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Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo- and heterobilayers that are obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculate the electronic band structure using a tight-binding model parametrized from first-principles density-functional theory. We find that the highest valence bands in these systems can derive either from $Gamma$-point or $K$/$K$-point states of the constituent monolayers. For homobilayers, the two highest valence bands are composed of monolayer $Gamma$-point states, exhibit a graphene-like dispersion and become flat as the twist angle is reduced. The situation is more complicated for heterobilayers where the ordering of $Gamma$-derived and $K$/$K$-derived states depends both on the material composition and also the twist angle. In all systems, qualitatively different band structures are obtained when atomic relaxations are neglected.
Accurately described excitonic properties of transition metal dichalcogenide heterobilayers (HBLs) are crucial to comprehend the optical response and the charge carrier dynamics of them. Excitons in multilayer systems posses inter or intralayer chara
A mismatch of atomic registries between single-layer transition metal dichalcogenides (TMDs) in a two dimensional van der Waals heterostructure produces a moire superlattice with a periodic potential, which can be fine-tuned by introducing a twist an
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