Three-dimensional Josephson Junction Arrays Research Articles

Finite-temperature phase-locking transition in three-dimensional arrays of Josephson coupled Bose–Einstein condensates

We consider theoretically a phase-locking transition in Bose–Einstein condensate in an optical lattice in the regime where system can realized as a three-dimensional Josephson junction array. The coherence between adjacent Bose condensates (trapped in the valleys of the periodic potential) caused by the Josephson tunneling can lead to a phase transition with a global phase coherence at certain critical temperature. Using a model Hamiltonian of Josephson weakly coupled Bose condensates we calculate the critical temperature for the three-dimensional system placed in a simple cubic lattice and discuss the result in the context of system parameters and possible experiments.

Superconducting-insulating transition in quantum three-dimensional Josephson junction arrays with magnetic and charge frustration

We study the effect of the competition between Josephson and charging energies on the phase coherence transition in three-dimensional anisotropic network of Josephson-coupled junctions. in the presence of external magnetic flux and charge frustration. To capture the effects of quantum and spatial fluctuations we employ a quantum spherical approximation for the Josephson-junction array Hamiltonian. We examine the T=0 and finite temperature superconductor-insulator phase transitions as functions of a number of control parameters which include self-capitance and junction capacitance, rational magnetic flux, and the charge frustration parameter as well as the lattice anisotropy.

Charging and magnetic field effects in three-dimensional Josephson junction arrays

We study the quantum phase transition in a three-dimensional network of Josephson-coupled junctions including the charging-energy effects in the presence of external magnetic flux f= Φ/ Φ 0. To capture the effects of quantum and spatial fluctuations we go beyond the mean-field level description and derive an effective quantum non-linear σ-model for the array Hamiltonian with a spherical closure relation. Subsequently, we examine the T=0 and finite temperature superconductor-paracoherent phase boundary as a function of various control parameters.

Superconducting phase transition in quantum three-dimensional Josephson junction arrays:c-axis anisotropy and charge frustration effects

We study the quantum phase transition in three-dimensional network of Josephson-coupled junctions including anisotropy and capacitance-matrix effects. The quantum effects are due to the charging energy ${E}_{C}$ which is related to interplay of self-${(C}_{0})$ and mutual (or junction ${C}_{1})$ capacitances. The anisotropy is defined as the ratio of the in-plane Josephson energy ${E}_{J\ensuremath{\Vert}}$ to the interlayer one ${E}_{J\ensuremath{\perp}}.$ The external charge frustration effects are also considered at both zero and finite temperatures. To capture the effects of quantum and spatial fluctuations we go beyond the mean-field level description. Noting that the invariant of phase fluctuation algebra between number and phase operators (given by the Euclidean group ${E}_{2})$ is related to the closure relation of the corresponding solvable quantum spherical model we map the quantum Hamiltonian of the array onto an effective action of a generalized spherical model in the path integral formalism. Subsequently, we examine the $T=0$ and finite-temperature superconductor-paracoherent phase boundary as a function of various control parameters.

Three-dimensional Josephson-junction arrays in the quantum regime.

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. We obtain a phase diagram as a function of temperature, Josephson coupling, and charging energy. We also analyze the corresponding fluctuation conductivity and its universal scaling form in the vicinity of the zero-temperature quantum critical point.

Dynamic electromagnetic response of three-dimensional Josephson junction arrays

We present a theoretical study on the dynamical properties of three-dimensional arrays of Josephson junctions. Our results indicate that such superconducting networks represent highly sensitive three-dimensional superconducting quantum interference devices (3D SQUIDs) having some major advantages in comparison with conventional planar SQUIDs. The voltage response function of 3D SQUIDs is directly related to the vector character of external electromagnetic fields. The theory developed here allows the three-dimensional reconstruction of a detected external field including phase information about the field variables. Applications include the design of magnetometers, gradiometers, and particle detectors.

Lower threshold field in three-dimensional Josephson-junction arrays

The static magnetic response of a three-dimensional Josephson-junction array is described. The dynamical equations for flux transitions in the network are derived taking into account the magnetic energy of the circulating currents. In particular, when the external magnetic field H is applied in a direction perpendicular to the network-base, we analytically calculate the lower-threshold field H (1).

Three-dimensional Josephson-junction arrays: Static magnetic response

In this work we present a simple three-dimensional Josephson-junction array model: a cube with twelve junctions, one on each edge. The low-field magnetic response of the system is studied numerically for arbitrary directions of the applied field. In this model the magnetic energy of the circulating currents is taken into account by introducing an effective mutual inductance matrix. The lower threshold field for flux penetration is determined in a closed analytic form for field directions perpendicular to one cube side. {copyright} {ital 1998} {ital The American Physical Society}

Coherence and Complexity in Condensed Matter: Josephson Junction Arrays

The importance of the mesoscopic bridge between microscopic and mesoscopic descriptions of complex, nonlinear-nonequilibrium extended dynamical systems is illustrated in a condensed matter context through three-dimensional Josephson junction arrays. Large-scale Langevin molecular dynamics is used to study novel transformer and melting effects, emphasizing the central roles of topological excitations (flux vortex lines) in determining mesoscopic patterns and dynamics — through flux line creation, annihilation, interaction and statistical mechanics.

