Rich phase diagram of the prototypical iridate Ba2IrO4 : Effective low-energy models and metal-insulator transition

In the quest for exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled ${j}_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the ${j}_{\mathrm{eff}}$ states is key. However, in particular, for its structurally simple member ${\mathrm{Ba}}₂{\mathrm{IrO}}₄$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-${j}_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling, and Coulomb interactions, we map out a rich phase diagram and identify a region of an effective one-band metal-insulator transition relevant to ${\mathrm{Ba}}₂{\mathrm{IrO}}₄$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of nonlocal fluctuations. In a broader context, we envisage the three- and five-band models developed in this paper to be relevant for the study of doped ${\mathrm{Ba}}₂{\mathrm{IrO}}₄$ and to further clarify the similarities and differences with cuprates.