The role of the apical oxygen in cuprate high-temperature superconductors

TL;DR

This study uses first-principles calculations to clarify how apical oxygen displacement affects superconductivity in cuprates, revealing that changes in hole doping, not charge-transfer gap, primarily drive observed variations.

Contribution

The paper provides a quantitative ab initio analysis linking apical oxygen displacement to superconducting properties, emphasizing the role of hole doping over charge-transfer gap effects.

Findings

Variations in superconducting order parameter are mainly due to changes in hole doping.

Apical oxygen displacement has negligible effect on the charge-transfer gap.

The framework can accurately model structural influences on superconductivity.

Abstract

Scanning tunneling microscopy measurements exploiting the natural superstructure modulation of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) have revealed a possible correlation between the Cu-apical-O distance $\delta_{\mathrm{api}}$ and the superconducting order parameter $m_{\mathrm{SC}}$, as reported recently by O'Mahony et al. (Proc. Natl. Acad. Sci. 119, e2207449119 (2022)). These observations were interpreted as evidence for a direct link between superconductivity and the charge-transfer gap, and more broadly revived the long-standing question of the role of apical oxygens in cuprate superconductivity. Using a combination of density-functional theory and cluster dynamical mean-field theory, we compute from first principles the variations of $m_{\mathrm{SC}}$ induced solely by apical oxygen displacement in Bi$_2$Sr$_2$CuO$_{6+\delta}$, Bi-2212, and HgBa$_2$CuO$_{4+\delta}$. The quantitative agreement between our calculations and experiments allows us to unambiguously attribute the observed variations of $m_{\mathrm{SC}}$ to changes in $\delta_{\mathrm{api}}$. We demonstrate, however, that these variations of $m_{\mathrm{SC}}$ originate predominantly from changes in the effective hole-doping of the CuO$_2$ planes, with negligible effect on the charge-transfer gap. The modest magnitude of the $m_{\mathrm{SC}}$ modulation induced by apical-oxygen displacement alone therefore warrants caution in interpreting correlations between $T_c$ and $\delta_{\mathrm{api}}$ inferred from comparisons across different cuprate compounds. Our work demonstrates that the present ab initio framework can quantitatively resolve the influence of specific structural degrees of freedom on superconductivity in correlated oxides.