  We investigated Ru-doped single-crystal 5$d$ iridiates,
Sr$_2$Ir$_{1-x}$Ru$_x$O$_{4}$, at three different doping concentrations ($x =$
0.01, 0.07 and 0.10) using optical spectroscopy. The undoped pristine compound
(Sr$_2$IrO$_{4}$) is known as a novel $J_{eff}$ = 1/2 Mott insulator.
Remarkably, the optical conductivity spectra of all three samples exhibited the
insulating behavior, although we observed weak Drude components in the optical
conductivity spectra down to the lowest temperature of 30 K. The charge-carrier
densities of the Ru-doped iridiates estimated from the Drude components are
significantly smaller than the expected values estimated from the nominal
Ru-doping concentrations. Herein, we provide temperature- and doping-dependent
electronic structure evolution of Ru-doped iridiates. We expect that our
results will be useful for understanding the intriguing Ru-doping-dependent
properties of 5$d$ iridiate Sr$_2$IrO$_{4}$.
