Nematic State Research Articles

Isotropic in-plane quenched disorder and dilution induce a robust nematic state in electron-doped pnictides

The phase diagram of electron-doped pnictides is studied varying the temperature, electronic density, and isotropic quenched disorder strength by means of computational techniques applied to a three-orbital ($xz$, $yz$, $xy$) spin-fermion model with lattice degrees of freedom. In experiments, chemical doping introduces disorder but in theoretical studies the relationship between electronic doping and the randomly located dopants, with their associated quenched disorder, is difficult to address. In this publication, the use of computational techniques allows us to study independently the effects of electronic doping, regulated by a global chemical potential, and impurity disorder at randomly selected sites. Surprisingly, our Monte Carlo simulations reveal that the fast reduction with doping of the N\'eel $T_N$ and the structural $T_S$ transition temperatures, and the concomitant stabilization of a robust nematic state, is primarily controlled by the magnetic dilution associated with the in-plane isotropic disorder introduced by Fe substitution. In the doping range studied, changes in the Fermi Surface produced by electron doping affect only slightly both critical temperatures.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

Origin of the Resistive Anisotropy in the Electronic Nematic Phase of BaFe(2)As(2) Revealed by Optical Spectroscopy.

We perform, as a function of uniaxial stress, an optical-reflectivity investigation of the representative "parent" ferropnictide BaFe(2)As(2) in a broad spectral range, across the tetragonal-to-orthorhombic phase transition and the onset of the long-range antiferromagnetic (AFM) order. The infrared response reveals that the dc transport anisotropy in the orthorhombic AFM state is determined by the interplay between the Drude spectral weight and the scattering rate, but that the dominant effect is clearly associated with the metallic spectral weight. In the paramagnetic tetragonal phase, though, the dc resistivity anisotropy of strained samples is almost exclusively due to stress-induced changes in the Drude weight rather than in the scattering rate, definitively establishing the anisotropy of the Fermi surface parameters as the primary effect driving the dc transport properties in the electronic nematic state.

Microphase separation in polydisperse rod-rod diblock copolymer melt

The stability limits of the isotropic state of melt of rod-rod AB polydisperse diblock copolymer have been studied within weak segregation theory. The number of units in A block is assumed to be a random variable distributed by the Schulz-Zimm distribution. Inspection of the spinodal curves shows that the copolymer melt with polydisperse rigid blocks is less stable with respect to formation of the nematic and microphase separated states than the monodisperse melt. The values of ratios between strengths of isotropic and anisotropic interactions in the system strongly influences the forms of isotropic-nematic boundary curves.

Magnetic Excitations of Spin Nematic State in Frustrated Ferromagnetic Chain

By exploiting density-matrix renormalization group techniques, we investigate the dynamical spin structure factor of a spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in an applied magnetic field. In a field-induced spin nematic regime, we find gapless longitudinal and gapped transverse spin excitation spectra, in accordance with quasi-long-ranged longitudinal and short-ranged transverse spin correlations, respectively. The gapless point coincides with the dominant longitudinal spin correlation, whereas the gap position exhibits a characteristic field dependence contradicting the dominant transverse spin correlation.

Phase transitions and separations in a distorted liquid crystalline mixture.

A theoretical method is proposed for modelling phase transitions and phase ranges in a multi-component liquid crystalline mixture where the liquid crystal structure is distorted and defects are formed. This method employs the Maier-Saupe and Kobayashi-McMillan theories of liquid crystalline ordering and the Flory-Huggins theory of mixtures. It builds on previous work on mixed systems that can form smectic-A and nematic phases by incorporating "distortion factors" into the expression for the local free energy of the mixture, which account for the effects of a deviation of the liquid crystal structure from the uniform nematic and smectic-A states. The method allows a simple description of chiral defect phases such as the blue phase and the twist grain boundary phase. In a previous work, it was shown that a model of the blue phase along these lines could effectively explain the observed effect whereby an added guest compound can stabilize the phase by separating into the high energy defect regions of the structure. It is shown here that with the correct choice of guest material a similar effect could be observed for the twist grain boundary phase.

An electric-field induced dynamical state in dispersions of highly charged colloidal rods: comparison of experiment and theory.

