Tunable square-lattice Hubbard models from twisted homobilayers

We study the band structures of twisted homobilayers of square lattice materials. At low twist angles, we demonstrate the emergence of flat moire bands. The approximate layer symmetry of the homobilayer further allows to create moire bands with exotic properties, such as dominant next-nearest neighbor hopping that can be tuned with external fields. We thus establish twisted rectangular-lattice bilayers as a platform for the realization of tunable extended $t-t'-U$ Hubbard and J-J' models, which may host exotic superconducting and spin liquid states. Finally, potential candidate materials will be discussed.