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Ab initio analyses of A2IrO4 (A=Sr, Ba) are presented. Effective Hubbard-type models for Ir 5d t2g manifolds downfolded from the global band structure are solved based on the dynamical mean- field theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the N´eel temperature TN . These compounds are classified not into Mott insulators but into Slater insulators. However, the insulating gap opens by a synergy of the N´eel order and significant band renormalization, which is also manifested by a 2D bad metallic behavior in the paramagnetic phase near the quantum criticality.
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