Phase diagram, depinning and sliding friction in the Phase Field Crystal model

We present results for commensurate-incommensurate transitions and non-linear sliding friction for a two-dimensional crystal lattice in the presence of an external pinning potential in the Phase Field Crystal model. This model provides a continuum description of lattice system, such as adsorbed monolayers or two-dimensional vortex lattice. The competition between the length scales associated with the intrinsic ordering and the pinning potential leads to commensurate-incommensurate transitions. The dynamical response of the system in the presence of a driving force has also been studied via the time dependent Ginzburg-Landau equation. We present results on non-linear dynamics and sliding mechanisms for commensurate phases.