed.
