Magnetoelectric Response in Electric Octupole State: Possible Hidden Order in Cuprate Superconductors

Motivated by recent studies of odd-parity multipole order in condensed matter physics, we theoretically study magnetoelectric responses in an electric octupole state. Investigating the Edelstein effect and spin Hall effect in a locally noncentrosymmetric bilayer Rashba model, we clarify characteristic properties due to parity violation in the electric octupole state. Furthermore, a possible realization of electric octupole order in bilayer high-Tc cuprate superconductors is proposed. Our calculation of magnetic torque is consistent with recent experimental observation of a kink above the superconducting transition temperature. We also show significant enhancement of the in-plane anisotropy in spin susceptibility due to the superconductivity, and propose an experimental test by means of the nuclear magnetic resonance in the superconducting state. A spin-orbit coupled metal state in Cd2Re2O7 is also discussed.