Crystalline order on Riemannian manifolds with variable Gaussian curvature and boundary

Luca Giomi, Mark Bowick

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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 languageEnglish (US)
Article number054106
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number5
StatePublished - Aug 3 2007

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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