Generation of Isolated Flat Bands with Tunable Numbers through Moiré Engineering*

In contrast to the Dirac-cone materials in which the low-energy spectrum features a pseudospin-1/2 structure, Lieb and Dice lattices both host triply degenerate low-energy excitations. Here, we discuss moiré structures involving twisted bilayers of these lattices, which are shown to exhibit a tunable number of isolated flat bands near the Fermi level due to the bipartite nature of their structures. 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 small twist angles, many isolated flat bands can be generated with a notable Berry curvature, which could provide a geometric contribution to the superfluid weight under a BCS-type pairing potential. Remarkably, the emergence of isolated flat bands is insensitive to the twist angle, so that fine-tuning of the twist angle in an experimental setup would not be required. Our study suggests a promising new and efficient avenue for exploring and engineering flat bands based on the twisted bilayer Lieb and Dice lattices.