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Chirality Cannot Be Ferroic in Phase Transitions Leading to Enantiomorphic Space-Group Pairs
F Gómez-Ortiz1, S Mamoudou Taganga1, Emma E McCabe2
1Université de Liège, Physique Théorique des Matériaux, Q-MAT, B-4000 Sart-Tilman, Belgium.
Physical Review Letters
|July 31, 2026
Summary
Chirality in solids cannot be a primary ferroic order parameter. Achiral-to-chiral transitions are not driven by zone-center instabilities, meaning fluctuations occur at finite-q, not as a uniform susceptibility divergence.
Area of Science:
- Solid-state physics
- Crystallography
- Materials science
Background:
- Growing interest in structural chirality in periodic solids.
- Chirality has been proposed as a new ferroic order parameter.
- Ferroic order parameters drive phase transitions and exhibit domain structures.
Purpose of the Study:
- To formally prove whether chirality can act as a primary ferroic order parameter.
- To analyze achiral-to-chiral transitions in periodic solids.
- To determine the nature of instabilities driving these transitions.
Main Methods:
- Formal group-theoretical proof.
- Systematic group-subgroup analysis.
- Analysis of phonon eigenvectors at the Brillouin zone center (Γ-point).
Main Results:
- Achiral-to-chiral transitions producing enantiomorphic pairs cannot be driven by Γ-point instabilities from a common achiral parent.
- No achiral parent space groups admitting symmetry-chiral phonon eigenvectors host them at the zone center.
- Transitions to enantiomorphic space groups are not primary ferroic transitions.
Conclusions:
- Chirality cannot be a primary ferroic order parameter in the studied context.
- Critical fluctuations associated with these transitions are predicted to occur at finite wavevector (q), not at the zone center.
- This finding impacts the understanding of ferroic orders and phase transitions in chiral materials.
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