Nonlinear Elasticity of the Sliding Columnar Phase

The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations between lattices in neighboring layers and a vanishing shear modulus for sliding lattices relative to each other. A simplified elasticity theory of the phase only allows intralayer fluctuations of the columns and has three important elastic constants: the compression, rotation, and bending moduli, $B$, $K_y$, and $K$. The rotationally invariant theory contains anharmonic terms that lead to long wavelength renormalizations of the elastic constants similar to the Grinstein-Pelcovits renormalization of the elastic constants in smectic liquid crystals. We calculate these renormalizations at the critical dimension $d=3$ and find that $K_y(q) \sim K^{1/2}(q) \sim B^{-1/3}(q) \sim (\ln(1/q))^{1/4}$, where $q$ is a wavenumber. The behavior of $B$, $K_y$, and $K$ in a model that includes fluctuations perpendicular to the layers is identical to that of the simple model with rigid layers. We use dimensional regularization rather than a hard-cutoff renormalization scheme because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format and 6 postscript figure

Structural Properties of the Sliding Columnar Phase in Layered Liquid Crystalline Systems

Under appropriate conditions, mixtures of cationic and neutral lipids and DNA in water condense into complexes in which DNA strands form local 2D smectic lattices intercalated between lipid bilayer membranes in a lamellar stack. These lamellar DNA-cationic-lipid complexes can in principle exhibit a variety of equilibrium phases, including a columnar phase in which parallel DNA strands from a 2D lattice, a nematic lamellar phase in which DNA strands align along a common direction but exhibit no long-range positional order, and a possible new intermediate phase, the sliding columnar (SC) phase, characterized by a vanishing shear modulus for relative displacement of DNA lattices but a nonvanishing modulus for compressing these lattices. We develop a model capable of describing all phases and transitions among them and use it to calculate structural properties of the sliding columnar phase. We calculate displacement and density correlation functions and x-ray scattering intensities in this phase and show, in particular, that density correlations within a layer have an unusual $\exp(- {\rm const.} \ln^2 r)$ dependence on separation r. We investigate the stability of the SC phase with respect to shear couplings leading to the columnar phase and dislocation unbinding leading to the lamellar nematic phase. For models with interactions only between nearest neighbor planes, we conclude that the SC phase is not thermodynamically stable. Correlation functions in the nematic lamellar phase, however, exhibit SC behavior over a range of length scalesComment: 28 pages, 4 figure

Sliding Columnar Phase of DNA-Lipid Complexes

We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We identify a new equilibrium phase in which there are long-range orientational but not positional correlations between DNA lattices. We discuss properties of this new phase such as its X-ray structure factor S(r), which exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane separation r.Comment: This file contains 4 pages of double column text and one postscript figure. This version includes interactions between dislocations in a given gallery and presents an improved estimate of the decoupling temperature. It is the published versio

Coarsening scenarios in unstable crystal growth

Crystal surfaces may undergo thermodynamical as well kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev. Let

The 0 and the pi phase Josephson coupling through an insulating barrier with magnetic impurities

We have studied temperature and field dependencies of the critical current $I_{C}$ in the Nb-Fe$_{0.1}$Si$_{0.9}$-Nb Josephson junction with tunneling barrier formed by paramagnetic insulator. We demonstrate that in these junctions the co-existence of both the 0 and the $\pi$ states within one tunnel junction takes place which leads to the appearance of a sharp cusp in the temperature dependence $I_{C}(T)$ similar to the $I_{C}(T)$ cusp found for the $0-\pi$ transition in metallic $\pi$ junctions. This cusp is not related to the $0-\pi$ temperature induced transition itself, but is caused by the different temperature dependencies of the opposing 0 and $\pi$ supercurrents through the barrier.Comment: Accepted in Physical Review

Classical motion in force fields with short range correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and mean-squared displacement is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, p^{2}(t) ~ t^{2/5} independently of the details of the potential and of the space dimension. Motion is then superballistic in one dimension, with q^{2}(t) ~ t^{12/5}, and ballistic in higher dimensions, with q^{2}(t) ~ t^{2}. These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: p^{2}(t) ~ t^{2/3} and q^{2}(t) ~ t^{8/3} in all dimensions d\geq 1

Fast coarsening in unstable epitaxy with desorption

Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small amount of desorption dramatically speeds up the coarsening of the mound array, leading to coarsening exponents between 1/3 and 1/2. The underlying mechanism is the faster growth of larger mounds due to their lower evaporation rate.Comment: 4 pages, 4 PostScript figure

Hydrodynamics of the quantum Hall smectics

We propose a dynamical theory of the stripe phase arising in a two-dimensional electron liquid near half-integral fillings of high Landau levels. The system is modelled as a novel type of a smectic liquid crystal with the Lorentz force dominated dynamics. We calculate the structure factor, the dispersion relation of the collective modes (magnetophonons), and their intrinsic attenuation rate. We find strong power-law renormalizations of the elastic and dissipative coefficients by thermal fluctuations familiar from the conventional smectics but with different dynamical scaling exponents.Comment: Replaced with the published versio

Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes

We predict the existence of a totally new class of phases in weakly coupled, three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding phases'' behave essentially like decoupled, independent 2D XY-models with precisely zero free energy cost associated with rotating spins in one layer relative to those in neighboring layers. As a result, the two-point spin correlation function decays algebraically with in-plane separation. Our results, which contradict past studies because we include higher-gradient couplings between layers, also apply to crystals and may explain recently observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript figur

Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology

Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental observations within a unified framework. We find that a periodic ripple morphology characterizes the initial stages of the evolution, whereas the surface displays self-affine scaling in the later time regime. Further, we argue that the stochastic continuum equation describing the surface height is a noisy version of the Kuramoto-Sivashinsky equation.Comment: 4 pages, 7 postscript figs., Revtex, to appear in Phys. Rev. Let