Smectic Fluctuations Research Articles

Unconventional density waves and superconductivities in Fe-based superconductors and other strongly correlated electron systems

To seek high-$T_c$ pairing mechanism, many scientists have focused on the mysterious spontaneous rotational symmetry breaking above Tc, such as nematic order at $q=0$ and smectic order at $q\ne0$. Such exotic correlation-driven symmetry breaking in metals has become a central issue in condensed matter physics. We demonstrate the emergence of the nematic and smectic orders due to orbital polarization ($n_{xz}\ne n_{yz}$) and the symmetry breaking in the correlated intersite hopping (= bond order $\delta t_{i,j}$) in Fe-based and cuprate superconductors. In addition, we discuss exotic spontaneous loop current orders driven by the pure imaginary $\delta t_{i,j}$. These interesting ``unconventional density-waves'' originate from the quantum interference between different spin fluctuations that is described by the vertex correction (VC) in the field theory. In the next stage, we discuss electron-correlation driven superconductivity due to the fluctuations of unconventional density-waves. For this purpose, we suggest the beyond-Migdal-Eliashberg gap equation by including the VCs into the equation. In Fe-based superconductors, high-$T_c$ $s$-wave superconductivity can be mediated by nematic and smectic fluctuations because the pairing interaction is magnified by the VCs. We also discuss the multipolar fluctuation pairing mechanism in heavy fermion systems, owing to the cooperation between the strong spin-orbit interaction and the strong electron correlation. To summarize, we suggest that the quantum interference mechanism described by the VCs is the key ingredients to explain not only various unconventional density-waves, but also exotic superconducting states in many strongly correlated metals. We finally discuss some interesting future issues with respect to the quantum interference mechanism.

The influence of multi-walled carbon nanotube doping on liquid crystalline phase transitions of a smectogen octylcyanobiphenyl: A high-resolution birefringence study

High-resolution optical birefringence measurements are reported on the weakly first order nematic-isotropic (N–I) and the continuous nematic-smectic A (N–Sm A) phase transitions in smectic liquid crystal 8CB (octylcyanobiphenyl) doped with both pristine multi-walled carbon nanotubes (p-MWCNTs) and carboxyl group (-COOH) functionalized MWCNTs (f-MWCNTs). It has been observed that the inclusion of MWCNTs substantially decreases both the N–I and the N–Sm A transition temperatures compared to 8CB host while the order of the transitions remains the same being the I–N weakly first-order and the N-SmA continuous for all 8CB-MWCNT composites regardless of the surface functionalization. The optical birefringence data have been used to probe the temperature behavior of the nematic order parameter S(T) in the vicinity of both the N–I and the N–Sm A transitions. Sufficiently far away from the Sm A phase, the average value of the critical exponent β characterizing the limiting behavior of S(T) near the N–I transition was found to be 0.245±0.002 This value of β seems to be in accord with the tricritical nature (TCH) of the N–I transition. Thus, concluded is the fact that the nature of the N–I transition of nanomaterial-based composites dispersed in liquid crystals remains tricritical up to at least the reported dopant contents and within the experimental resolution. The pre-transitional smectic behavior has also been noted to continue up to 4.3K on average above TNA for all 8CB-MWCNT composites. From the detailed inspection of S(T) data in the immediate vicintiy of the N–Sm A transition TNA, we have then obtained the upper limits for a possible latent heat ΔHNA across TNA for all 8CB-MWCNT composites. A slight change in ΔHNA has been observed due to the inclusion of MWCNTs as compared to 8CB host. By exploiting the fact that the temperature derivative of the order parameter S(T) near TNA exhibits the same power law divergence as the specific heat capacity, we have also extracted the effective critical exponent α values characterizing the critical fluctuations near the N-SmA transition for all 8CB-MWCNT composites. From both α and ΔHNA values, we have concluded that the nematic and smectic fluctuations remain essentially bulk-like for both 8CB-p-MWCNT and 8CB-f-MWCNT composites and thus the fact that the coupling between the N and the Sm A order parameters for all composites are comparable to that of 8CB host has been documented.

