We present a series of computer-assisted high resolution transmission electron (HRTEM) simulations to determine Moiré patters by induced twisting effects between slabs at rotational angles of 3°, 5°, 8°, and 16°, for molybdenum disulfide, graphene, tungsten disulfide, and tungsten selenide layered materials. In order to investigate the electronic structure, a series of numerical simulations using DFT methods was completed using CASTEP with a generalized gradient approximation to determine both band structure and density of states on honeycomb like new superlattices. Our results indicate metallic transitions when rotation approaches 8° with respect to each other for most of the two-dimensional systems that were analyzed.

As shown previously, a relation between the superconducting transition temperature and some characteristic distance in the crystal lattice holds, which enables the calculation of the superconducting transition temperature, Tc, based only on the knowledge of the electronic configuration and of some details of the crystallographic structure. This relation was found to apply for a large number of superconductors, including the high-temperature superconductors, the iron-based materials, alkali fullerides, metallic alloys, and element superconductors. When applying this scheme called Roeser-Huber formula to Moiré-type superconductivity, i.e., magic-angle twisted bi-layer graphene (tBLG) and bi-layer WSe2, we find that the calculated transition temperatures for tBLG are always higher than the available experimental data, e.g., for the magic angle 1.1∘, we find Tc≈ 4.2–6.7 K. Now, the question arises why the calculation produces larger Tc’s. Two possible scenarios may answer this question: (1) The given problem for experimentalists is the fact that for electric measurements always substrates/caps are required to arrange the electric contacts. When now discussing superconductivity in atomically thin objects, also these layers may play a role forming the Moiré patterns. The consequence of such substrate-induced super-Moiré patterns is that the resulting Moiré pattern always will show a larger cell size, and thus, a lower Tc of the final structure will result. (2) A correction factor to the Roeser-Huber formalism may be required to account for the low charge carrier density of the tBLG. Here, we test both scenarios and find that the introduction of a correction factor η enables a proper calculation of Tc, reproducing the experimental data. We find that η depends exponentially on the value of Tc.

As shown previously, a relation between the superconducting transition temperature and some characteristic distance in the crystal lattice holds, which enables the calculation of the superconducting transition temperature, Tc, based only on the knowledge of the electronic configuration and of some details of the crystallographic structure. This relation was found to apply for a large number of superconductors, including the high-temperature superconductors, the iron-based materials, alkali fullerides, metallic alloys, and element superconductors. When applying this scheme called Roeser-Huber formula to Moiré-type superconductivity, i.e., magic-angle twisted bi-layer graphene (tBLG) and bi-layer WSe2, we find that the calculated transition temperatures for tBLG are always higher than the available experimental data, e.g., for the magic angle 1.1∘, we find Tc≈ 4.2–6.7 K. Now, the question arises why the calculation produces larger Tc’s. Two possible scenarios may answer this question: (1) The given problem for experimentalists is the fact that for electric measurements always substrates/caps are required to arrange the electric contacts. When now discussing superconductivity in atomically thin objects, also these layers may play a role forming the Moiré patterns. The consequence of such substrate-induced super-Moiré patterns is that the resulting Moiré pattern always will show a larger cell size, and thus, a lower Tc of the final structure will result. (2) A correction factor to the Roeser-Huber formalism may be required to account for the low charge carrier density of the tBLG. Here, we test both scenarios and find that the introduction of a correction factor η enables a proper calculation of Tc, reproducing the experimental data. We find that η depends exponentially on the value of Tc.

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques also opened the door to study the optical properties of these nanomaterials. We present a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS₂, MoSe₂, WS₂ and WSe₂, with thickness ranging from one layer up to six layers. We analyze the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provides a route to employ differential reflectance spectroscopy for determining the number of layers of MoS₂, MoSe₂, WS₂ and WSe₂.