Variation of electron-electron interaction in pyrochlore structures

We conduct a comprehensive ab initio investigation of electron-electron interactions within the pyrochlore structures of ${R}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}, {R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}, {\mathrm{Ca}}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, and ${\mathrm{Cd}}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, where $R$ denotes a rare-earth element. Utilizing a multiorbital Hubbard model, we systematically explore the effects of various rare-earth elements and applied high pressure on the correlation strength in these compounds. Our calculations on the Coulomb interaction parameter $U$ and the bandwidth $W$ reveal that the chemical pressure for ${R}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ and ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ leads to an unusual increase in $U/W$ ratio, hence, an increase in correlation strength. Contrary to conventional understanding of bandwidth control, our study identifies that the Hubbard $U$ is more influential than the bandwidth $W$ behind the metal-insulator landscape of ${R}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ and ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, leading to an interaction-controlled metal-insulator transition. We also find unexpected behavior in physical pressure. Whereas physical pressure leads to a decrease in the correlation strength $U/W$ as usual in ${R}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, the effect is notably small in ${\mathrm{Ca}}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Cd}}_{2}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, which provides an important clue to understanding the unusual pressure-induced metal-insulator transition observed experimentally.