Statics and dynamics of Yukawa cluster crystals on ordered substrates

Abstract

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.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

“…The system has periodic boundary conditions in both the x and y directions. The dynamics of the particles is obtained by using an overdamped equation of motion, as in previous numerical studies [4,14,20,41]. The motion of a single particle i is given by integrating the following equation:…”

“…The periodic substrate in Ref. [4] is not an egg-carton potential of the type used in the recent driven colloidal experiments [45] or in static ordering studies for colloidal particles in 2D arrays [14,15,20] but is instead a muffin tin structure formed from a periodic array of localized pinning sites with small radii, so that beyond f = 1.0 the additional colloidal particles sit in the interstitial regions between the particles that are trapped directly by the pinning sites. Periodic pinning arrangements of this type have been experimentally realized in colloidal systems and studied in the range f = 4.0 to f = 5.5, with a triangular colloidal lattice observed at f = 4.0 when the pinning strength was such that each pinning site captures only one particle [48].…”

“…Experiments and computational studies have shown that in the absence of a drive, a variety of orderings can arise for colloidal particles interacting with one-dimensional (1D) periodic substrates [13,32,33], two-dimensional (2D) periodic substrates [15,20,21,[34][35][36][37][38], 2D quasiperiodic substrates [39][40][41][42][43], or 2D random substrates [44]. While these studies have provided a better understanding of several features of commensurateincommensurate behaviors, being able to dynamically control the particle ordering and dynamics could lead to a variety of applications, including self-assembled structures, particle separation, and photonic crystals.…”

“…The type of particle motion that occurs at depinning strongly depends on the filling fraction and on whether the configuration is commensurate or incommensurate. Specific examples of systems that exhibit commensurate-incommensurate depinning transitions include vortices in type-II superconductors interacting with nanostructured periodic pinning arrays [5][6][7][8][9][10], vortices in Bose-Einstein condensates with a co-rotating periodic optical trap array [11], sliding charge density wave systems [12], colloidal particles interacting with periodic substrates [13][14][15][16][17][18][19][20][21][22], and charged metallic balls on patterned surfaces [23]. There are also many models of frictional systems in which a monolayer of atoms is driven over a pinned periodic monolayer of atoms, producing behavior that depends on whether the driven monolayer is commensurate or incommensurate with the underlying pinned layer [24][25][26][27][28][29][30][31].…”

Self-assembly and tunable mechanics of reconfigurable colloidal crystals

“…with DC formation [32]. For this system, we choose a cluster geometry of the keys (blue) and locks (orange) that is both experimentally attainable and consistent with rigid cluster DC formation in order to directly compare with previous results [18].…”