Geometrically frustrated crystals : Elastic theory and dislocations

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the physical properties of the edge dislocations due to geometrical frustration (bending) is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the radius vs. thickness phase diagram of the ring crystal, which shows intriguing behaviors at nanoscales, is discussed. Relation of our theory to the actual experiments on ring crystals is also discussed.