Electron spectral functions of two-dimensional high-$T_c$ superconductors in the model of fermion ocndensation

Spectral functions 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 $\epsilon({\mathbf p})$. Unlike the previous models in the present study, the decay of single-particle states is properly taken into account. Results of our calculations are shown to be in qualitative agreement with ARPES data. The universal behavior of the ratio $\operatorname{Im}\Sigma({\mathbf p},\varepsilon,T)/T$ as a function of $x=\varepsilon/T$, uncovered in for the single-particle states around the diagonal of the Brillouin zone, are found to be reproduced reasonably well. However, in our model this behavior is destroyed in vicinities of the van Hove points where the fermion condensate resides.