Cuprate interband model and doping dependence of the coherence length

TL;DR

This paper develops a two-band superconductor model to analyze how the coherence length and critical magnetic fields vary with doping in cuprates, matching recent experimental observations.

Contribution

It introduces a doping-dependent two-band model for cuprates that explains the nonmonotonic behavior of the coherence length and critical fields across doping levels.

Findings

Coherence length $\xi_{ab}$ decreases rapidly with doping initially.

$\xi_{ab}$ shows a marked increase at overdoping.

Critical magnetic field $H_{c0}$ closely follows $T_c$ and superfluid density.

Abstract

The free energy expansion of a two-band pair-transfer superconductor is developed. A critical in temperature and a noncritical coherence length appear. The effective in-plane $\xi_{ab}$, $H_{c2}\sp c\sim \xi_{ab}\sp{-2}$ and the thermodynamic critical magnetic field ($H_{c0}$) on the whole hole doping ($p$) scale are calculated for a "typical'' cuprate. A doping-prepared bare spectrum with normal state gaps quenched by doping has been used. The coherence length $\xi_{ab}$ falls with $p$ first rapidly. A moderate enhancement starts when the "cold'' defect band overlap with the valence band is reached. At overdoping $\xi_{ab}$ rises markedly. The $H_{c2}\sp c$ curve shows a maximum before $T_{cmax}$. The bell-like $H_{c0}$-curve follows closely $T_c$, superconducting gaps, and superfluid density. The theoretical $\xi_{ab}(p)$ nonmonotonic curve on the whole doping scale agrees with a recent experimental finding.