Clustering in vibrated monolayers of granular rods.

We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. These clusters behave as a polydisperse mixture of long life-time 'superparticles', and some aspects of the system behaviour can be understood by applying mean-field theories for equilibrium hard rectangles, based on two-body correlations, to these 'superparticles'. Many other features of the granular system are different: (i) for small particle length-to-breadth ratio κ, we identify tetratic ordering at moderate packing fractions and smectic fluctuations at higher packing fractions, with no sharp transition between the two states. Both types of ordering can be explained in terms of clustering. (ii) For large κ, strong clustering precludes the stabilisation of a uniaxial nematic state, and the system exhibits a mixture of randomly-oriented clusters which, as packing fraction is increased, develops into states with smectic fluctuations, again through a diffuse transition. (iii) Vorticity excitations of the velocity field compete with smectic ordering, causing dynamic fluctuations and the absence of steady states at high densities; the tetratic state, by contrast, is very stiff against vorticity, and long-standing steady states, spatially and orientationally homogeneous except for four symmetrical defects located close to the wall, can be observed.

Short-range smectic fluctuations and the flexoelectric model of modulated nematic liquid crystals.

We show that the flexoelectric model of chiral and achiral modulated nematics predicts the compression modulus that is by orders of magnitude lower than the measured values. The discrepancy is much larger in the chiral modulated nematic phase, in which the measured value of the compression modulus is of the same order of magnitude as in achiral modulated nematics, even though the heliconical pitch is by an order of magnitude larger. The relaxation of a one-constant approximation in the biaxial elastic model used for chiral modulated nematics does not solve the problem. Therefore, we propose a structural model of the modulated nematic phase, which is consistent with the current experimental evidence and can also explain large compression modulus: the structure consists of short-range smectic clusters with a fourfold symmetry and periodicity of two molecular distances. In chiral systems, chiral interactions lead to a helicoidal structure of such clusters.

Dielectric Spectroscopy of the Electroclinic Effect in the Ferroelectric Liquid Crystal Materials

ABSTRACT We present the dielectric properties of two pure ferroelectric liquid crystal materials (C11 and C12) exhibiting cholesteric (N*), paraelectric smectic A (SmA*), and ferroelectric chiral smectic C (SmC*) phases. In the dielectric measurements carried out without a DC bias field, we studied the soft-mode relaxation in the SmA* phase. From experimental data and using the results of a Landau model, we evaluate the electroclinic coefficient in the SmA* phase. A soft-mode-like mechanism was also observed in the N* phase for a compound with a shorter chain (C11). This relaxation process is not detected for the homolog with a longer chain (C12). The observation of this mechanism is linked to smectic order fluctuations within the N* phase whose amplitude is more enhanced close to the SmC*−SmA*−N* multicritical point.

Smectic-Ato -Cphase transition in isotropic disordered environments

We study theoretically the smectic-A to -C phase transition in isotropic disordered environments. Surprisingly, we find that, as in the clean smectic-A to -C phase transition, smectic layer fluctuations do not affect the nature of the transition, in spite of the fact that they are much stronger in the presence of the disorder. As a result, we find that the universality class of the transition is that of the "random field XY model" (RFXY).

Active and passive viscosities of a bent-core nematic liquid crystal

We report the measurements of active and passive viscosities of a bent-core nematic liquid crystal. The active viscosity is measured using a rheometer and the passive viscosities are measured by measuring the self-diffusion coefficient of a microsphere in the aligned sample. The effective active viscosity is larger and the effect of presmectic fluctuations are observed much higher than the $N$--Sm-$C$ transition temperature than commonly seen in calamitic liquid crystals. The temperature dependence of passive viscosities is stronger than that of active viscosities. The self-diffusion of the microsphere is reduced and appears to be non-Gaussian as the $N$--Sm-$C$ transition is approached. The study of Brownian fluctuations is useful to understand the smectic fluctuations in bent-core nematic liquid crystals.

