  We examine possible low-temperature phases of a repulsively Rydberg-dressed
Fermi gas in a three-dimensional free space. It is shown that the collective
density excitations develop a roton minimum, which is softened at a wavevector
smaller than the Fermi wavevector when the particle density is above a critical
value. The mean field calculation shows that unlike the insulating charge
density waves states often observed in conventional condensed matters, a
self-assembled metallic density wave state emerges at low temperatures. In
particular, the density wave state supports a Fermi surface and a
body-center-cubic crystal order at the same time with the estimated critical
temperature being about one-tenth of the non-interacting Fermi energy. Our
results suggest the emergency of a fermionic quantum solid that should be
observable in current experimental setup.
