Theory and experiment traditionally play a game of leapfrog over time. My impression has been that in superconductivity, the experiments have been ahead for yea

Theory and experiment traditionally play a game of leapfrog over time. My impression has been that in superconductivity, the experiments have been ahead for years (possibly multiple decades). There are lots of "high temperature" superconductors known, but nobody has yet come up with a model that can give a compelling explanation of how they all work (or, more importantly, predict how to make newer, better ones). So the breakthroughs that you're looking for have already happened: we don't even have a preferred theory to upend at the moment. (Which is why research like this could be a big deal if it pans out.)