Concentrated dispersions of highly charged rod-like colloids (fd-virus particles) in isotropic-nematic coexistence exhibit a dynamical state when subjected to low-frequency electric fields [Soft Matter, 2010, 6, 273]. This dynamical state consists of nematic domains which persistently melt and form on time scales typically of the order of seconds. The origin of the dynamical state has been attributed to a field-induced, cyclic dissociation and association of condensed ions [Soft Matter, 2014, 10, 1987, Soft Matter, 2015, 11, 2893]. The ionic strength increases on dissociation of condensed ions, rendering the nematic domains unstable, while the subsequent decrease of the ionic strength due to association of condensed ions leads to a recurrent stabilization of the nematic state. The role of dissociation/association of condensed ions in the phase/state behaviour of charged colloids in electric fields has not been addressed before. The electric field strength that is necessary to dissociate sufficient condensed ions to render a nematic domain unstable, depends critically on the ambient ionic strength of the dispersion without the external field, as well as the rod-concentration. The aim of this paper is to compare experimental results for the location of transition lines and the dynamics of melting and forming of nematic domains at various ionic strengths and rod-concentrations with the ion-dissociation/association model. Phase/state diagrams in the field-amplitude versus frequency plane at two different ambient ionic strengths and various rod-concentrations are presented, and compared to the theory. The time scale on which melting and forming of the nematic domains occurs diverges on approach of the transition line where the dynamical state appears. The corresponding critical exponents have been measured by means of image time-correlation spectroscopy [Eur. Phys. J. E, 2009, 30, 333], and are compared to the theoretical values predicted by the ion-dissociation/association model.

Nematic state stabilized by off-site Coulomb interaction in iron-based superconductors

Using a variational Monte Carlo method, we investigate the nematic state in iron-base superconductors based on a three-band Hubbard model. Our results demonstrate that the nematic state, formed by introducing an anisotropic hopping order into the projected wave function, can arise in the underdoped regime when a realistic off-site Coulomb interaction $V$ is considered. {\color {red} We demonstrate that the off-site Coulomb interaction $V$, which is neglected so far in the analysis of iron-base superconductors, make a dominant contribution to the stabilization of nematic state. We calculate the doping dependencies of the anisotropic properties such as the unequal occupation of $d_{xz}$ and $d_{yz}$ orbitals, anisotropies of kinetic energy and spin correlations, and show that they are all suppressed upon electron doping, which are consistent with the intrinsic anisotropies observed by optical spectrum measurement and ARPES experiments.

Spin-liquid polymorphism in a correlated electron system on the threshold of superconductivity

We report neutron scattering measurements which reveal spin-liquid polymorphism in an "11" iron chalcogenide superconductor. It occurs when a poorly metallic magnetic state of FeTe is tuned toward superconductivity by substitution of a small amount of tellurium with isoelectronic sulfur. We observe a liquid-like magnetic response, which is described by the coexistence of two disordered magnetic phases with different local structures whose relative abundance depends on temperature. One is the ferromagnetic (FM) plaquette phase observed in undoped, nonsuperconducting FeTe, which preserves the C4 symmetry of the underlying square lattice and is favored at high temperatures, whereas the other is the antiferromagnetic plaquette phase with broken C4 symmetry, which emerges with doping and is predominant at low temperatures. These findings suggest the coexistence of and competition between two distinct liquid states, and a liquid-liquid phase transformation between these states, in the electronic spin system of FeTe(1-x)(S,Se)(x). We have thus discovered the remarkable physics of competing spin-liquid polymorphs in a correlated electron system approaching superconductivity. Our results facilitate an understanding of large swaths of recent experimental data in unconventional superconductors. In particular, the phase with lower C2 local symmetry, whose emergence precedes superconductivity, naturally accounts for a propensity for forming electronic nematic states which have been observed experimentally, in cuprate and iron-based superconductors alike.

ChemInform Abstract: Unusual Ordered Phases of Highly Frustrated Magnets: A Review

AbstractReview: 194 refs.

Orientational ordering and phase behaviour of binary mixtures of hard spheres and hard spherocylinders.

We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.

