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Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

Luca Giomi·Mark J. Bowick
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Abstract

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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Luca Giomi, Mark J. Bowick. 2007-02-20. Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary. https://doi.org/10.1103/physrevb.76.054106

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