Spatially resolved atomic-scale friction: Theory and Simulation.

We analyze the friction force exerted on a small probe particle sliding over an atomic-scale surface by means of a Green-Kubo relation and classical Molecular Dynamics simulations. We find that, on the atomic scale, the friction tensor can drastically vary as a function of position and sliding direction. The Green-Kubo relation yields this positional and directional dependence from equilibrium simulations of the time dependent covariance of force acting on the probe. We find, unexpectedly, that the positional and directional dependence of energy dissipation is related to the (much simpler) static force covariance, especially in the limit where the probe only mildly perturbs the surface particles. In contrast, the (free) energy landscape experienced by the probe is in general not a good indicator of local dissipation. We also discuss optimization strategies making use of the locally and directionally resolved friction tensor. This enables us to find optimal sliding paths and velocity protocols, e.g., minimizing energy dissipation, between two points on the surface in a given time.