A parity-breaking electronic nematic phase transition in the spin-orbit coupled correlated metal Cd$_2$Re$_2$O$_7$

Strong interactions between electrons are known to drive metallic systems toward a variety of well-known symmetry-broken phases, including superconducting, electronic liquid crystalline, and charge- and spin-density wave ordered states. In contrast, the electronic instabilities of correlated metals with strong spin-orbit coupling have only recently begun to be explored. We uncover a novel multipolar nematic phase of matter in the metallic pyrochlore Cd$_2$Re$_2$O$_7$ using spatially-resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic liquid crystalline phases, this multipolar nematic phase spontaneously breaks rotational symmetry while preserving translational invariance. However, it has the distinguishing property of being odd under spatial inversion, which is allowed only in the presence of spin-orbit coupling. By examining the critical behavior of the multipolar nematic order parameter, we show that it drives the thermal phase transition near 200 K in Cd$_2$Re$_2$O$_7$ and induces a parity-breaking lattice distortion as a secondary order parameter.