Occurrence of flat bands in strongly correlated Fermi systems and high-$T_c$ superconductivity of electron-doped compounds

We consider a class of strongly correlated Fermi systems that exhibit an interaction-induced flat band pinned to the Fermi surface, and generalize the Landau strategy to accommodate a flat band and apply the more comprehensive theory to electron systems of solids. The non-Fermi-liquid behavior that emerges is compared with relevant experimental data on heavy-fermion metals and electron-doped high-$T_c$ compounds. We elucidate how heavy-fermion metals have extremely low superconducting transition temperature $T_c$, its maximum reached in the heavy-fermion metal CeCoIn$_5$ does not exceed $2.3$ K, and explain the enhancement of $T_c$ observed in high-$T_c$ superconductors. We show that the coefficient $A_1$ of the $T$-linear resistivity scales with $T_c$, in agreement with the experimental behavior uncovered in the electron-doped materials. We have also constructed schematic temperature-doping phase diagram of the copper oxide superconductor La$_{2-x}$Ce$_x$CuO$_4$ and explained the doping dependence of its resistivity.