Chirality Cannot Be Ferroic in Enantiomorphic Space-Groups

TL;DR

This paper proves that chirality in enantiomorphic space groups cannot be a primary ferroic order parameter, as achiral-to-chiral transitions cannot be driven by zone-center instabilities, implying such transitions are fundamentally different from ferroic ones.

Contribution

The work provides a formal group-theoretical proof and systematic analysis showing chirality cannot be a ferroic order parameter in enantiomorphic space groups.

Findings

Achiral-to-chiral transitions cannot be driven by zone-center instabilities.

None of the achiral parent space groups host symmetry-chiral phonons at the zone center.

Chiral phase transitions are not classified as primary ferroic transitions.

Abstract

With growing interest in structural chirality in periodic solids, it has been suggested that chirality might constitute a new ferroic order parameter. In this work, we demonstrate, by means of a formal group-theoretical proof and a systematic group-subgroup analysis, that achiral-to-chiral transitions that produce either member of an enantiomorphic pair cannot be driven by a Brillouin-zone-center ($\Gamma$-point) instability from a common achiral parent. We further substantiate this result by explicitly showing that none of the achiral parent space groups that admit symmetry-chiral phonon eigenvectors host them at the zone center. Given that a primary ferroic order parameter must, among other requirements, transform according to a zone-center irreducible representation, we conclude that phase transitions leading to enantiomorphic space groups cannot be classified as primary ferroic transitions. This predicts that any critical enhancement of fluctuations must occur at finite-$q$ rather than as a divergence of a uniform macroscopic susceptibility.