DiscoBahb

Repeat after me: Flat bands do not imply superconductivity. DFT calculations cannot be used to predict superconductivity. DFT is a single-particle calculation. Superconductivity is a multi-particle phenomenon.

At most, the preprint(s) you're referring to suggest that maybe (under their unverified assumptions) electron-electron interactions could lead to interesting physics in that material. It provides no evidence for what that physics looks like and says nothing about what temperature these things will occur.

High temperature superconductivity is not well understood and we do not have the theoretical tools to make quantitative predictions about it. At best we run dodgy simulations, squint at the resulting plots, and say "hm, that's interesting".

Think of it this way: in something like copper, atoms are arranged in a 3d lattice, and electrons are able to jump (or "tunnel") from copper atom to copper atom freely in any of the x, y or z directions because the lattice looks the same in each direction.

Some more complex materials do not have this symmetry, and the ability of the electrons to tunnel is much stronger in some directions than others. In many known high temperature superconductors electrons are more or less confined to move in a 2d plane (even though a lump of the material is obviously a 3d object) so they are called "quasi-2d".

In other materials they are confined to move in only one direction, which seems to be the case with LK-99