Topologically ordered phases of smectics confined in anisotropic random media: smectic Bragg glasses

Abstract

We report the existence of two new topologically ordered glass phases of smectics in strained aerogel. In contrast to the case of unstrained aerogel, we find compelling theoretical arguments that a smectic in uniaxially stretched aerogel exhibits, for homeotropic nematic-aerogel alignment, a `smectic Bragg glass' in the universality class of the `XY Bragg glass'. On the other hand, a uniaxial compression, with homeotropic alignment, leads to an entirely novel type of anisotropic smectic elastic glass phase that we call the `m = 1 Bragg glass'. This latter phase exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We present a phase diagram for the system in the aerogel density-strain parameter space, which should be accessible experimentally. We also make numerous other scaling predictions for experimentally observable quantities.