Crossover From Under to Overdamped Dynamics in Free-Standing Smectic Films Close to the Smectic-A-Nematic Second Order Phase Transition

The hydrodynamic properties of free-standing smectic films close to a second order smectic-A (SmA) — nematic (N) phase transition are investigated. By using an extended McMillan model, the profiles of the smectic elastic constants are computed at different temperatures. We show that the amplitude of smectic fluctuations has a strong dependence on the film temperature. By considering the critical behavior of viscoelastic coefficients of thin films, we show that the typical underdamped relaxation of the smectic order is replaced by an overdamped behavior close to the bulk transition temperature.

Biaxial nematic order induced by smectic fluctuations

We report on a series of measurements on the microscopic structure and the magneto-optical properties of a calamitic liquid crystalline compound in its nematic phase. Structural studies show the existence of short-range, tilted smectic order consistent with pretransitional effects above an underlying smectic phase. Concomitantly, magneto-optical results exhibit the existence of an optic axis not collinear with the uniaxial director. This apparent biaxial nature is discussed within the context of coupling between the tensor nematic and the smectic order parameters.

Electroclinic effect in the chiral smectic A and cholesteric phases at the proximity of a N*–SmA–SmC* multicritical point

We studied the electro-optic and dielectric properties of three pure ferroelectric liquid crystal materials (C10, C11 and C12) of the same series exhibiting cholesteric (N*), smectic A (SmA) and chiral smectic C (SmC*) phases. From electro-optic investigations, the tilt angle and spontaneous polarisation were determined as a function of temperature. In the dielectric measurements carried out without a dc bias field, we studied the soft-mode relaxation in the SmA phase. From experimental data and using the results of a Landau model, we evaluated the soft-mode rotational viscosity and the electroclinic coefficient in the SmA phase. A soft-mode like mechanism was also observed in the N* phase for compounds with shorter chains (C10 and C11). This relaxation process is not detected for the homologue with a longer chain (C12). The observation of this mechanism is related to smectic order fluctuations within N* phase whose amplitude is increased when approaching the SmC*–SmA–N* multicritical point.

ChemInform Abstract: Liquid Crystal Properties of Metal-Salicylaldimine Complexes. Chemical Modifications Towards Lower Symmetry

Abstract A body of work involving liquid crystalline phases in the family of transition metal complexes of salicylaldimines has been reviewed. An account is given as to how the mesophases can be derived from archetypical coordination compounds in the liquid state by an approach of lowering symmetry. Attention is confined to reported examples of well-established metal–salicylaldimine mesogens. Firstly, it is shown that the nematic behavior can be related to the molecular shape anisotropy as a primary factor, which works advantageously to generate the orientational order. A group of bis[4-(4-alkoxy)benzoyloxy-N-alkylsalicylaldiminato]metal complexes represents the nematics. Smectic fluctuations in, and eventual ordering of, the nematic phases are treated together, and several other effects conducive to this tailoring of phase property are pointed out. Pure smectic phases are found in bis[4-alkoxy-N-arylsalicylaldiminato]metal complexes. The change in the rigid core shape and the packing considerations for the terminal alkyl chain substituents are discussed in relation to the positional ordering. The literature is cited to shed light on the increased biaxial character of the molecular structure possibly leading to unusual local ordering. Finally, columnar phases in complexes of [M(salen)] type with heavily incorporated long alkyl chains are introduced and contrasted to simpler dialkylated derivatives which are smectogenic.

Nuclear spin–lattice relaxation dispersion investigation of smectic order fluctuations in isotropic and nematic phases

Proton magnetic relaxation dispersion (PMRD) measurements are made with a view to investigating the influence of an underlying smectic phase, on the isotropic and nematic phases of the binary liquid crystalline mixture of 4DBT and 12CB, at two distinct concentrations, namely 50% 12CB (has no smectic phase) and 70% 12CB (retains S Ad phase of 12CB). Analyses of the data in terms of relevant molecular processes show that the influence of smectic clusters on the nematic order fluctuations persists even in the isotropic phase. Further, the molecular dynamics are qualitatively different in the respective nematic phases of the two mixtures.

Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition

We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes.'' We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective modes of the electron smectic (or stripe) phase are also investigated. The effects of the low-energy bosonic modes on the fermionic quasiparticles are studied perturbatively, for both a model with full rotational symmetry and for a system with an underlying lattice, which has a discrete point group symmetry. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, around which it is reconstructed, are not governed by a Landau Fermi liquid theory. Surprisingly, the quasiparticles in the smectic phase also exhibit non-Fermi liquid behavior. We also present a detailed analysis of the dynamical susceptibilities in the electron nematic phase close to this QCP (the fluctuating stripe regime) and in the electronic smectic phase.

Wetting of liquid-crystal surfaces and induced smectic layering at a nematic-liquid interface: An x-ray reflectivity study

We report the results of a synchrotron x-ray reflectivity study of bulk liquid-crystal surfaces that are coated by thin wetting films of an immiscible liquid. The liquid-crystal subphase consisted of the nematic or isotropic phase of 4-octyl- 4;{'} -cyanobiphenyl (8CB), and the wetting film was formed by the fluorocarbon perfluoromethylcyclohexane (PFMC), a volatile liquid. The thickness of the wetting film was controlled by the temperature difference DeltaT(micro) between the sample and a reservoir of bulk PFMC, contained within the sealed sample cell. Phase information on the interfacial electron density profiles has been extracted from the interference between the scattering from the PFMC-vapor interface and the surface-induced smectic order of the 8CB subphase. The liquid-crystal side of the nematic-liquid (8CB-PFMC) interface is characterized by a density oscillation whose period corresponds to the smectic layer spacing and whose amplitude decays exponentially toward the underlying nematic subphase. The decay length xi of the smectic amplitude is independent of the PFMC film thickness but increases as the nematic-smectic- A transition temperature T(NA) is approached, in agreement with the longitudinal correlation length xi(parallel) proportional, variant(T-T(NA))(-0.7} for the smectic fluctuations in the bulk nematic. The results indicate that the homeotropic orientation of the 8CB molecules is preferred at the 8CB-PFMC interface and that the observed temperature dependence of the smectic layer growth is consistent with the critical adsorption mechanism. The observed DeltaT(micro) dependence of the PFMC film thickness, L proportional, variant(DeltaT(micro))(-1/3) , implies that PFMC completely wets the 8CB surface and is dominated by the nonretarded dispersion interactions between hydro- and fluorocarbons. The complete wetting behavior of PFMC is nearly independent of the degree of interfacial smectic order in the subphase.

Influence of the proximity of a N*–SmA–SmC* multicritical point on the electroclinic effect in the cholesteric phase

Chiral liquid crystal material (C12 homologue of biphenyl benzoate series) exhibiting the cholesteric (N*), smectic A (SmA) and ferroelectric smectic C (SmC*) phases have been studied by structural, thermodynamic, electrooptical and dielectric investigations. The helical pitch, tilt angle and spontaneous polarization have been determined. In the dielectric measurements, we have studied the soft mode in the SmC* and SmA phases. From experimental data, we have evaluated the soft‐mode rotational viscosity and the electroclinic coefficient in the SmA phase. All results are discussed and compared with previous studies performed on other homologues of the same series. The main result is that the relaxation process detected in the N* phase for the C8, C10 and C11 homologues and explained as a soft‐mode‐like mechanism, is not observed for C12. This corroborates the idea that this mechanism is related to the appearance of smectic order fluctuations within N* phase, the amplitude of which is increased when approaching the SmC*–SmA–N* multicritical point.

Smectic layer displacement fluctuations in solid substrate supported smectic-A films.

