Microscopic contributions to the deviation from Amontons friction law

We investigate the nanoscale friction behaviour of MX ₂ monolayers (M = Mo, W; X = S, Se) on Au(111) and Ag(111) substrates with silicon tip using classical molecular dynamics simulations with machine-learning-based force fields. This approach enables an accurate description of tip-surface interactions and friction mechanisms at the atomic scale. We observe a pronounced nonmonotonic dependence of the friction force on the applied normal load, indicating a breakdown of Amontons's law at the nanoscale. Analysis of lateral force signals and their spatial Fourier transforms reveals the coexistence of multiple sliding modes, including longitudinal sliding, lateral slip, and zig-zag motions. We show that the overall friction response is governed by the relative contributions of these motions. While the qualitative features of friction are largely substrate-independent, both the magnitude of friction and the balance between sliding modes depend sensitively on the substrate-monolayer combination. In particular, Au/MoSe ₂ /Si exhibits significantly reduced friction due to suppression of lateral slip motion. Our results indicate that the method is broadly applicable for probing nanoscale friction in related heterostructures.