The exact diagonalization and the variational cluster approximation (VCA) are used to study the nature of a novel Mott insulator induced by a strong spin-orbit coupling for a two-dimensional three-band Hubbard model consisting of the t2g manifold of 5d orbitals. To characterize the ground state, we introduce a local Kramer's doublet which can represent a state with effective angular momentum J eff = |S - L| = 1/2 as well as spin S = 1/2. Our systematic study of the pseudo-spin structure factor defined by the Kramer's doublet shows that the J eff = 1/2 Mott insulator is smoothly connected to the S = 1/2 Mott insulator. Using the Kramer's doublet as a variational state for the VCA, we examine the one-particle excitations for the Mott insulating phase. These results are compared with recent experiments on Sr 2IrO 4.
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