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

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. The effect of confining liquid crystals to random porous structures continues to be a fascinating area of active research [1]. It was shown in a recent theoretical analysis that arbitrarily weak quenched disorder arising from such confinements destroys conventional (quasi-) long-ranged translational smectic order in 3D [2]. A translationally disordered but topologically ordered ‘smectic Bragg glass’ (SBG) phase was proposed as the new thermodynamically distinct lowtemperature phase in these smectic systems. Unfortunately, it proved impossible to make a compelling theoretical argument for the stability of such a glass phase in quenched random isotropic structures, e.g. aerogel. We show in this article that such a compelling argument can be made for smectics in a uniaxially strained aerogel, which certainly exhibit two types of low-T BG phase, that are thermodynamically distinct from the high-T nematic (or perhaps ‘nematic elastic glass’ (NEG)) and isotropic liquid phases. For parallel nematogen–surface alignment (assumed throughout), a stretch (figure 1(a)) of the aerogel will lead to an ‘XY BG’ in the isotropic universality class of randomly pinned vortex lattices, CDWs, and random-field XY magnets (RFXY ) [3], while a compression (figure 1(b)) will lead to a novel ‘m = 1 BG’, with triaxially anisotropic scaling, that should be similar to that of a discotic in isotropic aerogel [4]. For homeotropic alignment, the phases reverse with respect to stretch and compression. We predict two possible low, constant-T phase diagrams, depending on whether the SBG is stable (figure 2(b)) or not (figure 2(a)). Recent experiments [5] suggest the former possibility. The loci of the phase boundaries in figure 2(a), for small strain, σ , are universal and satisfy (σ ) ∝ (KB)(σ/B) (1)