A unified model for underdoped and overdoped cuprate superconductors based on a spinodal transition

TL;DR

This paper proposes a unified theory for cuprate superconductors based on a spinodal transition, explaining phenomena from insulators to overdoped metals, and linking charge order, pseudogap, and superconductivity.

Contribution

It introduces a spinodal or charge-separation transition model that unifies the behavior of cuprates across doping levels, incorporating charge density waves and mesoscopic superconductivity.

Findings

Thermodynamic transition indicated by Hall coefficient variations.

Charge density wave domains emerge from a double-well free-energy landscape.

Superconducting puddles form in confined regions, leading to granular superconductivity.

Abstract

Many years of intense research on cuprate superconductors have led to several discoveries, such as the pseudogap and charge density waves (CDW), yet a complete theory is still lacking. By analyzing some experiments and performing calculations, we provide a full interpretation of their properties; from the undoped insulator to the overdoped metallic compounds. The variation of the anomalous Hall coefficient ($R_{\rm H}(T)$) with temperature at half-filling ($n = 1$) and, combinations of undoped ($p = 0$) insulators and metallic films, which, among other things, are indicative of a thermodynamic transition. On the overdoped side, recent experiments near the superconducting-to-metal transition detecting superconducting puddles and a considerable degree of charge disorder, suggest that a similar thermodynamic transition operates at all doping levels. We propose a spinodal or charge-separation transition starting near the pseudogap temperature $T^*(p)$, which among other things generates the CDW domains with a typical double-well Landau free-energy functional. Thus, from the half-filled to the overdoped region, the free energy forms an array of wells with $n = 1$ {\it static} holes. With doping, {\it mobile} holes tend to occupy these wells with alternating high and low densities, generating the CDW pattern. The confined holes in small regions develop local superconducting amplitudes, giving rise to a mesoscopic granular superconductor. Similar to the XY model, the grains develop correlation effects mediated by Josephson coupling, which is proportional to the local superfluid density. This approach yields a unified theory of cuprate superconductors.