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Ultraflat bands have already been detected in twisted bilayer graphene (TBG)and twisted bilayer transition metal dichalcogenides (tb-TMDs), which provide aplatform to investigate strong correlations. In this paper, the electronicproperties of twisted trilayer molybdenum disulfide (TTM) are investigated viaan accurate tight-banding Hamiltonian. We find that the highest valence bandsare derived from $\Gamma$-point of the constituent monolayer, exhibiting agraphene-like dispersion or becoming isolated flat bands. The latticerelaxation, local deformation, and electric field can significantly tune theelectronic structures of TTM with different starting stacking arrangements.After introducing the spin-orbital coupling (SOC) effect, we find aspin-valley-layer locking effect at the minimum of conduction band at K- andK$^\prime$-point of the Brillouin zone, which may provide a platform to studyoptical properties and magnetoelectric effects.

Tuning the flat bands by the interlayer interaction, spin-orbital coupling and electric field in twisted homotrilayer MoS$_2$