Introduction to Magic Angles in Twisted Bilayer Graphene

I will introduce the theory of twisted bilayer graphene. A key feature of this material is the existence of flat bands, where effective quasiparticles become infinitely heavy. The resulting theory is equivalent to that of two-dimensional massless fermions in a non-abelian magnetic field, enabling us to derive many intriguing results using methods from high-energy physics and the theory of vector bundles. I will derive the Hamiltonian for this system, demonstrate that the emergence of these flat bands is inevitable, and illustrate the connection to Landau levels. If time permits, I will briefly discuss how twisted bilayer and trilayer graphene are related to each other.