Theory of chiral modulations and fluctuations in smectic-A liquid crystalsunder an electric field

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral s triped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applie d electric field. Using both continuum elastic theory and lattice simulatio ns, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A-smeceic-C* transition or when a high e lectric field is applied. Beyond that instability point, the system develop s chiral stripes in the tilt, which induce corresponding ripples in the sme ctic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system sh ows chiral fluctuations, including both incipient chiral stripes and locali zed chital vortices. We compare these predictions with observed chiral modu lations and fluctuations in smectic-A liquid crystals.