QuantAlps
An ecosystem for quantum sciences & technologies 

Scanning tunneling microscopy measurements exploiting the natural superstructure modulation of the cuprate superconductor Bi_2Sr_2CaCu_2O_{8+x} (Bi-2212) have revealed a possible correlation between the Cu-apical-O distance and the superconducting order parameter, as reported recently by O’Mahony et al. [1]. 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. In this talk, I will discuss the impact of apical oxygen displacement on the superconducting properties of Bi_2Sr_2CuO_{6+x}, Bi-2212, and HgBa_2CuO_{4+x} [2], leveraging a recently developed first-principles framework for high-temperature superconductors [3]. The quantitative agreement between our calculations and experiments allows us to unambiguously attribute the observed variations of superconducting order parameter to changes in the apical distance. We demonstrate, however, that the latter controls the former predominantly via the effective hole-doping of the CuO_2 planes, with negligible effect on the charge-transfer gap. The modest magnitude of the order parameter modulation induced by apical-oxygen displacement alone therefore warrants caution in interpreting correlations between T_c and the apical distance inferred from comparisons across different cuprate compounds.