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 vcm 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.