I taught this August in a summer school in Cargèse, Corsica, which is an island in the Mediterranean that is part of France. It was an especially fun trip for me as I attended a school at the same location in 1993, as a graduate student. Other students there with me were Leo Radzihovsky, Ali Yazdani, Katherine Moler, and Dan Dessau, to name a few that come immediately to mind. They all did rather well in physics since!
Anyway, I decided to lecture about twisted bilayer graphene (TBG), which was a bit of an undertaking – I gave 6 hours of lectures over 4 days. You can find my hand-written lecture notes on this site (under pedagogy), and I’m working on a latex version (I have them for 3 out of four of the 1.5 hour lectures).
I already benefited myself from the class, because it motivated me to finally work out an old idea I had. This is a derivation of the “continuum model” of Bistritzer and MacDonald (BM), which is what really started the whole TBG discovery by predicting the presence of “magic angles”. Their work is really nice, and many others have since used their formulation to elaborate or extend the treatment in many ways. I always felt though that the derivation in BM’s paper was not so intuitive, and the final result – the continuum model – is simpler than the way it was obtained. Specifically it just seems to capture the idea that locally TBG just “looks” like an untwisted bilayer with some relative shift between layers. I had the idea after reading their paper that one could derive the continuum model by turning that idea into a calculation.
There is some subtlety related to the difference between Eulerian and Lagrangian coordinate systems which stymied me initially. But since I had to teach the stuff I was motivated to spend the time and I was able to overcome that issue. The result is so simple it borders on trivial, but I like the simplicity of it. Maybe it makes the problem a bit more accessible to some people. You can read about it here: https://arxiv.org/abs/1909.01545.