Toward a topological scenario for high-temperature superconductivity of copper oxides

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites of an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $\rho (T)$, especially the observed gradual crossover from normal-state $T$-linear behavior $\rho (T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that at $x<x_c^h$, in agreement with available experimental data, the coefficient $A_1(x)$ is decomposed into the product of two factors, one of which changes linearly with doping $x$, while the second is universal, being of the Planckian form.