  We study Fermi liquid instabilities in spin-orbit-coupled metals with
inversion symmetry. By introducing a canonical basis for the doubly degenerate
Bloch bands in momentum space, we derive the general form of interaction
functions. A variety of time-reversal-invariant, parity-breaking phases is
found, whose Fermi surface is spontaneously deformed and spin-split. In terms
of symmetry, these phases possess gyrotropic, ferroelectric and multipolar
orders. The ferroelectric and multipolar phases are accompanied by structural
distortions, from which the electronic orders can be identified. The gyrotropic
phase exhibits a unique nonlinear optical property. Based on recent
experiments, we identify several interesting quantum materials including
pyrochlore oxides, which show evidence of these parity breaking orders.
