Mechanism of Enhanced Optical Second-Harmonic Generation in the Conducting Pyrochlore-Type ${\mathrm{Pb}}_2{\mathrm{Ir}}_2{\mathbf{O}}_{7\mathbf{\text{−}}x}$ Oxide Compound

The structural, electronic, and optical properties of pyrochlore-type ${\mathrm{Pb}}_2{\mathrm{Ir}}_2{\mathrm{O}}_6{\mathrm{O}}_{0.55}^{\prime }$, which is a metal without spatial inversion symmetry at room temperature, were investigated. Structural analysis revealed that the structural distortion relevant to the breakdown of the inversion symmetry is dominated by the $\mathrm{Pb}\mathrm{\text{−}}{\mathrm{O}}^{\prime }$ network but is very small in the Ir-O network. At the same time, gigantic second-harmonic generation signals were observed, which can only occur if the local environment of the Ir $5d$ electrons features broken inversion symmetry. First-principles electronic structure calculations reveal that the underlying mechanism for this phenomenon is the induction of the noncentrosymmetricity in the Ir $5d$ bands by the strong hybridization with ${\mathrm{O}}^{\prime }$ $2p$ orbitals. Our results stimulate theoretical study of inversion-broken iridates, where exotic quantum states such as a topological insulator and Dirac semimetal are anticipated.