From Strong Coupling Superconductivity to Fractionalization in Moire Materials

I will describe a strong coupling approach to flavor-ordered insulators and superconductivity in twisted bilayer graphene (TBG), in which the quantum geometry of the electronic bands plays a central role. I will discuss recent numerical simulations on realistic models of twisted bilayer graphene, involving >100 electrons, which confirm detailed aspects of this theory. An important outcome of this theory is the prediction of other platforms - the alternating twist multilayer graphene along with their associated magic angles - that retain the essential ingredients. I will highlight new features that are expected in these multilayer structures and compare them with recent experiments. Finally, I will describe how the unique quantum geometry of TBG makes it an ideal platform to realize fractional Chern insulators, and compare theory with new experimental observations.