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The pyrochlore oxide Cd₂Re₂O₇ is the only superconductor (T_c = 1.0 K) in the family of α-pyrochlore oxides [1]. Moreover, it exhibits two characteristic structural transitions losing the inversion symmetry below 200 K. Recently, it has attracted increasing attention as a candidate spin–orbit-coupled metal (SOCM), in which specific Fermi liquid instability can lead to odd-parity multipolar orders with spontaneous inversion-symmetry breaking [2] and parity-mixing superconductivity [3, 4]. More recent theoretical classifications based on the crystal symmetry reveal that the two parity-breaking phases are described by unconventional odd-parity multipoles, that are the electric toroidal quadrupoles (ETQs) with different components, x²−y² and 3z²−r² [5]. These ETQs are unique as they are cluster multipoles defined on the tetrahedral unit of the pyrochlore lattice, distinguished from conventional atomic multipoles realized in f-electron systems [6]. Here we report our recent experimental progress and review the present understanding of the SOCM Cd₂Re₂O₇.

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[6] S. Hayami, M. Yatsushiro, Y. Yanagi et al., Phys. Rev. B 98, 165110 (2018).