Flatland: How Topological Flat Bands and Heavy Fermions Mix (MCQST-Colloquium) (Prof. Andrei Bernevig)

This mapping not only links two major fields of condensed matter, but also allows for a physical understanding of a lot of the properties of moire systems. The interacting and noninteracting physics of the topologically nontrivial flat bands in twisted bilayer graphene can be mapped into that of a heavy localized fermion carrying the interaction and a topological conduction semi metal carrying the topology. We show new progress in this mapping, with new application to twisted trilayers, magnetic field, and an (unlikely) scenario of electron phonon - induced superconductivity, all of which can be analytically tracked in this formalism. We then move to show that, far from being confined to the TBG, the mapping of topological flat bands to heavy fermions and topological semi metals is a generic principle in interacting flat band electrons. We provide these maps for the Lieb lattice as well as for other twisted and untwisted lattices.