Topological scenario for high-temperature superconductivity in cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity $\rho(T)$, including the observed crossover from the linear temperature behavior $\rho(T,x)=A_1(x)T$ at doping levels $x$ below the critical value $x_c^h$ corresponding to the boundary of the superconducting region to the quadratic temperature behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient $A_1(x)$ is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the $D$-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the $S$ channel, leads to high-temperature superconductivity in the $D$ channel.