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The authors develop a Landau phenomenological theory to explain the spontaneous formation of nanoscale heliconical modulations in achiral twist-bend nematic liquid crystals. By framing the transition as the condensation of a hidden, short-range orientational order parameter at a finite wavevector, the work establishes a direct theoretical mapping to the de Gennes model of nematic–smectic-A transitions. The resulting framework predicts that thermal fluctuations drive the transition to be weakly first-order and reveals a novel Goldstone mode arising from the spontaneously broken continuous symmetry.
Nanoscale helical phases can spontaneously assemble from completely achiral molecules through the condensation of hidden short-range orientational fluctuations.
The discovery of the twist-bend nematic phase in liquid crystals composed of bent-core and dimeric molecules has revealed an unexpected mechanism for the spontaneous formation of nanoscale periodic structures in soft condensed matter. Unlike conventional liquid-crystalline phases, the twist-bend phase exhibits a nanoscale heliconical modulation despite the absence of molecular chirality. In this note, dedicated to the late R. Meyer, we discuss a Landau phenomenological interpretation of this phenomenon. The central idea is that a short-range orientational order parameter undergoes condensation, giving rise to a heliconical structure characterized by a finite wave vector. We emphasize that the conventional nematic order is already long-ranged, whereas the additional order parameter describes local orientational correlations hidden within the nematic state. The resulting phase transition bears a close analogy to the de Gennes theory of the nematic--smectic-A transition. Fluctuation effects are expected to drive the transition weakly first order. The theory also predicts a new Goldstone mode associated with the spontaneously broken continuous symmetry of the heliconical state