Elasticity and the Landau-Peierls instability in the smectic twist-grain-boundary phase

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Abstract
The elasticity theory of the twist-grain-boundary phase in chiral smectic liquid crystals for the case of α (where 2πα is the twist-grain-boundary angle) irrational is developed. It implies that fluctuations destroy long-ranged translational order, leading to algebraic (rather than δ-function) singularities in the x-ray scattering near both a cylinder in reciprocal space and isolated Bragg peaks along its axis. These results, which could be experimentally tested through high-resolution x-ray scattering, also apply to ‘‘nearly irrational’’ α=J/s, with J and s integers and s≫1, out to length scales exponentially large in s.