The rich phase diagram of the prototypical iridate Ba${}_2$IrO${}_4$: Effective low-energy models and metal-insulator transition

In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{e}\mathrm{f}\mathrm{f}}=1\mathrm{/}2$ 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 $j_{\mathrm{e}\mathrm{f}\mathrm{f}}$ states is key. However, in particular for its structurally simple member Ba${}_2$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-$j_{\mathrm{e}\mathrm{f}\mathrm{f}}$ 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 effective one-band metal-insulator transition relevant to Ba${}_2$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 non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba${}_2$IrO${}_4$ and to clarify further the similarities and differences with cuprates.