Classical Wigner Crystals on Flat and Curved Surfaces, Topological Defects, `Pleats ‘ and Particle Fractionalization

          @misc{ pirsa_PIRSA:12050037,
            doi = {10.48660/12050037},
            url = {https://pirsa.org/12050037},
            author = {Chaikin, Paul},
            keywords = {},
            language = {en},
            title = {Classical Wigner Crystals on Flat and Curved Surfaces, Topological Defects, {\textquoteleft}Pleats {\textquoteleft} and Particle Fractionalization},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {may},
            note = {PIRSA:12050037 see, \url{https://pirsa.org}}
          }
          

Abstract

Charged colloidal particles present a controllable system for study a host of condensed matter/many body problems such as crystallization. 2D crystals are invariably hexagonal. Hexagons perfectly tile a flat plane but a soccer ball requires exactly 12 pentagons dispersed among the hexagons on its curved surface. Pentagons and hexagons are positive and negative topological charges, disclinations, sources for positive and negative curvature. But we have discovered that “Pleats”, grain boundaries which vanish on the surface (and play a similar role to fabric pleats) can provide a finer control of curvature. We experimentally investigate the generation of topological charge as flat surfaces are curved. For positive curvature, domes and barrels, there is one pentagon added for every 1/12 of a sphere. Negative curvature is different! For capillary bridges forming catenoids, pleats relieve the stress before heptagons appear on the surface. Pleats are important for controlling curvature from crystals on surfaces, to the shape of the spiked crown of the Chrysler building. Adding a particle to a flat surface produces an interstitial - usually an innocuous point defect. On a curved surface interstitials are remarkable, forming pairs or triplets of dislocations which can fission dividing the added particles into fractions which migrate to disclinations.    Work done with William Irvine, e.g. Nature 468, 947 (2010).