Two New Topologically Ordered Glass Phases of Smectics Confined in Anisotropic Random Media

Smectics in strained aerogel exhibit two new glassy phases. The strain both ensures the stability of these phases and determines their nature. One type of strain induces an “ $\mathrm{XY}$ Bragg glass,” while the other creates a novel, triaxially anisotropic “ $m=1\mathrm{}$ Bragg glass.” The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase diagram, and numerous other experimentally observable scaling laws, for the system.