Fractionalization of Interstitials in Curved Colloidal Crystals

Abstract: Understanding the out-of equilibrium behaviour of point defects in crystals, yields insights into the nature and fragility of the ordered state, as well as being of great practical importance. In some rare cases defects are spontaneously healed - a one-dimensional crystal formed by a line of identical charged particles, for example, can accommodate an interstitial (extra particle) by a re-adjusting all particle positions to even out the spacing. In sharp contrast, particles organized into a perfect hexagonal crystal in the plane cannot accommodate an interstitial by a simple re-adjustment of the particle spacing - the interstitial remains instead trapped between lattice sites and diffuses by hopping, leaving the crystal permanently defected. Here we report on the behavior of interstitials in colloidal crystals on curved surfaces. Using optical tweezers operated independently of three dimensional imaging, we insert a colloidal interstitial in a lattice of similar particles on flat and curved (positively and negatively) oil-glycerol interfaces and image the ensuing dynamics. We find that, unlike in flat space, the curved crystals self-heal through a collective rearrangement that re-distributes the increased density associated with the interstitial. The self-healing process can be interpreted in terms of an out of equilibrium interaction of topological defects with each other and with the underlying curvature. Our observations suggest the existence of "particle fractionalization" on curved surface crystals.