Forming high- T Superconductors by the Topological FCQPT

In this chapter, we continue to consider the specific influence of the topological FCQPT on high-$$T:c$$ superconductors, see also Chaps. 5 and 6. We show that the topological FCQPT, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $${\mathrm{La}}:{2-{\mathrm{x}}}{\mathrm{Sr}}_{{\mathrm{x}}}{\mathrm{CuO}}_{4}$$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory. 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 (Figure presented.) $$T:c$$ 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 $$\rho (T)$$ varies linearly with temperature, $$\rho (T)\propto \alpha T$$, where $$\alpha $$ diminishes with $$T:c\rightarrow 0$$, while in the normal overdoped (nonsuperconducting) region with $$T:c=0$$, the resistivity becomes $$\rho (T)\propto T^2$$. The theoretical results presented are in good agreement with experimental observations, closing the colossal gap between these empirical findings and Bardeen-Cooper-Schrieffer-like theories. (The following chapter contains text from [1] that has been reprinted with the permission of the PCCP Owner Societies.)