  We are reporting a new non-Fermi liquid type normal phase that has a well
defined Fermi energy, but without showing any non-regularity in the momentum
distribution function in the whole momentum space, the sharp Fermi momentum
concept being undefinable. The system contains a natural built in gap that is
visible in the physical properties of the system at nonzero temperatures. The
presence of a flat band in multiband interacting Fermi systems with more than
half filling is the key feature leading to such a ground state, which is not
restricted to one spatial dimension and emerges in the proximity of an
insulating phase.
