Fig. 3: Mechanism of the load dependence of frictional dissipation at zero temperature.

a Total dissipation power and its directional contributions (x, y, z—see Fig. 1a) as a function of normal load. b Spatial distributions of dissipation power density in the z direction of the second pristine layer (left panel) and the fifth pristine layer (right panel) under a normal load of \(0.6\,{{{{{\rm{GPa}}}}}}\). The geometric configuration of the PolyGr layer is superimposed on the 2D maps. The pentagon–heptagon atoms are shown in cyan and the hexagon carbon atoms are represented in pink. The power density is calculated based on area elements with size of \({a}_{{{{{{\rm{cc}}}}}}}^{2}\) (\({a}_{{{{{{\rm{cc}}}}}}}=1.42039\,{{\mathrm {\AA}}}\) is the equilibrium C–C bond length in the REBO potential). c Representative dislocation trajectories (for two sliding periods at steady state) corresponding to the out-of-plane motion of the atoms with maximal RMS corrugation within each dislocation (different colors correspond to different dislocations) during sliding, under normal loads of \(0,0.6,\) and \(1.9\,{{{{{\rm{GPa}}}}}}\) (from top to bottom panels, respectively). Substantial buckling and unbuckling dynamics during sliding is observed under normal loads of \(0\) and \(0.6\,{{{{{\rm{GPa}}}}}}\). d Kinetic energy profiles corresponding to the traces appearing in panel (c). More details regarding the temperature effects on dislocation buckling can be found in Supplementary Note 3. Movies of typical simulations are also provided in the Supplementary Information.