In this paper we present results of calculations of static and dynamic characteristics of smectic layer displacement fluctuations in solid substrate supported smectic-A films with due regard for asymmetric profiles of the bending elastic constant K and the smectic layer compressibility B. We also take into account difference in properties of boundary surfaces of the film, namely, the surface tension of the free surface is taken to be finite whereas that of a film-substrate interface is assumed to be infinitely large. Profiles of the smectic layer displacement fluctuations and correlations between them are calculated for films formed of liquid crystalline compounds with the bulk smectic-A to nematic phase transition. The calculations are performed at temperatures much lower than that of the bulk phase transition and at maximum temperatures of existence of films of given thickness. The time dependent displacement-displacement correlation functions for thermal smectic layer displacement fluctuations and time dependent intensity-intensity correlation functions for diffuse x-ray scattering from the films are also calculated. It is shown that unlike free-standing smectic-A films, an effect of the temperature on dynamics of smectic layer displacement fluctuations in solid substrate supported smectic-A films can be observed in experiments on coherent x-ray dynamic scattering from not very thick films (N approximately 20) and at significantly smaller wave vector transfer component in the film plane.

Universal non-monotonic smectic fluctuations of liquid crystal films in a magnetic field

Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξH delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form.

Light scattering study of a twist grain boundary liquid crystal.

Dynamic light scattering is used to probe the fluctuation modes of a liquid crystal exhibiting twist grain boundary (TGB) structure. At the chiral nematic to proposed "chiral line liquid" phase transition, anomalous temperature dependence in the fluctuation spectrum and an instability in the helicoidal director structure signify developing TGB order. At lower temperatures, the behavior of the smectic layer-director fluctuations ("soft" mode) indicates that the previously identified commensurate TGB(A) phase may in fact be a TGB(C) phase with an unusually small tilt angle.

Photoresponsive vitrifiable chiral dimesogens: photo-thermal modulation of microscopic disordering in helical superstructure and glass-forming properties

Thermal, photooptical as well as glass-forming properties of a series of photoresponsive chiral dimesogenic compounds containing cholesterol–azobenzene moieties linked to varying alkyl chain lengths (6–14) are described. All compounds except the dimesogen containing 7 methylene spacers show a cholesteric phase. Selective reflections observed in the cholesteric liquid crystals were found to be blue shifted upon increasing the temperature due to variations in smectic fluctuations. X-Ray diffraction studies of these compounds in the cholesteric phase show a low intensity reflection at small angles, the half widths of which decrease on decreasing the temperature, confirming the presence of smectic cybotactic groups. These materials also exhibit a strong odd–even effect in their reflection wavelength as a function of spacer length. Compounds with even numbers of methylene units show a drastic change in their reflection wavelength (102–225 nm) on temperature change compared to those with odd numbers of methylene units (9–14 nm). UV photolysis, using light of 366 nm wavelength, in the cholesteric super-cooled state exhibits a hypsochromic shift in the reflection wavelength. This can be explained by the formation of the cis isomer destroying the smectic clusters in the helical superstructure due to its bent geometry, which in turn causes a decrease in the reflected wavelength. A maximum wavelength shift of 215 nm (703–488 nm) has been observed on photolysis at 80 °C (cooling cycle) for the dimesogen having 12-methylene spacers. By rapid cooling of the compounds from the cholesteric temperature to 0 °C glassy liquid crystalline films maintaining helical molecular order were obtained. The optical properties of these dimesogens, such as cholesteric reflections, controlled by light and temperature combined with their glass forming properties, can be utilized for the construction of information storage materials.

Elastic coupling of silica gel dynamics in a liquid-crystal-aerosil dispersion.

The dynamics of a thixotropic silica aerosil gel dispersed in an octylcyanobiphenyl liquid crystal were directly probed by x-ray intensity fluctuation spectroscopy. For all samples, the time-autocorrelation function of the gel was well described by a modified-exponential function over the q range studied. Compared to a pure gel sample, a dilute (0.06 g cm(-3)) gel embedded within the liquid crystal displayed more complex and temperature dependent dynamics. Near the second-order smectic-A-to-nematic phase transition of the liquid crystal the gel relaxation became significantly more complex and slower (tau approximately 2150 s) compared to relaxations observed well within either phase. This clearly demonstrates coupling between the dynamics of the gel and the host liquid crystal, consistent with critical slowing down of smectic and director fluctuations. A random dampening field, elastically coupled to the liquid crystal, would explain the earlier observed crossover of this transition towards 3d-XY behavior.