Computational Demonstrations of Density Wave of Cooper Pairs and Paired-Electron Liquid in the Quarter-Filled Band -- a Brief Review

TL;DR

This paper reviews theoretical and computational evidence for density wave states of Cooper pairs and paired-electron liquids in quarter-filled bands, highlighting their relevance to superconductivity in organic solids and cuprates.

Contribution

It provides a comprehensive review of the authors' work on paired-electron crystals and their role in superconductivity, extending insights to cuprate phase diagrams.

Findings

Paired-electron crystal observed in organic superconductors.

Superconductivity evolves from the paired-electron crystal state.

Carrier density of one charge per two sites is crucial for PEC formation.

Abstract

There has been strong interest recently in the so-called Cooper pair density wave, subsequent to the proposition that such a state occurs in the hole-doped cuprate superconductors. As of now there is no convincing demonstration of such a state in the cuprate theoretical literature. We present here a brief but complete review of our theoretical and computational work on the paired-electron crystal (PEC), which has been also experimentally seen in the insulating phase proximate to superconductivity (SC) in organic charge-transfer solid (CTS) superconductors. Within our theory, SC in the CTS does indeed evolve from the PEC. A crucial requirement for the finding of the PEC is that the proper carrier density of one charge carrier per two sites is taken into consideration at the outset. Following the discussion of CTS superconductors, we briefly discuss how the theory can be extended to understand the phase diagram of the cuprate superconductors that has remained mysterious after nearly four decades of the discovery of SC in this family.