Probing the special angle in twisted bilayer MoS2 via angle-dependent scanning tunneling microscopy studies

Twisted transition metal dichalcogenides (TMDs) homo-bilayers host unique quantum properties, which can be tuned by interlayer twist angle theta. However, the systematic evolution of their typical electronic properties with respect to the twist angle theta, which is crucial for identifying the "special angle" analogous to the "magic angle" of twisted bilayer graphene in correlation physics studies, remains incompletely understood. Here, via scanning tunneling microscopy (STM) and spectroscopy (STS), we investigate the variation of the moir & eacute; potential, flat band, and layer polarization characteristics across a wide range of twist angle theta in twisted bilayer MoS2 (TB-MoS2). The moir & eacute; potential of the valence band exhibits a non-monotonic variation with theta, peaking at a maximum value up to 204 meV at theta similar to 1.7 degrees. Concurrently, at the same theta, the bandwidth of the flat band at the Gamma(V) point of the valence band attains its minimum, precisely signifying the "special angle" theta(c)similar to 1.7 degrees in TB-MoS2. Interestingly, layer polarization in the moir & eacute; superlattice is spatially visualized through the distribution of local density of states (LDOS) at the energies of both Gamma(V) and K-V points of the valence band, where the polarization degree at the Gamma(V) point demonstrates a close dependency on theta. Our findings deepen understanding of twist-angle effect in TMDs, advancing both fundamental physics and practical application.