The influence of topological phase transition on the superfluid density of overdoped copper oxides

We show that a quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by La_2-xSr_xCuO₄, whose superconductivity features differ from what is predicted by the classical Bardeen-Cooper-Schrieffer theory. This observation can open avenues for chemical preparation of high-T_c materials. We demonstrate that (1) at temperature T = 0, the superfluid density n_s turns out to be considerably smaller than the total electron density; (2) the critical temperature T_c is controlled by n_s rather than by doping, and is a linear function of the n_s; (3) at T > T_c the resistivity ρ(T) varies linearly with temperature, ρ(T) ∝ αT, where α diminishes with T_c → 0, whereas in the normal (non superconducting) region induced by overdoping, T_c = 0, and ρ(T) ∝ T². Our results are in good agreement with recent experimental observations.