Interlayer couplings in cuprates: structural origins, analytical forms, and structural estimators

TL;DR

This paper identifies microscopic mechanisms behind interlayer couplings in cuprates using first-principle calculations, relates them to structural features, and provides analytical estimators for these couplings based on crystal structure.

Contribution

It introduces analytical formulas to estimate interlayer couplings from structural data and benchmarks the approach on YBa2Cu3O7.

Findings

Interlayer couplings are mediated by specific orbital hoppings.

Structural distortions influence the magnitude of interlayer couplings.

Analytical estimators can predict couplings from crystal structure.

Abstract

We quantitatively identify the multiple distinct microscopic mechanisms contributing to effective interlayer couplings (EICs) by performing first-principle calculations for two prototype superconducting cuprate families, pristine and doped Bi$_2$Sr$_2$CaCuO$_2$O$_{8+x}$ and Pr$_{x}$Y$_{1-x}$Ba$_2$Cu$_3$O$_7$. The major mechanisms are mediated by interlayer oxygen $p_{\sigma}$-$p_{\sigma}$ and $p_z$-$p_z$ hoppings as well as interlayer copper $d_{z^2}$-oxygen $p_{\sigma}$ hoppings. Furthermore, we show how EICs are closely related to structural distortions such as layer bucklings and bond length changes. This allows us to provide analytical formulae that permit direct estimation of the key interatomic hoppings and the EICs based only on the crystal structure. Finally, we benchmark our method on YBa$_2$Cu$_3$O$_7$ to estimate the strength and anisotropy of the EIC.