Anisotropic electronic mobilities in the nematic state of the parent phase NaFeAs

Hall effect and magnetoresistance have been measured on single crystals of the parent phase NaFeAs under a uniaxial pressure. Although significant difference of the in-plane resistivity ${\ensuremath{\rho}}_{xx}(I\ensuremath{\parallel}a)$ and ${\ensuremath{\rho}}_{xx}(I\ensuremath{\parallel}b)$ with the uniaxial pressure along the $b$ axis was observed, the transverse resistivity ${\ensuremath{\rho}}_{xy}$ shows a surprisingly isotropic behavior. Detailed analysis reveals that the Hall coefficient ${R}_{\mathrm{H}}$ measured in the two orthogonal configurations $(I\ensuremath{\parallel}a$ axis and $I\ensuremath{\parallel}b$ axis) coincide very well and exhibit a deviation from the high temperature background at around the structural transition temperature ${T}_{\mathrm{s}}$. Furthermore, the magnitude of ${R}_{\mathrm{H}}$ increases remarkably below the structural transition temperature. This enhanced Hall coefficient is accompanied by the nonlinear transverse resistivity versus magnetic field and enhanced magnetoresistance, which can be explained very well by the two-band model with anisotropic mobilities of each band. Our results together with the two-band model analysis clearly show that the anisotropic in-plane resistivity in the nematic state is closely related to the distinct quasiparticle mobilities when they are moving parallel or perpendicular to the direction of the uniaxial pressure.

Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching

We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator. The latter phase breaks the rotational, but not the time-reversal symmetry, and may be relevant to materials such as gray tin or mercury telluride at low temperatures. The critical point represents a simple quantum analogue of the familiar classical isotropic-to-nematic transition in liquid crystals. The properties and the consequences of this quantum critical point are discussed. Its existence supports the scenario of the "fixed-point collision", according to which three-dimensional Fermi systems with quadratic band touching and long-range Coulomb interactions are unstable towards the gapped nematic ground state at low temperatures.

Lattice structure in liquid-crystal blue phase with various chiral concentrations

Lattice structures, including reflection lattice planes and lattice constant, of liquid-crystal blue phase I (BPI) are studied via the measurements on reflection spectrum and Kossel diagram as concentration of a chiral dopant is changed. Peaks of the reflection wavelength in BPI are mainly dominated by the lattice plane and the lattice constant, which are affected by the chiral concentration. In the chiral nematic state, as decreasing the chiral concentration the reflection peak will shift to a longer wavelength because the helical pitch linearly depends on the chiral concentration and becomes longer. However, this dependence of the chiral concentration and reflection wavelength is broken in the BPI. The reflection peak of BPI moves to a short wavelength when the chiral concentration is less due to the contraction of the lattice constant as well as helical pitch. Moreover, when the concentration of the chiral dopant increases over a certain value, a discontinuous shift in reflection peak occurs due to the production of the different lattice planes. It means that the relationship between the chiral concentration and the helical pitch in BPI is not the same as it in the chiral nematic phase and should be reconsidered.

Fast Photoswitching Azo Dyes

SummaryFast photoswitching azobenzene molecules were incorporated into isoflavone moieties. These molecules exhibit a liquid crystalline nematic state at certain temperature intervals. UV/Vis spectrophotometry investigations on solutions reveal that E/Z conversion takes place around 1 s, whereas thermal back relaxation, namely Z/E, takes around 6 min. This is the first example of fast photoswitching isoflavones in solution. This study has potential to create optical data storage devices when transferred to solid surfaces.

Spin-orbital interplay and topology in the nematic phase of iron pnictides

The origin of the nematic state is an important puzzle to be solved in iron pnictides. Iron superconductors are multiorbital systems and these orbitals play an important role at low energy. The singular $C_4$ symmetry of $d_{zx}$ and $d_{yz}$ orbitals has a profound influence at the Fermi surface since the $\Gamma$ pocket has vortex structure in the orbital space and the X/Y electron pockets have $yz$/$zx$ components respectively. We propose a low energy theory for the spin--nematic model derived from a multiorbital Hamiltonian. In the standard spin--nematic scenario the ellipticity of the electron pockets is a necessary condition for nematicity. In the present model nematicity is essentially due to the singular $C_4$ symmetry of $yz$ and $zx$ orbitals. By analyzing the ($\pi, 0$) spin susceptibility in the nematic phase we find spontaneous generation of orbital splitting extending previous calculations in the magnetic phase. We also find that the ($\pi, 0$) spin susceptibility has an intrinsic anisotropic momentum dependence due to the non trivial topology of the $\Gamma$ pocket.

