Observation of algebraic decay of positional order in a smectic liquid crystal

Als‐Nielsen, J.; Litster, J. D.; Birgeneau, R. J.; Kaplan, M. L.; Safinya, Cyrus R.; Lindegaard-Andersen, A.; Mathiesen, S. Ipsen

doi:10.1103/physrevb.22.312

Cited by 250 publications

(127 citation statements)

References 12 publications

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“…The second way uses Eq. (13). Fig.10 shows that the simulated P f l can be reasonably represented by an exponential using either method of computation, thereby supporting both theory and experiment.…”

Section: Comparison To Experimentssupporting

confidence: 55%

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Simulations of a single membrane between two walls using a Monte Carlo method

Gouliaev

Nagle

1998

Phys. Rev. E

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Quantitative theory of interbilayer interactions is essential to interpret x-ray scattering data and to elucidate these interactions for biologically relevant systems. For this purpose Monte Carlo simulations have been performed to obtain pressure P and positional fluctuations σ. A new method, called Fourier Monte-Carlo (FMC), that is based on a Fourier representation of the displacement field, is developed and its superiority over the standard method is demonstrated. The FMC method is applied to simulating a single membrane between two hard walls, which models a stack of lipid bilayer membranes with non-harmonic interactions. Finite size scaling is demonstrated and used to obtain accurate values for P and σ in the limit of a large continuous membrane. The results are compared with perturbation theory approximations, and numerical differences are found in the non-harmonic case. Therefore, the FMC method, rather than the approximations, should be used for establishing the connection between model potentials and observable quantities, as well as for pure modeling purposes.

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Section: Comparison To Experimentssupporting

confidence: 55%

“…However, for modeling the structure factor for low angle x-ray scattering (in contrast to modeling the form factor), it is customary and appropriate [12][13][14][15] to model the membrane as an infinitely thin flexible sheet as shown in Fig.1.…”

Section: Introductionmentioning

confidence: 99%

Simulations of a single membrane between two walls using a Monte Carlo method

Gouliaev

Nagle

1998

Phys. Rev. E

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“…For example, as illustrated in Fig.21, we predict that in 3d [133] the static structure function S(q) in the LO state exhibits universal anisotropic quasi-Bragg peaks (akin to a conventional smectic liquid crystal [134,135]), with n-th order peak given by…”

Section: B Resultsmentioning

confidence: 99%

“…As for n k , we find that the logarithmically divergent 3d phonon fluctuations lead to a structure function, with highly anisotropic (q z ∼ q 2 ⊥ /λ) quasi-Bragg peaks (see Fig.21) replacing the true Bragg peaks characteristic of the mean-field long-range periodic order. These predictions are a reflection of the wellknown [129,130] and experimentally tested [135] behavior of conventional smectic liquid crystals.…”

Section: T > 0 Thermal Fluctuationsmentioning

confidence: 99%

Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas

Radzihovsky

2011

Phys. Rev. A

122

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Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states and use it to analyze fluctuations, stability, and phase transitions in these enigmatic finite momentum-paired superfluids. Focusing on the unidirectional LO pair-density wave state, that spontaneously breaks the continuous rotational and translational symmetries, we show that it is characterized by two Goldstone modes, corresponding to a superfluid phase and a smectic phonon. Because of the liquidcrystalline "softness" of the latter, at finite temperature the 3d state is characterized by a vanishing LO order parameter, quasi-Bragg peaks in the structure and momentum distribution functions, and a "charge"-4, paired Cooper-pairs, off-diagonal-long-range order, with a superfluid-stiffness anisotropy that diverges near a transition into a nonsuperfluid state. In addition to conventional integer vortices and dislocations the LO superfluid smectic exhibits composite half-integer vortexdislocation defects. A proliferation of defects leads to a rich variety of descendant states, such as the "charge"-4 superfluid and Fermi-liquid nematics and topologically ordered nonsuperfluid states, that generically intervene between the LO state and the conventional superfluid and the polarized Fermi-liquid at low and high imbalance, respectively. The fermionic sector of the LO gapless superconductor is also quite unique, exhibiting a Fermi surface of Bogoliubov quasiparticles associated with the Andreev band of states, localized on the array of the LO domain-walls.

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“…(13c) then in turn implies that the helical state inherits all the novel nonlinear elastic effects previously discovered in the context of conventional, thermotropics and lyotropic smectic liquid crystals and other spontaneously layered states that emerge from an isotropic state. These include thermal fluctuations [10,11,19] and heterogeneous [20] anomalous elasticity effects, the undulation instability [21], and many others.…”

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confidence: 99%

Nonlinear smectic elasticity of helical state in cholesteric liquid crystals and helimagnets

Radzihovsky

Lubensky

2011

Phys. Rev. E

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General symmetry arguments, dating back to de Gennes dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free-energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director/magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators [1].

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Observation of algebraic decay of positional order in a smectic liquid crystal

Cited by 250 publications

References 12 publications

Simulations of a single membrane between two walls using a Monte Carlo method

Simulations of a single membrane between two walls using a Monte Carlo method

Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas

Nonlinear smectic elasticity of helical state in cholesteric liquid crystals and helimagnets

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