Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field

TL;DR

This paper explores how electric fields induce chiral modulations and fluctuations in smectic-A liquid crystals, revealing instabilities and stripe formations near phase transitions through theoretical and simulation methods.

Contribution

It introduces a theoretical framework and lattice simulations showing the emergence of chiral stripes and fluctuations in smectic-A under electric fields, extending understanding of chiral phenomena in liquid crystals.

Findings

Chiral stripes form near the smectic-A--smectic-C* transition.

Chiral fluctuations include incipient stripes and vortices.

Modulations disappear beyond a critical electric field.

Abstract

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applied electric field. Using both continuum elastic theory and lattice simulations, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A--smectic-C* transition, or when a high electric field is applied. Beyond that instability point, the system develops chiral stripes in the tilt, which induce corresponding ripples in the smectic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system shows chiral fluctuations, including both incipient chiral stripes and localized chiral vortices. We compare these predictions with observed chiral modulations and fluctuations in smectic-A liquid crystals.