Smectic Liquid Crystals in Random Environments

TL;DR

This paper demonstrates that quenched disorder in random environments like aerogel destroys smectic and nematic order in liquid crystals, challenging the existence of a smectic Bragg glass phase and the sharp Nematic-Smectic-A transition.

Contribution

It provides a low temperature analysis showing disorder destroys smectic order and argues that the smectic Bragg glass phase does not exist in such systems.

Findings

Quenched disorder destroys smectic order even at low densities.

No smectic Bragg glass phase exists in the studied system.

Disorder destroys the Nematic-Smectic-A transition.

Abstract

We study smectic liquid crystals in random environments, e.g., aerogel. A low temperature analysis reveals that even arbitrarily weak quenched disorder (i.e., arbitrarily low aerogel density) destroys translational (smectic) order. A harmonic approximation to the elastic energy suggests that there is no ``smectic Bragg glass'' phase in this system: even at zero temperature, it is riddled with dislocation loops induced by the quenched disorder. This result implies the destruction of orientational (nematic) order as well, and that the thermodynamically sharp Nematic-Smectic-A transition is destroyed by disorder, in agreement with recent experimental results. We also show that the anharmonic elastic terms neglected in the above treatment are important (i.e., are ``relevant'' in the renormalization group sense); whether they alter the above conclusions about the smectic Bragg glass, orientational disorder, and the existence of sharp transitions, remains an open question. However, they do not alter our conclusion that translational (smectic) order is always destroyed. In contrast, we expect that weak annealed disorder should have no qualitative effects on the smectic order.