Electronic structure changes in novel $J_{eff}$=1/2 system: Ruddlesden-Popper series Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ (n=1, 2, and $\infty )$

We investigated the electronic structures of Ruddlesden-Popper series Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ (n=1, 2, and $\infty )$ compounds with optical spectroscopy and first-principles calculation. Among Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$, while SrIrO$_{3}$ is a metal, Sr$_{2}$IrO$_{4}$ and Sr$_{3}$Ir$_{2}$O$_{7}$ are insulators. In optical conductivity spectra \textit{$\sigma $}(\textit{$\omega $}), we found unique bandwidth-driven changes of the electronic structures which were quite different from those of 3$d $or 4$d \quad S$=1/2 systems. From the comparison between \textit{$\sigma $}(\textit{$\omega $}) and the results of first-principles calculation, we found that the intriguing changes of the electronic structures can be realized by the cooperative interaction between the SO coupling and the electron correlation. These results clearly demonstrate that Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ should be considered as a $J_{eff}$=1/2 single band system.