Geometry-Driven Moiré Engineering in Twisted Bilayers of High-Pseudospin Fermions

Abstract: Moir\'e engineering offers new pathways for manipulating emergent states in twisted layered materials and lattice-mismatched heterostructures. With the key role of the geometry of the underlying lattice in mind, here we introduce the watermill lattice, a two-dimensional structure with low-energy states characterized by massless pseudospin-3/2 fermions with high winding numbers. Its twisted bilayer is shown to exhibit magic angles, where four isolated flat bands emerge around the Fermi level, featuring elevated Wilson-loop windings and enhanced quantum geometric effects, such as an increase in the ratio of the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature to the mean-field critical temperature under a weak Bardeen-Cooper-Schrieffer (BCS) pairing. We discuss how the watermill lattice could be realized in the MXene and group-IV materials. Our study highlights the potential of exploiting lattice geometry in moir\'e engineering to uncover novel quantum phenomena and tailor emergent electronic properties in materials.