Electronic states of metallic electric toroidal quadrupole order in Cd2Re2O7 determined by combining quantum oscillations and electronic structure calculations

Abstract

Pyrochlore oxide ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ exhibits successive structural transitions upon cooling that break its inversion symmetry. The low-temperature noncentrosymmetric metallic phases are believed to be some odd-parity multipole ordered states that are associated with a Fermi-liquid instability due to the strong spin-orbit interaction (SOI) and electronic correlation. However, their microscopic ordering pictures and the driving force of the phase transitions are still unclear. We determined the electronic structure of the lowest temperature phase of ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ by combining quantum oscillation measurements with electronic structure calculations. The observed Fermi surfaces were well reproduced based on the optimized crystal structure, and we demonstrated the strong influence of the antisymmetric SOI. From the mass enhancement factor, we elucidated the strongly correlated nature of the electronic states. In addition, we visualized the microscopic picture of the $3{z}^{2}\ensuremath{-}{r}^{2}$-type metallic electric-toroidal-quadrupole (ETQ) order characterized by the Re-O bond order. These results corroborate that the metallic ETQ order is driven by a Fermi-liquid instability associated with the strong SOI and electronic correlation, as has been theoretically proposed. Our results provide the basis for exploring unconventional phenomena expected in the metallic ETQ order.