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Electronic Structure and Mott Localization in Iron Deficient TlFe$_{1.5}$Se$_2$ with Superstructures

Electronic structure and magnetic properties for iron deficient TlFe$_{2-x}$Se$_2$ compounds are studied by first-principles calculations. We find that for the case of $x=0.5$ with a Fe-vacancy ordered orthorhombic superstructure, the ground state exhibits a stripe-like antiferromagnetic ordering and opens a sizable band gap if the short-ranged Coulomb interaction of Fe-3d electrons is moderately strong, manifesting a possible Mott insulating state. While increasing Fe-vacancies from the $x=0$ side, where the band structure is similar to that of a heavily electron-doped FeSe system, the Mott localization can be driven by kinetic energy reduction as evidenced by the band narrowing effect. Implications of this scenario in the recent experiments on TlFe$_{2-x}$Se$_2$ are discussed.