The cuprate superconductors: a phenomenological overlook

TL;DR

This paper presents a phenomenological model of high-temperature superconductivity in cuprates, dividing the doping range into underdoped and overdoped regions based on a quantum critical point, and links localization to pseudogap formation.

Contribution

It introduces a new phenomenological framework that distinguishes the electronic states in cuprates across the quantum critical point, connecting localization, pseudogap, and superconductivity.

Findings

Localization is essential for pseudogap formation.

Superconducting gap and coherence emerge simultaneously.

Coherence induces phonons around the node.

Abstract

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.