Flat bands in flatlands: a correlated quantum matter laboratory

Controlling and understanding electron correlations in quantum matter presents an outstanding goal in materials engineering. In the past years, new correlated states have been found by carefully stacking and twisting two-dimensional van der Waals materials of different kind. Unique to these stacked structures is the emergence of correlated phases not foreseeable from the single layers alone. Here, we discuss the emergence of Mott-Hubbard, heavy fermion and Hund physics, in Moiré superlattices. We show how to switch between Mott-Hubbard and Hund physics in multiband Moiré systems and elucidate the interplay of (doped) Mott Hubbard and heavy fermion physics in 1T-1H TaS₂ bilayers as well as magic angle twisted bilayer graphene. With the latter system, we illustrate how the formation and ordering of local moments shapes electronic behavior of Moiré quantum materials.