Effective J=1/2 insulating state in Ruddlesden-Popper iridates: An LDA+DMFT study

Using {\it ab-initio} methods, we\footnote{H. Zhang, K. Haule and D. Vanderbilt, arXiv:1308.4471 (2013).} investigate the metal-insulator transition across the Ruddlesden-Popper (RP) iridates and explore the robustness of the effective $J\!=\!1/2$ insulating state\footnote{B.J. Kim {\it et al.}, Phys. Rev. Lett. {\bf 101}, 076402 (2008).} against band effects due to itineracy, tetragonal distortion, octahedral rotation and Coulomb interaction. The electronic structures we obtained are in good agreement with recent ARPES measurements.\footnote[3]{B.M. Wojek, {\it et al.}, J. Phys.: Condens. Matter {\bf 24}, 415602 (2012).}$^,$\footnote[4]{Q. Wang, {\it et al.}, Phys. Rev. B {\bf 87}, 245109 (2013).}$^,$\footnote[5]{Y. Nie, P. King, and K. Shen, private communication.} We predict the effects of epitaxial strain on the optical conductivity, magnetic moments and effective $J\!=\!1/2$ ground-state wave functions in the RP series. We demonstrate that the deviation from the ideal effective $J\!=\!1/2$ state is negligible at short time scales for both Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$, while it becomes quite significant for Sr$_3$Ir$_2$O$_7$ at long times and low energy, leading to a reconciliation of previous contradictory experimental results.