Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

Details Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

2007-02-20

arxiv.org/abs/cond-mat/0702471v1

Phys. Rev. B 76, 054106 (2007)

Physics

Condensed Matter

Soft Condensed Matter

12 pages, 8 figures

Scientific paper

10.1103/PhysRevB.76.054106

We investigate the zero temperature structure of a crystalline monolayer constrained to lie on a two-dimensional Riemannian manifold with variable Gaussian curvature and boundary. A full analytical treatment is presented for the case of a paraboloid of revolution. Using the geometrical theory of topological defects in a continuum elastic background we find that the presence of a variable Gaussian curvature, combined with the additional constraint of a boundary, gives rise to a rich variety of phenomena beyond that known for spherical crystals. We also provide a numerical analysis of a system of classical particles interacting via a Coulomb potential on the surface of a paraboloid.

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