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.
Original language | English (US) |
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Article number | 054106 |
Journal | Physical Review B - Condensed Matter and Materials Physics |
Volume | 76 |
Issue number | 5 |
DOIs | |
State | Published - Aug 3 2007 |
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics