Real-space Moiré potential, lattice corrugation, and band gap variation in a MoTe₂/MoS₂ heterobilayer

To have a first-principles description of the Moiré pattern in a transition metal dichalcogenide heterobilayer, we have carried out DFT calculations, taking full accounts of both atomic registry in and the lattice corrugation out of the atomic layers, on a MoTe₂/MoS₂ system which has a moderate size of superlattice larger than an exciton yet not large enough to justify a continuum model treatment. We find that the local potential in the midplane of the bilayer can serve as an excellent illustration of the Moiré pattern in the van der Waals heterostructure. In the Mo atomic planes, the array of local potential planar maximum (LPPM), rather than the local potential itself, makes the Moiré pattern more obvious. Significant lattice corrugation is found in both MoTe2 (0.30Å) and MoS2 (0.77Å) layers. The interlayer Moiré potential, defined as the LPPM difference between the Mo atomic planes, has a depth of 0.20 eV and changes in direct correlation to the band gap variation in the Moiré cell, which has an amplitude of 0.04 eV. Wrinkling of the MoTe₂/MoS₂ bilayer enhances the spatial variation of the local band gap by 5 meV; by contrast, its influence on the global band gap is within 1 meV.