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Electronic and magnetic phase diagram in K$_x$Fe$_{2-y}$Se$_2$ superconductors

The correlation and competition between antiferromagnetism and superconductivity are one of the most fundamental issues in all of high temperature superconductors. The superconductivity in high temperature cuprate superconductors arises from suppressing an antiferromagnetic (AFM) Mott insulator phase by doping1 while that in iron-pnictide high temperature superconductors arises from AFM semimetals and can coexist with AFM orders2-9. This key difference marked in their phase diagrams has raised many intriguing debates about whether the two materials can be placed in the same category to understand the mechanism of superconductivity. Recently, superconductivity at 32 K has been reported in iron-chalcogenide superconductors AxFe2-ySe2 (A=K, Rb, and Cs)10-12, which have the same structure as that of iron-pnictide AFe2As2 (A=Ba, Sr, Ca and K)13-15. Here, we report electronic and magnetic phase diagram of KxFe2-ySe2 system as a function of Fe valence. We find two AFM insulating phases and reveal that the superconducting phase is sandwiched between them, and give direct evidence that the superconductivity in AxFe2-ySe2 originates from the AFM insulating parent compounds. The two insulating phases are characterized by two distinct superstructures caused by Fe vacancy orders with modulation wave vectors of q1=(1/5, 3/5, 0) and q2=(1/4, 3/4, 0), respectively. These experimental results strongly indicate that iron-based superconductors and cuprates share a common origin and mechanism of superconductivity.