Multi-ultraflatbands tunability and effect of spin-orbit coupling in twisted bilayer transition metal dichalcogenides

Ultraflatbands that have been theoretically and experimentally detected in a bunch of van der Waals stacked materials showing some peculiar properties, for instance, highly localized electronic states and enhanced electron-electron interactions. In this Letter, using an accurate tight-binding model, we study the formation and evolution of ultraflatbands in transition metal dichalcogenides (TMDCs) under low rotation angles. We find that, unlike in twisted bilayer graphene, ultraflatbands exist in TMDCs for almost any small twist angles and their wave function becomes more localized when the rotation angle decreases. Lattice relaxation, pressure and local deformation can tune the width of the flatbands, as well as their localization. Furthermore, we investigate the effect of spin-orbit coupling on the flatbands and discover spin/orbital/valley locking at the minimum of the conduction band at the K point of the Brillouin zone. The ultraflatbands found in TMDCs with a range of rotation angle below $7^\circ$, may provide an ideal platform to study strongly correlated states.