Quasiparticle dispersion and lineshape in a strongly correlated liquid with the fermion condensate

A model of a strongly correlated electron liquid based on the fermion condensation (FC) is applied to the consideration of high temperature superconductors in its superconducting and normal states. Within our model the appearance of FC presents a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. We show that at temperatures $T<T_c$ the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses $M^*_{FC}$ and $M^*_L$, respectively, and intersecting near the binding energy which is of the order of the superconducting gap. This same picture persists in the normal state being modified only by the presence of the quasiparticle width. We argue that this strong change of the quasiparticle dispersion can be enhanced in underdoped samples due to strengthening the FC influence. The single particle excitation width and lineshape are also studied.