Roughly, one of the "properties" that shows up with these materials is that the 3d orbitals of coper atoms are involved in forming the bands near the fermi level. Couple that with the fun story of Cu electron configuration being [Ar] 3d^10 4s^1, which suggests that spin-effects are "at play" with these electrons near their filling levels. Combine that with the spin-character properties of cuprate paring (eg. s-wave vs. d-wave superconductors, (d-wave for BSCCO for instance)). All together it lends itself to a nice spin-orbit coupled band "setup" at the fermi energy that I have a hunch somehow backs the underlying mechanism of these d-wave superconductors. Fully admit, there's some leaps there in the raw logic -- if I could fully explain it I probably would still be in the field, haha.
I'll note: I've been out of the field for ~8 years, but a quick google search led to some more recent papers [1][2] working through plausible explanations based on some of these copper d orbital shenanigans.
[1] https://www.scirp.org/journal/paperinformation.aspx?paperid=... [2] https://arxiv.org/abs/2105.11664 (d-p, but includes the Cu d-orbital and also specifically states "We also show that the effect of the nearest-neighbor d-d Coulomb interaction Vdd is actually quite important for the stability of superconductivity and phase competition.")
