Nonlinear smectic elasticity of a helical state in cholesterics and helimagnets

TL;DR

This paper derives the fully nonlinear elasticity of helical states in cholesterics and helimagnets, revealing a reduction of orientational modes to a single phonon mode at long scales, with implications for their phenomenology.

Contribution

It provides a transparent derivation of nonlinear Goldstone mode elasticity in chiral nematics and helimagnets, highlighting an Anderson-Higgs-like mechanism that locks director frames to layers.

Findings

Reduction of three orientational modes to one phonon mode at scales longer than the pitch

Explicit derivation of nonlinear elasticity involving an Anderson-Higgs mechanism

Connection to classical results by Lubensky and collaborators

Abstract

General symmetry arguments, dating back to de Gennes dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free-energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director/magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators.