Influence of atomic relaxations on the moiré flat band wavefunctions in antiparallel twisted bilayer WS₂

Twisting bilayers of transition metal dichalcogenides (TMDs) gives rise to a periodic moiré potential resulting in flat electronic bands with localized wavefunctions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image bilayer WS₂ marginally twisted off of antiparallel alignment. Room temperature scanning tunneling spectroscopy reveals the presence of localized electronic states in the vicinity of the valence band onset. However, the experimentally observed electronic structure was found not to agree with first principles density-functional theory calculations, in particular differing on the real-space location of the valence band onset wavefunctions, which are predicted to correspond to a flat band. Agreement with theory is recovered when the calculations are carried out on bilayers in which the atomic displacements from the unrelaxed positions have been reduced, reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.