Negative differential friction in van der Waals layered materials: The role of interlayer quasibonding repulsion

The emergence of negative differential friction (NDF) in two-dimensional (2D) layered materials, which does not obey the classical Da Vinci--Amontons law of friction, has attracted much attention in recent years. Although there has been a great deal of study on NDF, a universal understanding for its appearance in 2D materials remains lacking. Here, we try to give general insights from the common existence of interlayer quasibonding (QB) interaction in 2D materials, which is usually a repulsion interaction for some typical 2D materials. Based on density-functional theory calculations, we study the friction of four homobilayers of 2D materials ($H$- and $R$-stacking $\mathrm{Mo}{\mathrm{S}}_{2}, h$-BN, and graphene) with increasing load. The interlayer QB repulsion becomes stronger as the normal load increases, which is beneficial to the appearance of NDF. The appearance of NDF can be attributed to the competition of (1) the relative rapid increase in the interlayer repulsion (which is correlated to interlayer QB) and (2) the relatively slow increase of the interlayer London dispersion attraction of van der Waals interaction. Further analysis manifests that the magnitude of the interlayer QB-induced splitting of energy bands is related to NDF, and then we provide a quantitative analysis of interlayer bonding strength to support this view. Since QB exists commonly in 2D layered materials, our insights are general and inspire perspectives on tuning the interlayer friction.