Smectics: Symmetry Breaking, Singularities, and Surfaces

Abstract

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.

9 pages, 3 included figures

References in corpus (6)

• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• Disclinations, dislocations and continuous defects: a reappraisal
• Geometric Theory of Columnar Phases on Curved Substrates
• Topology and Geometry of Smectic Order on Compact Curved Substrates
• Certain Constant Angle Surfaces Constructed on Curves

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