Evidence for Dirac flat band superconductivity enabled by quantum geometry

Offtopic, personal bugbear on a grumpy early morning:

I have a physics degree, which is true of only a minority of HN users, and I have no idea what TBG and BCS stand for here. Using abbreviations when communicating with audiences that can't be expected to know them wastes everyone else's time to save you seconds of typing.

Edit: TBG - Twisted Bilayer Graphene, BCS - Bardeen–Cooper–Schrieffer.

Whenever I read about bilayer twisted graphene or topological insulators, I can’t help thinking that these are going to be the basis for next-gen transistors. Of I totally agree that understanding nature is its own goal, please raise my taxes for graphene research!

Not my area, so I may have some wrong details...

The energy of a normal electron in vacuum is E = 1/2 m v^2 that is a nice curved parable.

Inside a crystal, thing are more weird. There is a maximum speed, or to be more precise, the repetition of the atoms make the speed v and the speed v+2K equivalent, where K is a number that you can calculate using the distance between the atoms. So instead of speeds from -infinity to +infinity, you only have to consider speeds from -K to K.

The energy is something like -cos(pi*v/K) that is again a nice curve. It's actually more complicated, so the shape is not exactly cos, but most of the times something similar enough. It's much more complicated, some have peaks in some points, some have the oposite sign with the maximum at 0 instead of K, ... but I don't want to go down that rabbit hole. Anyway, they are curved functions. These are called "bands".

The first interesting part is that in some materials like two sheets of graphene when you get an horizontal line instead of a curved line. It's weird because it means that the energy of a moving electron inside this crystal is equal t the energy of an electron that is not moving inside this crystal!! That is a "flat band". [Sorry, no idea why it happens.]

Dirac probably predicted them, or it was later misaligned to him, so they are "Dirac flat bands". [Dirac has a few extremely important/interesting results, I'm just not sure about this one.]

For some reason this sheets of graphene are superconductive, probably when they are very cold, but I'm guessing.

I have absolutely no idea what "quantum geometry" means here.

TL;DR: After reading the abstract, it looks safe to ignore unless you work in superconductivity, or graphene, or other similar stuff. Some results are interesting for a small group of cutting edge researches, and they may have applications in the future, but for a layman my recommendation is just to ignore it.

HN is not a layman's blog. It presumes that readers have a substantial technical background. Of course no one is versed in all areas so when you see something that is beyond your knowledge feel free to google it.