Interacting topological defects on frozen topographies

Mark John Bowick, David R. Nelson, Alex Travesset

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Abstract

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 the physics of interacting disclinations is mapped to a Laplacian sine-Gordon Hamiltonian suitable for numerical simulations. We discuss general features of the ground state and thereafter specialize to the spherical case. The ground state is analyzed as a function of the ratio of the defect core energy to the Young's modulus. We argue that the core energy contribution becomes less and less important in the limit R≫a, where R is the radius of the sphere and a is the particle spacing. For large core energies there are 12 disclinations forming an icosahedron. For intermediate core energies unusual finite-length grain boundaries are preferred. The complicated regime of small core energies, appropriate to the limit R/a→∞, is also addressed. Finally we discuss the application of our results to the classic Thomson problem of finding the ground state of electrons distributed on a two sphere.

Original languageEnglish (US)
Pages (from-to)8738-8751
Number of pages14
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume62
Issue number13
DOIs
StatePublished - Oct 1 2000

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ASJC Scopus subject areas

  • Condensed Matter Physics

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