Universal state transition from soliton network to soliton-free incommensurate stacking in reconstructed van der Waals bilayers

The atomic reconstruction and moiré patterns within moiré superlattices resulting from twist, stretch and vertical pressure have generated significant interest in the exploration of novel physical phenomena. In this study, we reveal a universal structural transition in moiré superlattices through comprehensive numerical simulations and theoretical analyses. This transition is characterized by a shift in the moiré pattern from a strain soliton network state at large moiré periods to a soliton-free state at smaller moiré periods. This transition is marked by the convergence of two branches of total energy solutions at a critical moiré period. We propose an intuitive size rule, highlighting that one third of the moiré periods smaller than the width of strain solitons serve as a universal trigger for this transformation. Additionally, our research shows that applying external vertical pressure can enhance interlayer van der Waals interactions, resulting in a decrease in the critical moiré period. We also demonstrate that during this state transition, the maximum elastic interaction occurs in proximity to the critical moiré period. Such structural transition regulated by the adjustment of parameters such as twist angle, in-plane stretch and pressure, provides opportunities for manipulating the exotic electronic properties of van der Waals materials.