Phonon assisted optical excitation in narrow bandgap spin-orbit insulator Sr$_{3}$Ir$_{2}$O$_{7}$

We examined the temperature (T) evolution of the optical conductivity spectra of Sr$_{3}$Ir$_{2}$O$_{7}$ crystal. We found that the features of low energy $d$-$d$ excitation ($\hbar\omega$ $<$ 300 meV) between two $J_{\mathrm{eff}}$ = 1/2 states, evolve drastically in a wide temperature range (4 K $<$ T $<$ 400 K). This large T evolution in the low energy feature is not observed in O K-edge x-ray absorption spectra, suggesting that it is presumably originated from phonon-assisted indirect optical transitions. The results of the simulation in which the phonon-absorbing and phonon-emitting processes is considered, show a consistency with the experimental spectra. The peak energy of the transition between two $J_{\mathrm{eff}}$ = 1/2 bands also decreases apparently by $\sim$100 meV along with the abundance of phonon-assisted charge excitations in the narrow bandgap semiconductor Sr$_{3}$Ir$_{2}$O$_{7}$.