My extremely layman understanding notices the currently known high temperature super conductors are crystalline, structure seems to matter, but whether a nanoscale structure above this could possibly have any significant effect? It would be nice to get the opinion of someone less vaguely educated on the subject :)
Another point to consider is that most chemically homogeneous solids are in principle crystalline, although in practice a chunk of matieral may be made of very many tiny crystals stuck together in random orientations.
As for whether nanoscale structure could have a significant effect, that question forms a pretty major part of my current research. The stuff I'm actively working on isn't ready to publish yet, but to repeat the example I mentioned elsewhere in the comments, my colleagues were able to increase the superconducting transition temperature of strontium titanate by almost a factor of 2 by plastic deformation (i.e. squeezing it until we start messing up the structure) [0][1] (full disclosure: I'm one of the authors of this paper). We think this basically occurs by modifying the nanoscale structure in a way that introduces mechanical strain in the crystal, and this strain in turn influences the electronic interactions in such a way as to locally increase the superconducting transition temperature. In a general sense, this is somewhat similar to the fact that in many cases, applying high pressure to many superconductors will increase their transition temperature.
[0] https://www.nature.com/articles/s41563-021-01102-3 [1] https://arxiv.org/abs/2005.00514 (same paper as above, but in a non-peer-reviewed and paywall-free version)
I've always wondered if there could be something to this, and now it sounds like there might be. I have no way to judge the merits of it personally, I just keep my eye out for things that indicate it might have been real.
Also, there's this patent[2] from 3 years ago that might have been using strain to make a superconductor that previously wasn't.