Ordering in granular-rod monolayers driven far from thermodynamic equilibrium.

The orientational order in vertically agitated granular-rod monolayers is investigated experimentally and compared quantitatively with equilibrium Monte Carlo simulations and density functional theory. At sufficiently high number density, short rods form a tetratic state and long rods form a uniaxial nematic state. The length-to-width ratio at which the order changes from tetratic to uniaxial is around 7.3 in both experiments and simulations. This agreement illustrates the universal aspects of the ordering of rod-shaped particles across equilibrium and nonequilibrium systems. Moreover, the assembly of granular rods into ordered states is found to be independent of the agitation frequency and strength, suggesting that the detailed nature of energy injection into such a nonequilibrium system does not play a crucial role.

Two Glass Transitions Associated to Different Dynamic Disorders in the Nematic Glassy State of a Non-Symmetric Liquid Crystal Dimer Dopped with g-Alumina Nanoparticles

In the present work, the nematic glassy state of the non-symmetric LC dimer α-(4-cyanobiphenyl-4′-yloxy)-ω-(1-pyrenimine-benzylidene-4′-oxy) undecane is studied by means of calorimetric and dielectric measurements. The most striking result of the work is the presence of two different glass transition temperatures: one due to the freezing of the flip-flop motions of the bulkier unit of the dimer and the other, at a lower temperature, related to the freezing of the flip-flop and precessional motions of the cyanobiphenyl unit. This result shows the fact that glass transition is the consequence of the freezing of one or more coupled dynamic disorders and not of the disordered phase itself. In order to avoid crystallization when the bulk sample is cooled down, the LC dimer has been confined via the dispersion of γ-alumina nanoparticles, in several concentrations.

Simple theory of transitions between smectic, nematic, and isotropic phases.

The transitions between smectic, nematic, and isotropic phases are investigated in the framework of a unified molecular-statistical approach. The new translational order parameter is different from the one introduced in K. Kobayashi [Phys. Lett. A 31, 125 (1970)] and W. L. McMillan [Phys. Rev. A 4, 1238 (1971)]. The variance of the square sine of intermolecular shift angle along the director is introduced to take self-consistently into account the most probable location of the molecules with respect to each other, which is unique for every liquid crystal (LC) material and is mainly responsible for the order parameters and phase sequences. The mean molecular field was treated in terms of only two parameters specific to any intermolecular potential of elongated molecules: (1) its global minimum position with respect to the shift of two interacting molecules along the director and (2) its inhomogeneity/anisotropy ratio. A simple molecular model is also introduced, where the global minimum position is determined by the linking groups elongation Δ/d, while the inhomogeneity/anisotropy ratio Gβ/Gγ is determined by the ratio of electrostatic and dispersion contributions. All possible phase sequences, including abrupt/continuous transformation between the smectic and nematic states and the direct smectic-isotropic phase transition, are predicted. The theoretical prediction is in a good agreement with experimental data for some simple materials correlating with our molecular model, but it is expected to be valid for any LC material.

Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates

We consider the lightly doped cuprates Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ and La$_{2-x}$Sr$_x$CuO$_4$ (with $x=0.02$,0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe (or, more generically, charge-density wave) phase, which sets in at higher doping. We phenomenologically assume a quantum critical character for the longitudinal and transverse nematic, and for the charge-ordering fluctuations, and investigate the effects of these fluctuations in Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferred momentum account well for the anomalous Raman absorption observed in these systems in the $B_{2g}$ channel, while the absence of such effect in the $B_{1g}$ channel may be due to the overall suppression of Raman response at low frequencies, associated with the pseudogap. While in Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ the low-frequency lineshape is fully accounted by longitudinal nematic collective modes alone, in La$_{2-x}$Sr$_x$CuO$_4$ also charge-ordering modes with finite characteristic wavevector are needed to reproduce the shoulders observed in the Raman response. This different involvement of the nearly critical modes in the two materials suggests a different evolution of the nematic state at very low doping into the nearly charge-ordered state at higher doping.