Asymmetric frictional sliding between incommensurate surfaces

TL;DR

This study investigates frictional sliding between incommensurate surfaces with an intermediate lubricating sheet, revealing a quantized velocity asymmetry determined solely by the incommensurability ratio, independent of other parameters.

Contribution

It demonstrates that the velocity asymmetry in incommensurate sliding systems is exactly quantized and solely dictated by the incommensurability ratio, overcoming previous assumptions of static pinning.

Findings

Velocity asymmetry is exactly quantized.

Quantization is determined solely by the incommensurability ratio.

Behavior differs between golden mean and spiral mean incommensurabilities.

Abstract

We study the frictional sliding of two ideally incommensurate surfaces with a third incommensurate sheet - a sort of extended lubricant - in between. When the mutual ratios of the three periodicities in this sandwich geometry are chosen to be the golden mean \phi=(1+\sqrt 5)/2, this system is believed to be statically pinned for any choice of system parameters. In the present study we overcome this pinning and force the two "substrates" to slide with a mutual velocity V_ext, analyzing the resulting frictional dynamics. An unexpected feature is an asymmetry of the relative sliding velocity of the intermediate lubricating sheet relative to the two substrates. Strikingly, the velocity asymmetry takes an exactly quantized value which is uniquely determined by the incommensurability ratio, and absolutely insensitive to all other parameters. The reason for quantization of the velocity asymmetry will be addressed. This behavior is compared and contrasted to the corresponding one obtained for a representative cubic irrational, the spiral mean \omega.