Topology of Smectic Order on Compact Substrates

Details Topology of Smectic Order on Compact Substrates Topology of Smectic Order on Compact Substrates

2007-08-23

arxiv.org/abs/0708.3182v3

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 3 eps figures, accepted by physical review letters

Scientific paper

10.1103/PhysRevLett.101.147801

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on torus as well as on sphere, we find that both systems exhibit many topologically distinct low energy states, that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.

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