Statics and dynamics of Yukawa cluster crystals on ordered substrates

We examine the statics and dynamics of particles with repulsive Yukawa interactions in the presence of a two-dimensional triangular substrate for fillings of up to 12 particles per potential minimum. We term the ordered states Yukawa cluster crystals and show that they are distinct from the colloidal molecular crystal states found at low fillings. As a function of substrate and interaction strength at fixed particle density we find a series of novel crystalline states that we characterize using the structure factor. For fillings greater than four, shell and ring structures form at each potential minimum and can exhibit sample-wide orientational order. A disordered state can appear between ordered states as the substrate strength varies. Under an external drive, the onsets of different orderings produce clear changes in the critical depinning force, including a peak effect phenomenon that has generally only previously been observed in systems with random substrates. We also find a rich variety of dynamic ordering transitions that can be observed via changes in the structure factor and features in the velocity-force curves. The dynamical states encompass a variety of moving structures including one-dimensional stripes, smectic ordering, polycrystalline states, triangular lattices, and symmetry locking states. Despite the complexity of the system, we identify several generic features of the dynamical phase transitions which we map out in a series of phase diagrams. Our results have implications for the structure and depinning of colloids on periodic substrates, vortices in superconductors and Bose-Einstein condensates, Wigner crystals, and dusty plasmas.