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Mechanism of enhanced optical second-harmonic generation in the conducting pyrochlore-type Pb$_{2}$Ir$_{2}$O$_{7-x}$ oxide compound

The structural, electronic, and optical properties of pyrochlore-type Pb$_{2}$Ir$_{2}$O$_{6}$O'$_{0.55}$, 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 Pb-O' 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 5$d$ 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 5$d$ bands by the strong hybridization with O' 2$p$ orbitals. Our results stimulate theoretical study of inversion-broken iridates, where exotic quantum states such as a topological insulator and Dirac semimetal are anticipated.