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

Highlights: • Phase diagram of cuprates analyzed, focusing on hole-overdoped regime. • Resistivity measurements support existence of topological critical point. • Topological critical point gives rise to interaction-induced flat band. • Explanation of observations by conventional fluctuation scenarios fails. - Abstract: 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 for 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 $\rho \left(T\right)$, especially the observed gradual crossover from normal-state T-linear behavior $\rho (T,x)=A_1\left(x\right)T$ at doping x below the critical value $x_c^h$ of hole doping 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 the slope of the coefficient $A_1$ is universal, being the same on both boundaries of the joint phase diagram of cuprates, in agreement with available experimental data.