Kibble-Zurek mechanism in curved elastic surface crystals

  title={Kibble-Zurek mechanism in curved elastic surface crystals},
  author={Norbert Stoop and J{\"o}rn Dunkel},
  journal={arXiv: Soft Condensed Matter},
  • N. StoopJ. Dunkel
  • Published 10 March 2017
  • Materials Science
  • arXiv: Soft Condensed Matter
Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified… 
6 Citations

Figures from this paper

Curved colloidal crystals of discoids at near-critical liquid-liquid interface.

The assembly of disc-shaped particles at curved liquid-liquid interfaces was studied by using confocal microscopy, which will open up a new research avenue to investigate the effect of varying curvature on the crystallization, defects, and phase diagram of colloidal assemblies.

Non-uniform curvature and anisotropic deformation control wrinkling patterns on tori.

It is shown from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkled patterns develop for soft cores, and that Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness.

Dynamic Buckling of an Elastic Ring in a Soap Film.

The influence of dynamic loading is explored and it is shown numerically that, by imposing a rate of loading that competes with the growth rate of instability, the observed pattern can be selected and controlled.

Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation

It is suggested that cell motion governed by repulsive cell-cell interactions can play an important role in establishing regular patterns in living systems, such as growth on a curved surface, where long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.



Observation of the Kibble-Zurek scaling law for defect formation in ion crystals.

This work determines the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects, and demonstrates that the scaling laws also apply in the mesoscopic regime.

Kibble-Zurek Scaling during Defect Formation in a Nematic Liquid Crystal.

Nematic liquid crystals is used as a different system to demonstrate the validity of the predicted scaling relation for defect formation, and it is found that the scaling exponent is independent of temperature and material employed, thus universal, as predicted.

Kibble–Zurek mechanism in colloidal monolayers

This work investigates the nonequilibrium dynamics in a condensed matter analog, a 2D ensemble of colloidal particles that obeys the so-called Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) melting scenario with continuous (second order-like) phase transitions and observes the scaling predicted by the Kibble–Zurek mechanism for the KTHNY universality class.

Curvature-Controlled Defect Localization in Elastic Surface Crystals.

It is suggested that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges, thus promising improved control over hierarchical bending, buckling, or folding processes.

Elastic Instability of a Crystal Growing on a Curved Surface

The results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.

Colloidal crystal grain boundary formation and motion

“low-dimensional” models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage are introduced and reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion.

Wrinkling crystallography on spherical surfaces

The results provide quantitative evidence that the macroscopic wrinkling system can be mapped into and described within the framework of curved crystallography, albeit with some important differences attributed to the far-from-equilibrium nature of the authors' patterns.

Pleats in crystals on curved surfaces

This work shows that, for more general curved surfaces, curvature may be relaxed by pleats: uncharged lines of dislocations that vanish on the surface and play the same role as fabric pleats, and experimentally investigates crystal order on surfaces with spatially varying positive and negative curvature.

Theory of interacting dislocations on cylinders.

It is shown that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind, and the thermal nucleation rate of dislocation unbinding is calculated.

Interacting topological defects on frozen topographies

We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature