The cuprate superconductors: a phenomenological overlook

We, basing on the quantum critical point (QCP)($p = 0.19$), propose a phenomenological description on high-$T_c$ superconductivity in the cuprate superconductors, and suggest it divides the whole doping region into two parts: the underdoped region ($p < 0.19$) and the overdoped region ($p> 0.19$). The electrons in the former are localized and form the localized Fermi liquid, a kind of the non-Fermi liquid, where the carriers are the holes; the electrons in the latter are itinerant and form the Fermi liquid, where the carriers are the electrons. We further argue that localization is a prerequisite to the pseudogap; the superconductivity gap and coherence forms at the same time, which both share the same energy scale; coherence induces phonon around the node.

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