Theory of the incommensurate smectic-A phases in dimesogenic liquid crystals

A mechanism assuming a mismatch between the basic smectic periodicity and the amplitude and phase modulations periods of the mass density wave order parameter is proposed, for describing the incommensurate smectic-A structure found in dimesogenic liquid crystals. The different sequences of phases found in this family of compounds are described theoretically.PACS: 61.30.Cz Molecular and microscopic models and theories of liquid crystal structure - 64.70.Md Transitions in liquid crystals     

Nonlinear phenomena in A2MX4 type crystals with incommensurate phases

Investigations of the nonlinear phenomena in A₂MX₄ type crystals (A, organic cation or alkaline metal ion; M, metal ion; X, halogen ion) with incommensurate phases are very interesting from both a scientific and a practical point of view. In the crystals many interesting nonlinear phenomena are observed, e.g., thermal hysteresis of birefringence and absorption coefficient, piezooptic effect, electrooptic effect. Different anomalies (e.g., a discontinuity or change of sign of the briefringence coefficient, a distinct increase of the value of piezooptic and electrooptic coefficients) exist in the phase transition regions. They are especially distinct for a transition from the incommensurate phase to the commensurate phase. Some possibilities of detection and recognition of the existence of incommensurate phases by optical methods are suggested.     

Features of the optical response of dielectric crystals with incommensurate phases

The constitutive relation describing the optical response of dielectric crystals in incommensurately modulated phases is derived for the plane-wave range of modulation. The symmetry properties of modulation corrections to the permittivity tensor of such crystals are analyzed with allowance for spatial dispersion. These properties are dictated by the Onsager principle for a nonabsorbing medium and by the mesoscopic periodicity of the medium. It is shown that the basic results are consistent with the general conventional approach in crystal optics of spatially inhomogeneous media.     

Conformal invariance in incommensurate phases

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f _–A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.     

Optical spectroscopy in incommensurate phases

Institut de Physique Nucléaire, IN2P3-CNRS, 91406 Orsay Cedex, France. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 62, pp. 167–178, July–August, 1995.     

Linear defects in incommensurate phases

It is shown that the boundary between incommensurate (I) and commensurate (C) phases, or between two I regions with different periodicities, consists of an array of linear defects. A topological classification of these defects is given for one-component complex order parameters and their significant in interpreting C-I transitions and properties of I phases is outlined.     

Global hysteresis in ferroelectrics with incommensurate phases

A review of the basic experimental results connected with the formation of long-living metastable states in the incommensurate phases of ferroelectric crystals and related phenomena is given. The interpretation and appropriate physical mechanisms underlying the global hysteresis phenomena associated with these states are considered.     

Sound modes in composite incommensurate crystals

We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of the system. It is shown that at high frequencies there are two longitudinal sound modes with standard attenuation, while in the low frequency region there is one propagating sound mode and an over-damped phase mode. The crossover between these two regions is analyzed numerically and the dynamical structure factor is calculated. It is shown that the qualitative features of the experimentally observed spectra can be consistently described by our model. Received 28 November 2001 and Received in final form 23 January 2002     

Symmetry of elementary excitations in incommensurate crystals

A generalized notion of symmetry in quantum mechanics is used for the classification of elementary excitations in incommensurate crystal phases.     

Optical activity of incommensurate crystals with plane-wave modulation

A phenomenological approach is used to discuss the propagation of polarized light in the incommensurately modulated phases of crystals of the family A₂BX₄ with spatially averaged inversion symmetry. The Jones-matrix technique for an anisotropic inhomogeneous medium is used to calculate the optical parameters of a crystal with sinusoidally modulated dielectric parameters. It is demonstrated that these crystals can exhibit a weak optical activity, i.e., weaker than that of crystals without inversion symmetry. Also discussed are boundary conditions on the phase of the modulation wave at the surface of a crystal plate. Results are obtained suggesting that the optical properties of an incommensurately modulated crystal need not depend on the shape of the modulation wave. Fiz. Tverd. Tela (St. Petersburg) 39, 1360–1365 (August 1996)     

The commensurate and incommensurate TGBC^* liquid crystal phases

We propose complements to the Renn model of the liquid crystal TGBC^* phase. We argue that the rotation angle per helislab is spontaneously in the radian range, not too small to limit the energy cost of the twist grain boundaries between the helislabs, not too large to preserve the double twisting efficiency. Taking the elastic interactions between the helislabs into account, we show that the structure may undergo two different lock-ins, provided that the uncontrolled interactions at the sample surfaces are small enough. First, for appropriate values of the elastic constants, an angular lock-in may fix the rotation angle per helislab at values exactly commensurate to π. Three characteristic lengths of the TGBC^* phase, the TGB period and the thicknesses of both the smectic blocks and of the helislabs are then commensurate to one another, with moreover, integer ratios at the most efficient commensurabilities. The TGBC^* phase could thus exist in several versions, incommensurate and commensurate, according to the steps of a restricted Devil's staircase. A second elastic lock-in should then arise in the commensurate TGBC^* phases, to set the arrays of disclination lines between the helislabs in simple rectangular lattices, arranged in a helical manner. Being placed right behind one another, the disclination lines then coincide when observed along the TGB axis. This could explain the typical textures with square or hexagonal grids, observed in oriented samples. The commensurability of the TGBC^* phases could be analyzed with X-ray scattering experiments in the same manner as already reported for the TGBC phase. Received 30 November 1999 and Received in final form 5 May 2000     

Inhomogeneous chiral symmetry breaking phases

We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.     

Planar defects and incommensurate phases in highly ordered perovskite solid solutions

A first-principles-derived approach is used to study the effects of planar defects on structural properties of a rocksalt-ordered Pb(Sc0.5Nb0.5)O3 alloy. These defects lead to unusual features, including a less symmetrical ground state with respect to the perfectly ordered material. We also propose that a simple and original mechanism, involving these defects, may be responsible for the existence and anomalous characteristics of the incommensurate phases observed in insulating perovskites.