Smectics: Symmetry Breaking, Singularities, and Surfaces

Details Smectics: Symmetry Breaking, Singularities, and Surfaces Smectics: Symmetry Breaking, Singularities, and Surfaces

2009-05-21

arxiv.org/abs/0905.3535v3

Proc. Natl. Acad. Sci. 106 (2009) 15577

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 3 included figures

Scientific paper

10.1073/pnas.0905242106

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, while disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need for compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.

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