Atomic relaxation and flat bands in strain-engineered transition metal dichalcogenide bilayer moiré systems

Strain-induced lattice mismatch leads to moir\'e patterns in homobilayer transition metal dichalcogenides (TMDs). We investigate the structural and electronic properties of such strain-induced moir\'e patterns in TMD homobilayers. These moir\'e patterns consist of several stacking domains separated by tensile solitons. Relaxation of these systems distributes the strain unevenly in the moir\'e superlattice, with the maximum strain energy concentrating at the highest-energy stackings. The order parameter distribution shows the formation of aster topological defects at the same sites. In contrast, twisted TMDs host shear solitons at the domain walls, and the order parameter distribution in these systems shows the formation of vortex defects. The strain-induced moir\'e systems also show the emergence of several well-separated flat bands at both the valence- and conduction-band edges, and we observe a significant reduction in the band gap. These flat bands in these strain-induced moir\'e superlattices provide platforms for studying the Hubbard model on a triangular lattice as well as the ionic Hubbard model on a honeycomb lattice. Furthermore, we study the localization of the wave functions corresponding to these flat bands. The wave functions localize at different stackings compared to twisted TMDs, and our results on the localization of flat bands at the conduction band edge are in excellent agreement with spectroscopic experiments.