Nonlinear smectic elasticity of helical state in cholesteric liquid crystals and helimagnets

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 [1].

Fluctuation Modes of a Twist-Bend Nematic Liquid Crystal

“…Thus, the effective elasticity associated with the pseudolayered N TB phase is equivalent to a smectic-A phase, with B eff , K eff , and D eff playing the roles of the elastic moduli for compression and bending of the smectic layers, and for tilt of the director away from the layer normal, respectively. In that way, coarse-graining of the N TB phase is analogous to earlier work on coarse-graining of the cholesteric phase, which also has effective smectic elasticity [13,14]. On the other hand, it is important not to overplay the analogy, especially as far as details of the pretransitional temperature dependence of elastic constants are concerned.…”

“…However, as mentioned in the Introduction, we can simplify this calculation through a coarse-graining approximation, which averages over the director modulation to find the larger-scale properties of the phase. Such coarse-graining has previously been done for the cholesteric phase [13,14], and it shows that the cholesteric has the same macroscopic elastic properties as a smectic phase. In this section, we generalize the coarse-graining procedure to the more complex case of the N TB phase.…”

“…As discussed in Refs. [13,14] for the cholesteric case, such rotations are analogous to gauge transformations. Hence, we make the specific choice of gauge in Eq.…”

“…The coarse-graining approximation, inspired by significant earlier theoretical work on cholesterics [13,14] and appropriate in the limit of helical pitch much shorter than an optical wavelength, treats surfaces of constant phase in the heliconical structure as "pseudolayers." Within this approximation, which has previously been used to explain the effect of high magnetic fields on the N TB phase [15] and to account for its flow properties [16], the normal fluctuation modes involving the director may be mapped onto those of a chiral smectic-A phase, with effective layer spacing equal to the pitch, effective director parallel to the local pitch axis, and effective elastic constants that arise from the short-pitch orientational modulation rather than from a true mass density wave.…”

Spin vortices in the Abelian–Higgs model with cholesteric vacuum structure

“…Due to the cholesteric behavior of the vacuum I solution, the U (1) J z vortices are stable to deformation [13]. The low energy effective field theory of these vortices thus gives rise to a 1 + 1 dimensional field theory of translational excitations.…”