The influence of topological phase transition on the superfluid density of overdoped copper oxides
We show that a topological 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 $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bozović, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. 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, $ρ(T)\propto αT$, where $α$ diminishes with $T_c\to 0$, while in the normal overdoped (non superconducting) region with $T_c=0$, the resistivity becomes $ρ(T)\propto T^2$. The theoretical results presented are in good agreement with recent experimental observations, closing the colossal gap between these empirical findings and Bardeen-Cooper-Schrieffer-like theories.