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 "XY Bragg glass", while the other creates a novel, triaxially anisotropic "m=1 Bragg glass". The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase diagram for the system, and numerous other experimentally observable scaling laws. 64.60Fr,05.40,82.65Dp Liquid crystals confined in random porous structures, have become a subject of considerable interest.[1] A recent theoretical study unambiguously demonstrated that conventional (quasi-) long-ranged smectic order is impossible in 3d in the presence of (even arbitrarily weak) quenched pinning imposed by these random structures, e.g., aerogel.[2] It was proposed that a positionally disordered but topologically ordered "smectic Bragg glass" (SBG) phase would become the new thermodynamically distinct low-temperature phase in these smectic systems. However, for quenched random isotropic structures it was impossible to make a compelling theoretical argument for the stability of such a glass phase.In this Letter, we show that we can make such a compelling argument for smectics in a uniaxially strained aerogel, which certainly exhibit two types of low-T BG phases, 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 (Fig.1a) of the aerogel will lead to an "XY-BG" in the isotropic universality class of randomly pinned vortex lattices, CDW's, and random field XY magnets (RFXY), [3] while a compression (Fig.1b) 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 (Fig.2b) or not (Fig.2a). Recent experiments [5] suggest the former possibility. The locii of the phase boundaries in Fig.2a, for small strain, σ, are universal and satisfywhere σ is proportional to the uniaxial stress applied to the aerogel fibers, ∆ is a measure of the tilt disorder, B and K are bulk smectic elastic moduli, and ρ a universal exponent expressible in terms of anomalous elasticity exponentsη B andη K for unstrained aerogel. Our best estimate is ρ ≈ 1/3 in 3d.[2] Our model of the smectic in aerogel treats the local smectic layer displacement u(r) and the local nematic directorn(r) as the only important fluctuating quantities, ignoring fluctuations in the magnitude |ψ| of the smectic order parameter ψ = |ψ|e iqou(r) about its mean |ψ o |. The important effects of the aerogel are completely described by only two disorder types. One is the random-field translational disorder δH rf = Re d d r|ψ o |V (r)e iqo u(r) , coupling to u(r), with V (r) a com...

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C �v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals �D �h � in that it contains terms violating the n → −n symmetry. First we show that these Z 2 -odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

We show that Landau theory for the isotropic (I), nematic (N), smectic-A, and smectic-C phases generically, but not ubiquitously, implies ''de Vries'' behavior: i.e., a continuous A-C transition can occur with little layer contraction while the birefringence increases significantly once the system moves into the C phase. Our theory shows that 1st order A-C transitions are also possible. These transitions can be de Vries-like, but in general need not be. Generally, de Vries behavior occurs in models with unusually small orientational order and is preceded by a first order I-A transition. These results correspond well with experimental work to date. DOI: 10.1103/PhysRevLett.98.197801 PACS numbers: 64.70.Md, 61.30.Gd, 61.30.Cz Recently, an unusual new class of liquid crystals known as ''de Vries smectic liquid crystals'' [1] has drawn interest. They possess two defining features. First, there is little change with temperature T of the layer spacing dT upon entry to the C phase, in contrast to the rapid geometrical contraction dT / cosT expected if the molecules tilt by a strongly temperature dependent angle T. Second, the birefringence increases significantly upon entering the C phase from the A phase. In fact, for de Vries materials with a 2nd order A-C transition, the birefringence is seen [2,3] to decrease with decreasing temperature as the A-C transition as approached, reaching a minimum at the A-C transition. This is the first example known to us of decreasing order as a lower symmetry phase is approached. For de Vries materials with a 1st order transition, the birefringence increases moderately as the A-C transition is approached and then jumps significantly at the transition [4]. Generally, de Vries smectic liquid crystals exhibit the phase sequence I-A-C, without a nematic phase. First order A-C transitions are not always de Vries-like [4], contrary to some recent speculations.In de Vries' ''diffuse cone model '' [5] of these materials, the molecules ''pretilt'' in the A phase as the A-C transition is approached, but in azimuthally random directions (hence reducing orientational order), so that there is no long range order in the tilting. Upon entering the C phase, the molecules azimuthally order (hence increasing orientational order) without the significant layer contraction that occurs in conventional smectics whose molecules tilt at the A-C transition.In this Letter, we show that in a complete, nonchiral Landau mean field theory for the isotropic (I), nematic (N), A and C phases, in which all three order parameters (orientational, layering, azimuthal tilt) and the layer spacing are coupled, de Vries behavior occurs in a finite fraction of parameter space, while other regions exhibit conventional behavior. The mean field phase diagram for our model is shown in Fig. 1. Here, t s and t n are Landau theory parameters that control layering and orientational order, respectively. We find that two main features are necessary for de Vries behavior-an unusually weak coupling between layering and orientational...

Ferromagnetic order in superconductors can induce a spontaneous vortex (SV) state. For external field H = 0, rotational symmetry guarantees a vanishing tilt modulus of the SV solid, leading to drastically different behavior than that of a conventional, external-field-induced vortex solid. We show that quenched disorder and anharmonic effects lead to elastic moduli that are wavevectordependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields H, the magnetic induction scales universally like B(H) ∼ B(0) + cH α , with α ≈ 0.72. For weak disorder, we predict the SV solid is a topologically ordered vortex glass, in the "columnar elastic glass" universality class. 64.60Fr,05.40,82.65Dp Rare-earth borocarbide materials exhibit a rich phase diagram that includes superconductivity, antiferromagnetism, ferromagnetism and spiral magnetic order. [1][2][3] In particular, there is now ample experimental evidence that, at low temperatures, superconductivity and ferromagnetism competitively coexist in ErNi 2 B 2 C compounds. Other possible examples of such ferromagnetic superconductors (FS) are the recently discovered high temperature superconductor Sr 2 Y Ru 1−x Cu x O 6 and the putative p-wave triplet strontium ruthenate superconductor, Sr 2 Ru O 4 , which spontaneously breaks time reversal symmetry. For sufficiently strong ferromagnetism, such FS's have been predicted [3] to exhibit a spontaneous vortex (SV) state driven by the spontaneous magnetization, rather than by an external magnetic field H. The novel phenomenology of the associated SV solid is the subject of this Letter.Here we will show that for H = 0, the elastic properties of the resulting SV solid differ dramatically and qualitatively from those of a conventional Abrikosov lattice. The key underlying difference is the vanishing of the tilt modulus, which is guaranteed by the underlying rotational invariance (but see below). Although this invariance is broken by the magnetization, M, the tilt modulus remains zero because this breaking is spontaneous. This contrasts strongly with a conventional vortex solid, where the rotational symmetry is explicitly broken by the applied field H. All of our conclusions, e.g., the unusual B(H) relation, illustrated in Fig.1 are a direct consequence of this important observation.In particular, we find that this "softness" (i.e., vanishing tilt modulus) of the SV lattice drastically enhances the effects of quenched disorder. As in conventional vortex lattices [4], any amount of disorder ∆ V , however weak, is sufficient to destroy translational order in SV lattices. Here the finite ordered domains are divergently anisotropic, with dimensions ξ

We show that a generalized Landau theory for the smectic-A-smectic-C �Sm-A-Sm-C� phases exhibits a biaxiality induced Sm-A-Sm-C tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the Sm-A-Sm-C transition is threedimensional XY-like, while for sufficiently small orientational order, it is either tricritical or first order. We investigate each of the three types of Sm-A-Sm-C transitions near tricriticality and show that for each type of transition, small orientational order implies de Vries behavior in the layer spacing, an unusually small layer contraction. This result is consistent with, and can be understood in terms of, the "diffuse cone" model of de Vries. Additionally, we show that birefringence grows upon entry to the Sm-C phase. For a continuous transition, this growth is more rapid the closer the transition is to tricriticality. Our model also predicts the possibility of a nonmontonic temperature dependence of birefringence.