  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 twelve 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.
