New non-Fermi-liquid-type behaviour by a two-band system in normal phase

We are reporting a new non-Fermi-liquid-type normal phase that has a well d efined Fermi energy, but without showing any non-regularity in the momentum distribution function nk in the whole momentum space, the sharp Fermi mome ntum concept being undefinable. The system contains a natural builtin gap t hat is visible in the physical properties of the system at nonzero temperat ures. The presence of a flat band in multi-band interacting Fermi systems w ith more than half filling is the key feature leading to such a ground stat e, which is not restricted to one spatial dimension and emerges in the prox imity of an insulating phase.