The Mott Insulating Nature of Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$ : DFT$+$DMFT Study

We have investigated the insulating nature of Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$, employing both the density-functional theory (DFT) and the combination of the DFT and the dynamical mean-field theory (DFT$+$DMFT). We have obtained the paramagnetic (PM) insulating state even above the Neel temperature (T$_{\mathrm{N}})$, which reveals that Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$ is a Mott-type insulator. The photoemission spectrum is well described by the density of states from the DFT$+$DMFT in this PM insulating state. However, the analysis of optical conductivity suggests that the non-local correlation effect is also important in Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$. We have also found sizable redistribution of both charge and spin densities upon cooling below T$_{\mathrm{N}}$ which suggests that Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$ is not a standard Mott insulator having rigid charge density. Therefore, despite the Mott-type insulating state of Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$, the itineracy and the non-local correlation are important as well in describing its electronic and magnetic properties due to the extended nature of Ir 5$d$ state.