Phase diagram of high-Tcsuperconductors: Influence of anisotropy and disorder

We propose a phase diagram for the vortex structure of high-temperature superconductors which incorporates the effects of anisotropy and disorder. It is based on numerical simulations using the three-dimensional Josephson-junction array model. We support the results with an estimation of the internal energy and configurational entropy of the system. Our results give a unified picture of the behavior of the vortex lattice, from the very anisotropic ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ to the less anisotropic ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, and from the first-order melting ocurring in clean samples to the continuous transitions observed in samples with defects.

Ginzburg-Landau theory for three-dimensional Josephson junction arrays

We have derived a mean-field theory and a Ginzburg-Landau (GL) theory for classical three-dimensional Josephson junction arrays. We show that the full GL theory for arrays is formally equivalent to the GL theory for a bulk superconductor, demonstrating that for low fields and close to the critical temperature, the two systems are electrodynamically equivalent. We derive expressions for the penetration depth and coherence length, the effective superfluid density, critical fields, and the current-phase relationship for arrays. Using the Ginzburg criterion, we show that the critical region is very wide and that three-dimensional critical fluctuations should be experimentally accessible. Although the wide critical region casts doubt on the strict validity of the GL theory, suitable modifications of the coefficients should allow it to be used at lower temperatures, as is done for bulk superconductors.

Simulations of current driven three-dimensional Josephson junction arrays

We present Langevin simulations of anisotropic three-dimensional Josephson arrays driven by an external current. We study the superconducting phase transition at zero magnetic field, by analyzing both the helicity modulus and the voltage. We find that there is a well defined phase transition at any finite current smaller than the Josephson critical current. The critical temperature T c( I) obtained decreases linearly with current I. We also find that the onset of voltage occurs at temperatures smaller than T c( I). We discuss the consequences of this result for the interpretation of recent experiments in the flux transformer configuration.

Percolation transition of the vortex lattice and c-axis resistivity in high-temperature superconductors.

We use the three-dimensional Josephson junction array system as a model for studying the temperature dependence of the c-axis resistivity of high temperature superconductors, in the presence of an external magnetic field H applied in the c-direction. We show that the temperature at which the dissipation becomes different from zero corresponds to a percolation transition of the vortex lattice. In addition, the qualitative features of the resistivity vs. temperature curves close to the transition are obtained starting from the geometrical configurations of the vortices. The results apply to the cases H greater than 0 and H=0.

Vortex dynamics and non-Ohmic current-voltage characteristics of high- T c layered superconductors

We have calculated the non-Ohmic current-voltage characteristics of anisotropic three-dimensional Josephson-junction arrays as a model of layered high- T c oxides. Langevin dynamic simulations are performed for various Josephson-coupling anisotropies ( γ = J | c / J ⊥ c ) at finite temperature in zero and finite magnetic fields. We find that interlayer coupling gives rise to the non-vanishing critical current ( I c ), and that the low-temperature phase displays non-Ohmic power-law behavior ( V ( I − I c ) α−1 ). Moreover, in the γ-dependence of I c , we see the two-to three-dimensional crossover associated with thermally excited vortex-antivortex pairs.

Phase boundaries of three-dimensional superconducting networks in a magnetic field

We investigate the phase boundaries of three-dimensional cubic superconducting networks made of thin wires and three-dimensional Josephson junction arrays. The transition temperature is calculated numerically by solving the eigenvalue problem which is a generalization of the two-dimensional Hofstadter problem. It is shown that the transition temperature depends not only on the amplitude of the magnetic field but also on its orientation, i.e. it has cusp-like maximum when any component of the flux is an integer or a rational number with a small denominator.

Nonlinear current-voltage characteristics of three-dimensional Josephson-junction arrays with anisotropic interactions.

We perform Langevin dynamic simulations to calculate the current-voltage ([ital I]-[ital V]) characteristics for anisotropic three-dimensional arrays of resistively shunted Josephson junctions as a high-[ital T][sub [ital c]] oxide model. In zero and finite applied magentic fields, at various Josephson-coupling anisotropies ([gamma]=[ital J][sub [vert bar][vert bar][ital c]]/[ital J][sub [perpendicular][ital c]]), we see that the interlayer Josephson coupling gives rise to a nonvanishing critical current ([ital I][sub [ital c]]), and the low-temperature phase displays non-Ohmic power-law [ital I]-[ital V] characteristics [[ital V][proportional to][ital I]([ital I][minus][ital I][sub [ital c]])[sup [alpha][minus]1]]. Based on the [gamma] dependence of [ital I][sub [ital c]], we discuss the two- to three-dimensional crossover associated with thermal excitations of vortex-antivortex pairs.