Variation of Electron-electron interaction in pyrochlore structures

We conduct a comprehensive ab initio investigation of electron-electron interactions within the pyrochlore structures of R₂Ru₂O₇, R₂Ir₂O₇, Ca₂Ru₂O₇, and Cd₂Ru₂O₇, 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 R₂Ru₂O₇ and R₂Ir₂O₇ leads to an unusual increase in $U/W$ ratio, hence, 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 R₂Ru₂O₇ and R₂Ir₂O₇, 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 R₂Ru₂O₇, the effect is notably small in Ca₂Ru₂O₇ and Cd₂Ru₂O₇, which provides an important clue to understanding unusual pressure-induced metal-insulator transition observed experimentally.