Fermi Liquid without Quasiparticles and Electron Spectral Functions of Two-Dimensional High-$T_c$ Superconductors

Properties of strongly correlated two-dimensional (2D) electron systems in solids are studied on the assumption that these systems undergo a phase transition, called fermion condensation, whose characteristic feature is flattening of the electron spectrum $ϵ(\text{pf}p)$. Unlike the previous models in the present study, the decay of single-particle states is properly taken into account. Remarkably, the value of the topological charge ($N=1\mathrm{/}2$) remains unchanged, supporting the view that systems with a fermion condensate form a separate class of Fermi liquids. Results of calculations are found to be in qualitative agreement with ARPES data.