Title: A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd$_2$Re$_2$O$_7$,
Abstract: Strong electron interactions can drive metallic systems toward a variety of
well-known symmetry-broken phases, but the instabilities of correlated metals
with strong spin-orbit coupling have only recently begun to be explored. We
uncovered a 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 nematic phases, this
multipolar 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 kelvin in Cd$_2$Re$_2$O$_7$ and induces a parity-breaking lattice
distortion as a secondary order.