Role of transverse displacements for a quantized-velocity state of a lubricant

Within the idealized scheme of a one-dimensional Frenkel–Kontorova-like model, a special 'quantized' sliding state was found for a solid lubricant confined between two periodic layers (Vanossi et al 2006 Phys. Rev. Lett. 97 056101). This state, characterized by a nontrivial geometrically fixed ratio of the mean lubricant drift velocity and the externally imposed translational velocity vext, was understood as due to the kinks (or solitons) formed by the lubricant due to incommensuracy with one of the substrates, pinning to the other sliding substrate. A quantized sliding state of the same nature is demonstrated here for a substantially less idealized two-dimensional model, where atoms are allowed to move perpendicularly to the sliding direction and interact via Lennard-Jones potentials. Clear evidence for quantized sliding at finite temperature is provided, even with a confined solid lubricant composed of multiple (up to six) lubricant layers. Characteristic backward lubricant motion produced by the presence of 'anti-kinks' is also shown in this more realistic context.