Theoretical analysis of the origin of the double-well band dispersion in the CuO double chains of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ and its impact on superconductivity

TL;DR

This paper theoretically investigates the origin of the double-well band dispersion in Pr$_2$Ba$_4$Cu$_7$O$_{15-}$ and its implications for superconductivity, revealing the key role of local distortions and specific hopping paths.

Contribution

It identifies the microscopic origin of the large electron hopping parameter in the double chains, linking structural distortions to electronic properties and superconductivity.

Findings

Large $|t|$ results from cancellation of $d$-$d$ and $d$-$p$-$p$-$d$ contributions.

Local distortion enhances $d$-$p$-$d$ hopping, increasing $|t|$.

Double-well band dispersion promotes spin-fluctuation-mediated superconductivity.

Abstract

Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ is a unique member of cuprate superconductors where many studies suggest that CuO double chains are responsible for superconductivity. One characteristic and non-trivial feature of its electronic structure is a relatively large electron hopping $t$ between nearest neighbor Cu sites with a Cu-O-Cu angle of around 90 degrees. In this study, we have theoretically pinned down the origin of a large $|t|$ in the double-chain structure of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ using first-principles calculation and tight-binding-model analysis. We have found that, in the nearest neighbor hopping $t$, $d$-$d$ and $d$-$p$-$p$-$d$ contributions roughly cancel each other out and the $d$-$p$-$d$ hopping path enhanced by the local distortion of the double chain is a key to get the large $|t|$. Double-well band dispersion arising from the relatively large $|t/t'|$ allows the enhancement of spin-fluctuation-mediated superconductivity by the incipient-band mechanism, where the one band bottom plays a role of the incipient valley. Our study provides the important knowledge to understand the unique superconductivity in Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$.