A general mechanism for long-range friction modulation in graphene-based moiré heterostructures

The moiré scale friction modulation is a well-known phenomenon for tip sliding on van der Waals heterostructures. In this study, we have discovered a general rule that governs the long-range friction modulation in graphene-based moiré heterostructures. Firstly, the moiré in-plane lattice reconstruction regulates out-of-plane moiré morphology. Secondly, the in-plane deformation of graphene induced by tip sliding on the reconstructed moiré surface can significantly amplify the local movement of the moiré surface. Thirdly, the out-of-plane morphology and local movement of the moiré surface change the contact trajectory of the tip, thereby modulating the moiré scale friction. As the moiré reconstruction is closely related to the stacking status of heterostructures, an explicit expression of the reconstructed moiré morphology is derived based on the local registry index. Then, the tip contact trajectory is obtained by considering the tip indentation and in-plane deformation-induced moiré patterns movement for twisted and strained graphene heterostructures. Based on the tip contact trajectory, the long-range friction modulation of graphene heterostructures is perfectly characterized. Furthermore, a deformation-coupled Prandtl-Tomlinson model was developed, which well reproduces the friction behaviors of graphene-based moiré heterostructures. Our findings highlight the crucial role of internal dynamics of contact interfaces on frictional behaviors of van der Waals (vdW) moiré superlattices, offering valuable insights for the rational design and control of frictional response at the nanoscale.