Flat Electronic Bands and Where to Find Them

It is possible to classify all the flat bands in the quantum materials in a "periodic table".

W. Kandinsky - Intersecting Lines (1923)

Dispersionless electronic states ("flat bands") is a paradigm change in condensed matter physics. Occasionally, in past we were discovering different cases of flat bands, such as (nearly) flat bands in Argon ice, Landau levels (flat bad in magnetic field), and more theoretical constructions such as flat bands in artificial atomic lattices (Lieb, Kagome, etc.). However, with advent of twisted bilayer graphene (TBG), where the controllable engineering of flat bands is possible, we have entered into the new era of the flat band research.

It has become clear shortly after that the [direct experiment] that the flat bands in twisted bilayer graphene are no coincidence, and not a lucky choice of material parameters; in fact, they are of the fundamental origin, the same way as the Landau levels. We have later realized that this construction is not limited to twisted bilayer, but one can add extra layers to enhance the Tc (trilayer; multilayer and "infinite"-laye