Crystalline order on Riemannian manifolds with variable Gaussian curvature and boundary
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.
- Publication:
-
Physical Review B
- Pub Date:
- August 2007
- DOI:
- 10.1103/PhysRevB.76.054106
- arXiv:
- arXiv:cond-mat/0702471
- Bibcode:
- 2007PhRvB..76e4106G
- Keywords:
-
- 61.72.Bb;
- 61.72.Lk;
- Theories and models of crystal defects;
- Linear defects: dislocations disclinations;
- Condensed Matter - Soft Condensed Matter
- E-Print:
- 12 pages, 8 figures