Apex oxygen and critical temperature in copper oxide superconductors: Universal correlation with the stability of local singlets

Polarized x-ray absorption spectroscopy study of the symmetry of unoccupied electronic states near the Fermi level in the system

“…Another report [35] in the case of the 1-2-3 system indicates an increase in the weight of the O 2p x,y orbital but no change in the weight of the O 2p z orbital when these go from the normal to the superconducting state. This would then be in contradiction to the theoretical predictions such as those in [24,34]. Another question related to these is whether these predominantly arise from the apical oxygen atom and whether any increase in the number of holes at the apical O sites are detrimental to superconductivity.…”

“…It is still unclear whether some of the oxygen holes with p z symmetry are, in accordance with the theoretical models that involve d z 2 holes, situated in the CuO 2 planes or the p z holes predominantly belong to the apex oxygen atom [23]. There is also evidence quoted against this argument [24,34] which claims that these, if present, would suppress superconductivity.…”

“…Moreover, not only is the significance of the high out-of-plane O 2p z difficult to understand but also one may want to question whether the observed O 2p z content directly reflects the coupling of the apical oxygen atoms with the in-plane orbitals. Many models, especially those proposed by Weber [22] and Kamimura [23], depend on the presence of out-of-plane Cu 3d and O 2p orbitals while others such as that of Ohto et al [24] report that the presence of these would act against superconductivity.…”

Van Hove exciton-cageons and high-Tc superconductivity XA. Role of spin-orbit coupling in generating a diabolical point

“…Hence, anything which reduces the Cu-apical O separation also reduces the d − d splitting, in turn reducing the effective value of t OO . The correlation between small T c and small optimum hole doping has been known for a long time, and it is also known that the apical oxygen plays some role, since a larger apical O potential correlates with higher T c [38]. An important role in the theory is played by the magnitude of the spin-orbit coupling.…”

“…Appendix III: Distortion of CuO 6 Octahedra Ohta, et al [38], by compiling data on a large number of cuprate superconductors, were able to find only one consistent correlation between T c and a molecular property: the larger the apical oxygen -planar oxygen energy splitting, ∆V A , the higher is T c . In the text, I suggest a related correlation: a smaller value of the d − d splitting ∆V d should cause a smaller effective value of t OO [33], which in turn correlates with a lower value of T c .…”