Manipulating the interlayer twist angle is a powerful tool to tailor the properties of layered two-dimensional crystals. The twist angle has a determinant impact on these systems’ atomistic structure and electronic properties. This includes the corrugation of individual layers, formation of stacking domains and other structural elements, and electronic structure changes due to the atomic reconstruction and superlattice effects. However, how these properties change with the twist angle, θ, is not yet well understood. Here, we monitor the change of twisted bilayer MoS2 characteristics as a function of θ. We identify distinct structural regimes, each with particular structural and electronic properties. We employ a hierarchical approach ranging from a reactive force field through the density-functional-based tight-binding approach and density-functional theory. To obtain a comprehensive overview, we analyzed a large number of twisted bilayers with twist angles in the range of θ = 0.2° . . . 59.6°. Some systems include up to half a million atoms, making structure optimization and electronic property calculation challenging. For 13° ≤ θ ≤ 47°, the structure is well-described by a moiré regime composed of two rigidly twisted monolayers. At small twist angles (θ ≤ 3° and 57° ≤ θ), a domain-soliton regime evolves, where the structure contains large triangular stacking domains, separated by a network of strain solitons and short-ranged high-energy nodes. The corrugation of the layers and the emerging superlattice of solitons and stacking domains affects the electronic structure. Emerging predominant characteristic features are Dirac cones at K and kagome bands. These features flatten for θ approaching 0° and 60°. Our results show at which range of θ the characteristic features of the reconstruction, namely extended stacking domains, the soliton network, and superlattice, emerge and give rise to exciting electronics. We expect our findings also to be relevant for other twisted bilayer systems.
Angeli and MacDonald reported a superlattice-imposed Dirac band in twisted bilayer molybdenum disulphide (tBL MoS2) for small twist angles towards the R_h^M (parallel) stacking. Using a hierarchical set of theoretical methods, we show that the superlattices differ for twist angles with respect to metastable R_h^M (0°) and lowest-energy H_h^h (60°) configurations. When approaching R_h^M stacking, identical domains with opposite spatial orientation emerge. They form a honeycomb superlattice, yielding Dirac bands and a lateral spin texture distribution with opposite-spin-occupied K and K’ valleys. Small twist angles towards the H_h^h configuration (60°) generate H_h^h and H_h^X stacking domains of different relative energies and, hence, different spatial extensions. This imposes a symmetry break in the moiré cell, which opens a gap between the two top-valence bands, which become flat already for relatively small moiré cells. The superlattices impose electronic superstructures resembling graphene and hexagonal boron nitride into trivial semiconductor MoS2.
Angeli and MacDonald reported a superlattice-imposed Dirac band in twisted bilayer molybdenum disulphide (tBL MoS2) for small twist angles towards the R_h^M (parallel) stacking. Using a hierarchical set of theoretical methods, we show that the superlattices differ for twist angles with respect to metastable R_h^M (0°) and lowest-energy H_h^h (60°) configurations. When approaching R_h^M stacking, identical domains with opposite spatial orientation emerge. They form a honeycomb superlattice, yielding Dirac bands and a lateral spin texture distribution with opposite-spin-occupied K and K’ valleys. Small twist angles towards the H_h^h configuration (60°) generate H_h^h and H_h^X stacking domains of different relative energies and, hence, different spatial extensions. This imposes a symmetry break in the moiré cell, which opens a gap between the two top-valence bands, which become flat already for relatively small moiré cells. The superlattices impose electronic superstructures resembling graphene and hexagonal boron nitride into trivial semiconductor MoS2.
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