Interesting. Before reading the abstract and press release, I assumed "vanish" was PR-speak for "join into Cooper pairs". It sounds like it's something else, though. A "Fermi Surface" seems to be defined in terms of a bunch of other things I have no idea about, so unless someone comes along with a really good ELI5 I don't think I'm going to get it...
> I assumed "vanish" was PR-speak for "join into Cooper pairs".
I don't think so, because that is a known and well-understood feature of any superconductor (not just high temperature), and the press release makes it seem like whatever this "electron vanishing" thing is, it's something just discovered in this paper, or at least something that's particular to the high temperature superconductors being studied in this paper.
> A "Fermi Surface" seems to be defined in terms of a bunch of other things I have no idea about
Electrons are fermions, which means they obey the Pauli exclusion principle. So if you imagine a piece of material like this "cuprate" semiconductor and start out with zero electrons anywhere in it, and then you start to put electrons in, no two electrons can be in the same state so they will start filling energy levels from the lowest level on up, in much the same way as electrons fill energy levels in a single atom. So you can, very roughly, think of the material as being "filled" with electrons the way a container fills with a fluid. The "Fermi surface" is then just the "surface" of the electron "fluid" filling the material, when the material has its usual number of electrons based on how many atoms are in it and what type of atoms they are. In less metaphorical language, it is the "surface" formed by the highest energy levels that are filled.
In a single atom, the energy levels are pretty much fixed regardless of external variables like temperature (external electric or magnetic fields can change them some, but not a lot, and not in ways that change the qualitative behavior of the atom). But in a material containing a very large number of atoms (there will be something like 10^23 of them in a typical sample of superconductor material like those in this experiment), the energy levels can change as temperature and other external variables (like the magnetic field) change, not just by small shifts, but by changing the whole "shape" of the levels, and hence of the Fermi surface. That appears to be what is happening in these superconductors.
Turns out it's not a super esoteric concept. It is a "map of where the electrons are", but (and of course the uni PR won't tell you this) it's not a literal position map, it's a map in momentum space. And like you say, it's focused on the highest energy electrons. So it's really saying how the highest energy electrons are distributed in momentum space.
I read that page before posting. It's pretty dense. :) Eventually I got to the "map in momentum space" part and it started making more sense, but I still had to read the page about energy bands a couple times, and it's still pretty hazy.