Theory of high-T_c superconductivity based on the fermion-condensation quantum phase transition

A theory of high temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap which can be as big as ${\mathrm{\Delta }}_1\sim 0.1{ϵ}_F$, with ${ϵ}_F$ being the Fermi level. We show that the critical temperature $2T_c\simeq {\mathrm{\Delta }}_1$. If there exists the pseudogap above $T_c$ then $2T^{\ast }\simeq {\mathrm{\Delta }}_1$, and $T^{\ast }$ is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at $T_c$ is calculated. The transition from conventional superconductors to high-$T_c$ ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered.