Depinning transition of colloidal monolayers

We propose to study the melting and depinning transition of colloidal monolayers subjected to commensurate periodic substrate potentials which are realized by arrays of optical light traps. In particular, we want to use Monte- Carlo and Langevin simulations to compute phase-diagrams as a function of filling factor, temperature and strength of the substrate potential. With these diagrams we intend to check quantitatively whether the Halperin/Nelson criterion for the stability of the floating colloidal solid is valid in our system. Furthermore, we will compute the elastic constants of the system by means of which we can check if the crystal on the surface melts as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. We will study the effect of substrate defects on the elastic band-structure and the elastic constants, to investigate their role in the melting process. Finally, we would like to start studying nucleation and crystal growth in the colloidal monolayer.