Phase diagram of 2D array of mesoscopic granules

A lattice boson model is used to study ordering phenomena in regular 2D array of superconductive mesoscopic granules, Josephson junctions or pores filled with a superfluid helium. Phase diagram of the system, when quantum fluctuations of both the phase and local superfluid density are essential, is analyzed both analytically and by quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density $n_0$ is increased the boundary of ordered superconducting state shifts to {\it lower temperatures} and at $n_0 > 8$ approaches its limiting position corresponding to negligible relative fluctuations of moduli of the order parameter (as in an array of "macroscopic" granules). In the region of weak quantum fluctuations of phases mesoscopic phenomena manifest themselves up to $n_0 \sim 10$. The mean field theory and functional integral $1/n_0$ - expansion results are shown to agree with that of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY model.Comment: 7 pages, 5 Postscript figure

Quantum effects in a superconducting glass model

We study disordered Josephson junctions arrays with long-range interaction and charging effects. The model consists of two orthogonal sets of positionally disordered $N$ parallel filaments (or wires) Josephson coupled at each crossing and in the presence of a homogeneous and transverse magnetic field. The large charging energy (resulting from small self-capacitance of the ultrathin wires) introduces important quantum fluctuations of the superconducting phase within each filament. Positional disorder and magnetic field frustration induce spin-glass like ground state, characterized by not having long-range order of the phases. The stability of this phase is destroyed for sufficiently large charging energy. We have evaluated the temperature vs charging energy phase diagram by extending the methods developed in the theory of infinite-range spin glasses, in the limit of large magnetic field. The phase diagram in the different temperature regimes is evaluated by using variety of methods, to wit: semiclassical WKB and variational methods, Rayleigh-Schr\"{o}dinger perturbation theory and pseudospin effective Hamiltonians. Possible experimental consequences of these results are briefly discussed.Comment: 17 pages REVTEX. Two Postscript figures can be obtained from the authors. To appear in PR

Inertial Mass of a Vortex in Cuprate Superconductors

We present here a calculation of the inertial mass of a moving vortex in cuprate superconductors. This is a poorly known basic quantity of obvious interest in vortex dynamics. The motion of a vortex causes a dipolar density distortion and an associated electric field which is screened. The energy cost of the density distortion as well as the related screened electric field contribute to the vortex mass, which is small because of efficient screening. As a preliminary, we present a discussion and calculation of the vortex mass using a microscopically derivable phase-only action functional for the far region which shows that the contribution from the far region is negligible, and that most of it arises from the (small) core region of the vortex. A calculation based on a phenomenological Ginzburg-Landau functional is performed in the core region. Unfortunately such a calculation is unreliable, the reasons for it are discussed. A credible calculation of the vortex mass thus requires a fully microscopic, non-coarse grained theory. This is developed, and results are presented for a s-wave BCS like gap, with parameters appropriate to the cuprates. The mass, about 0.5 $m_e$ per layer, for magnetic field along the $c$ axis, arises from deformation of quasiparticle states bound in the core, and screening effects mentioned above. We discuss earlier results, possible extensions to d-wave symmetry, and observability of effects dependent on the inertial mass.Comment: 27 pages, Latex, 3 figures available on request, to appear in Physical Review

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version of the pape

Landau theory of bi-criticality in a random quantum rotor system

We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of non-zero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange interactions has non-zero mean. The solution to the saddle point equations is presented in the vicinity of the bi-critical point characterized by the intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the paramagnetic and spin glass phases. All transitions are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is non-analytic in the parameter that controls the paramagnet/ferromagnet transition in the absence of disorder. Also for M=1, we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for M=1, are {\it identical} to what is observed experimentally in the random magnetic alloy $LiHo_xY_{1-x}F_4$.Comment: 20 pages, 5 figure

First Order Transition in the Ginzburg-Landau Model

The d-dimensional complex Ginzburg-Landau (GL) model is solved according to a variational method by separating phase and amplitude. The GL transition becomes first order for high superfluid density because of effects of phase fluctuations. We discuss its origin with various arguments showing that, in particular for d = 3, the validity of our approach lies precisely in the first order domain.Comment: 4 pages including 2 figure

Well-Tempered Metadynamics Simulations Predict the Structural and Dynamic Properties of a Chiral 24-Atom Macrocycle in Solution

Inspired by therapeutic potential, the molecular engineering of macrocycles is garnering increased interest. Exercising control with design, however, is challenging due to the dynamic behavior that these molecules must demonstrate in order to be bioactive. Herein, the value of metadynamics simulations is demonstrated: the free-energy surfaces calculated reveal folded and flattened accessible conformations of a 24-atom macrocycle separated by barriers of c.a. 6 kT under experimentally relevant conditions. Simulations reveal that the dominant conformer is folded-an observation consistent with a solid-state structure determined by X-ray crystallography and a network of rOes established by 1H NMR. Simulations suggest that the macrocycle exists as a rapidly interconverting pair of enantiomeric, folded structures. Experimentally, 1H NMR shows a single species at room temperature. However, at lower temperature, the interconversion rate between these enantiomers becomes markedly slower, resulting in the decoalescence of enantiotopic methylene protons into diastereotopic, distinguishable resonances due to the persistence of conformational chirality. The emergence of conformational chirality provides critical experimental support for the simulations, revealing the dynamic nature of the scaffold-a trait deemed critical for oral bioactivity

Mean Field Theory of Josephson Junction Arrays with Charge Frustration

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit of the path integral approach is that it allows to provide an elegant derivation of the Ginzburg-Landau free energy for a general model with charge frustration and non-diagonal capacitance matrix. The partition function factorizes as a product of a topological term, depending only on a set of integers, and a non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure

Dendritic Surfactants Show Evidence for Frustrated Intercalation: A New Organoclay Morphology

Mixing a smectite clay with some dendritic surfactants shows that despite the large size of some of these molecules, a property that frustrates complete intercalation into the gallery of the clay, organoclay materials are obtained. X-ray powder diffraction (XPD) reveals no significant increases in lattice spacing as these surfactants are added. Infrared (IR) spectroscopy and thermal gravimetric analysis (TGA) show that interlayer water is preserved. Consistent with an undisturbed interlayer, the amount of organic material in organoclays derived from frustrated surfactants does not exceed 15% of the cationic exchange capacity (CEC) of the composite. Smaller dendritic surfactants do not display frustrated intercalation and instead readily enter into the gallery of the smectic clay yielding traditional organoclay materials. A range of organic compositions (5-50% w/w) that exceed the CEC of the materials are observed. The organic content is corroborated by UV spectroscopy and TGA. XPD reveals increasing lattice spacings with increasing organic content. IR spectroscopy and TGA support an increasingly hydrophobic interlayer. A linear isomer of a frustrated surfactant can intercalate into the gallery (5-33% w/w) yielding morphologies that depend on the amount of surfactant added. These results support the hypothesis that shape, and not only size, is important for producing frustrated intercalation

The mechanism of hole carrier generation and the nature of pseudogap- and 60K-phases in YBCO

In the framework of the model assuming the formation of NUC on the pairs of Cu ions in CuO$_{2}$ plane the mechanism of hole carrier generation is considered and the interpretation of pseudogap and 60 K-phases in $YBa_{2}Cu_{3}O_{6+\delta}$. is offered. The calculated dependences of hole concentration in $YBa_{2}Cu_{3}O_{6+\delta}$ on doping $\delta$ and temperature are found to be in a perfect quantitative agreement with experimental data. As follows from the model the pseudogap has superconducting nature and arises at temperature $T^{*}>T_{c\infty}>T_{c}$ in small clusters uniting a number of NUC's due to large fluctuations of NUC occupation. Here $T_{c\infty}$ and $T_{c}$ are the superconducting transition temperatures of infinite and finite clusters of NUC's, correspondingly. The calculated $T^{*}(\delta)$ and $T_{n}(\delta)$ dependences are in accordance with experiment. The area between $T^{*}(\delta)$ and $T_{n}(\delta)$ corresponds to the area of fluctuations where small clusters fluctuate between superconducting and normal states owing to fluctuations of NUC occupation. The results may serve as important arguments in favor of the proposed model of HTSC.Comment: 12 pages, 7 figure