Infrared study of the electronic structure of metallic pyrochlore iridate Bi$_2$Ir$_2$O$_7$

We investigated the electronic properties of a single crystal of metallic pyrochlore iridate Bi$_2$Ir$_2$O$_7$ by using the infrared spectroscopy. Our optical conductivity data show the splitting of t$_{\mathrm{2g}}$ bands into J$_{\mathrm{eff}}$ ones due to strong spin-orbit coupling. We observed a sizable mid-infrared absorption near 0.2 eV within the J$_{\mathrm{eff,1/2}}$ bands, which indicates that this material may belong to a class of correlated system. Our findings suggest that the electronic structure of Bi$_2$Ir$_2$O$_7$ is governed by the strong spin-orbit coupling and the correlation effect, which is prerequisite for theoretically proposed non-trivial topological phases in pyrochlore iridates. We also discuss possible existence of the very far-infrared region of suppression in the optical conductivity of the compound.