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 θ. However, the systematic evolution of their typical electronic properties with respect to the twist angle θ, 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 moiré potential, flat band, and layer polarization characteristics across a wide range of twist angle θ in twisted bilayer MoS₂ (TB-MoS₂). The moiré potential of the valence band exhibits a non-monotonic variation with θ, peaking at a maximum value up to 204 meV at θ∼1.7°. Concurrently, at the same θ, the bandwidth of the flat band at the Γ_V point of the valence band attains its minimum, precisely signifying the “special angle” θ_c∼1.7° in TB-MoS₂. Interestingly, layer polarization in the moiré superlattice is spatially visualized through the distribution of local density of states (LDOS) at the energies of both Γ_V and K_V points of the valence band, where the polarization degree at the Γ_V point demonstrates a close dependency on θ. Our findings deepen understanding of twist-angle effect in TMDs, advancing both fundamental physics and practical application.