Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.Comment: 21 RevTeX pgs, 7 eps figures uuencoded; corrected typos, published versio

Continuous Melting of a "Partially Pinned" Two-Dimensional Vortex Lattice in a Square Array of Pinning Centers

The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition.Comment: 5 pages, 4 figure

Universality in the Screening Cloud of Dislocations Surrounding a Disclination

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which can be computed from the properties of the grain boundaries forming the dislocation cloud. Expressions are also given when the crystal is subjected to an external two-dimensional pressure. The analytical results are generalized to a scaling form for the energy which up to core energies is given by the Young modulus of the crystal times a universal function. The accuracy of the universality hypothesis is numerically checked to high accuracy. The numerical approach, based on a generalization from previous work by S. Seung and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own and allows to compute the energy for an {\em arbitrary} distribution of defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy} with very minor additional computational effort. Some implications for recent experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file

Frustrated two-dimensional Josephson junction array near incommensurability

To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 $(\approx (3-\sqrt{5})/2)$, 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transition and the vortex configuration near the transition at the high-order rational frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple frustration f=2/5. This finding suggests that the behaviors of Josephson junction arrays in the wide range of frustrations might be understood from those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.

Liquid antiferromagnets in two dimensions

It is shown that, for proper symmetry of the parent lattice, antiferromagnetic order can survive in two-dimensional liquid crystals and even isotropic liquids of point-like particles, in contradiction to what common sense might suggest. We discuss the requirements for antiferromagnetic order in the absence of translational and/or orientational lattice order. One example is the honeycomb lattice, which upon melting can form a liquid crystal with quasi-long-range orientational and antiferromagnetic order but short-range translational order. The critical properties of such systems are discussed. Finally, we draw conjectures for the three-dimensional case.Comment: 4 pages RevTeX, 4 figures include

Vortex states in 2D superconductor at high magnetic field in a periodic pinning potential

The effect of a periodic pinning array on the vortex state in a 2D superconductor at low temperatures is studied within the framework of the Ginzburg-Landau approach. It is shown that attractive interaction of vortex cores to a commensurate pin lattice stabilizes vortex solid phases with long range positional order against violent shear fluctuations. Exploiting a simple analytical method, based on the Landau orbitals description, we derive a rather detailed picture of the low temperatures vortex state phase diagram. It is predicted that for sufficiently clean samples application of an artificial periodic pinning array would enable one to directly detect the intrinsic shear stiffness anisotropy characterizing the ideal vortex lattice.Comment: 8 pages, 5 figure

Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study

The nature of freezing and melting transitions for a system of hard disks in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants etc. are used to map the phase diagram of the system for various values of the density and the amplitude of the external potential. We find clear indication of a re-entrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of hard disks behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a re-melting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. Detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting.Comment: 36 pages, 16 figure

Selectivity and functional diversity in arbuscular mycorrhizas of co-occurring fungi and plants from a temperate deciduous woodland

1 The arbuscular mycorrhizal (AM) fungi colonizing plants at a woodland site in North Yorkshire (UK) have been characterized from the roots of five plant species (Rubus fruticosus agg. L., Epilobium angustifolium L., Acer pseudoplatanus L., Ajuga reptans L. and Glechoma hederacea L.), and identified using small-subunit rRNA (SSUrRNA) gene amplification and sequencing. 2 Interactions between five plant species from the site and four co-occurring glomalean fungi were investigated in artificial one-to-one AM symbioses. Three of the fungi were isolated from the site; the fourth was a culture genetically similar to a taxon found at the site. Phosphorus uptake and growth responses were compared with non-mycorrhizal controls. 3 Individual fungi colonized each plant with different spatial distribution and intensity. Some did not colonize at all, indicating incompatibility under the conditions used in the experiments. 4 Glomus hoi consistently occupied a large proportion of root systems and outperformed the other fungi, improving P uptake and enhancing the growth of four out of the five plant species. Only G. hoi colonized and increased P uptake in Acer pseudoplatanus, the host plant with which it associates almost exclusively under field conditions. Colonization of all plant species by Scutellospora dipurpurescens was sparse, and beneficial to only one of the host plants (Teucrium scorodonia). Archaeospora trappei and Glomus sp. UY1225 had variable effects on the host plants, conferring a range of P uptake and growth benefits on Lysimachia nummularia and T. scorodonia, increasing P uptake whilst not affecting biomass in Ajuga reptans and Glechoma hederacea, and failing to form mycorrhizas with A. pseudoplatanus. 5 These experimental mycorrhizas show that root colonization, symbiont compatibility and plant performance vary with each fungus-plant combination, even when the plants and fungi naturally co-exist. 6 We provide evidence of physical and functional selectivity in AM. The small number of described AM fungal species (154) has been ascribed to their supposed lack of host specificity, but if the selectivity we have observed is the general rule, then we may predict that many more, probably hard-to-culture glomalean species await discovery, or that members of species as currently perceived may be physiologically or functionally distinct

Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid Crystals: 4-ϵ\epsilon Renormalization Group Calculations Revisited

Simple symmetry considerations would suggest that the transition from the smectic-A phase to the long-range bond orientationally ordered hexatic smectic-B phase should belong to the XY universality class. However, a number of experimental studies have constantly reported over the past twenty years "novel" critical behavior with non-XY critical exponents for this transition. Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982), using a $4-\epsilon$ renormalization-group calculation, that short-range molecular herringbone correlations coupled to the hexatic ordering drive this transition first order via thermal fluctuations, and that the critical behavior observed in real systems is controlled by a `nearby' tricritical point. We have revisited the model of Bruinsma and Aeppli and present here the results of our study. We have found two nontrivial strongly-coupled herringbone-hexatic fixed points apparently missed by those authors. Yet, those two new nontrivial fixed-points are unstable, and we obtain the same final conclusion as the one reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order transition. We also discuss the effect of local two-fold distortion of the bond order as a possible missing order parameter in the Hamiltonian.Comment: 1 B/W eps figure included. Submitted to Physical Review E. Contact: [email protected]

Crystallization of a classical two-dimensional electron system: Positional and orientational orders

Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and the orientational correlation functions are calculated for the first time. We have found an indication that the solid phase has a quasi-long-range (power-law) positional order along with a long-range orientational order. This indicates that, although the long-range Coulomb interaction is outside the scope of Mermin's theorem, the absence of ordinary crystalline order at finite temperatures applies to the electron system as well. The `hexatic' phase, which is predicted between the liquid and the solid phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne