  We investigate the ground-state properties and the collective modes of a
two-dimensional two-component Rydberg-dressed Fermi liquid in the
dipole-blockade regime. We find instability of the homogeneous system toward
phase separated and density ordered phases, using the Hartree-Fock and
random-phase approximations, respectively. The spectral weight of collective
density oscillations in the homogenous phase also signals the emergence of
density-wave instability. We examine the effect of exchange-hole on the
density-wave instability and on the collective mode dispersion using the
Hubbard local-field factor.
