'Fountains' of Flat Bands through Moiré Engineering

Moiré engineering provides an extraordinary platform for realizing controllable systems with strongly correlated physics, where the isolated flat bands near the Fermi level play a vital role. Here, we propose Moiré structures hosting tunable numbers of isolated flat bands near the Fermi level, in which the number of isolated flat bands directly relates to the size of the Moiré supercell. These flat bands remain isolated from the high-energy bands even in the presence of small higher-order terms and chiral-symmetry-breaking interlayer tunneling. At a small twist angle, thousands of isolated flat bands ('fountains') can be generated by the Moiré pattern to amplify flat band physics. The dramatic change in the number of flat bands in the Moiré Brillouin zone as the twist angle varies gives rise to a new platform for manipulating strongly correlated physics. We show that the isolated flat bands carry substantial quantum weights. Adding a BCS-type pairing potential generates superfluid weight. The large and adjustable density-of-state around the Fermi level contributed by the flat bands implies a high and tunable critical superconducting transition temperature.