Spin-Orbit Coupling Assisted Mott Insulator Sr$_{2}$IrO$_{4}$

We have systematically investigated the effect of spin-orbit coupling to the optical conductivity spectra \textit{$\sigma $}(\textit{$\omega $}) of Sr$_{2}$IrO$_{4}$. Both Sr$_{2}$RhO$_{4}$ and Sr$_{2}$IrO$_{4}$ have five $d$ electrons and similar crystal structures. However, Sr$_{2}$RhO$_{4}$ and Sr$_{2}$IrO$_{4}$ are metallic and insulating, respectively. The insulating ground state of Sr$_{2}$IrO$_{4}$ is rather surprising, since it has 5$d$ electrons, which are commonly thought to have extended orbitals. We observed a sharp absorption at about 0.5 eV in \textit{$\sigma $}(\textit{$\omega $}). This spectral feature cannot be explained in terms of orbital degeneracy and/or density wave. Note that Ir has 5$d$ electrons, so that its spin-orbit coupling should be larger than that of 4$d$ Rh ions. With the aid of the first principles calculation based on the LDA+$U$ scheme, we took into account of the effect of spin-orbit coupling. Our results clearly demonstrate that spin-orbit coupling plays a crucial role to the Mott insulating ground state of Sr$_{2}$IrO$_{4}$.