Josephson Junction Array Model Research Articles

Phase coherence in out-of-equilibrium supersolid states of ultracold dipolar atoms

A supersolid is a counterintuitive phase of matter that combines the global phase coherence of a superfluid with a crystal-like self-modulation in space. Recently, such states have been experimentally realized using dipolar quantum gases. Here we investigate the response of a dipolar supersolid to an interaction quench that shatters the global phase coherence. We identify a parameter regime in which this out-of-equilibrium state rephases, indicating superfluid flow across the sample as well as an efficient dissipation mechanism. We find a crossover to a regime where the tendency to rephase gradually decreases until the system relaxes into an incoherent droplet array. Although a dipolar supersolid is, by its nature, ‘soft’, we capture the essential behaviour of the de- and rephasing process within a rigid Josephson junction array model. Yet, both experiment and simulation indicate that the interaction quench causes substantial collective mode excitations that connect to phonons in solids and affect the phase dynamics. A supersolid is a phase of matter featuring both crystalline order as a solid and global phase coherence as a superfluid. Now an experiment shows how this global phase coherence can be established across the system in a non-equilibrium process.

Local spectroscopies across the superconductor-insulator transition

We explore the manifestation of quantum fluctuations across the superconductor-insulator transition (SIT) in three different local measurements: the two-particle density of states $P(\mathbf{r},\omega)$, compressibility $\kappa(\mathbf{r})$, and diamagnetic susceptibility $\chi(\mathbf{r})$. We perform Monte Carlo simulations on the 2D quantum Josephson junction array model and present local maps of these quantities as the system is tuned across the SIT. $P(\mathbf{r},\omega)$, obtained using Maximum Entropy analytic continuation techniques, shows strongly diminished zero-energy spectral weight in nearly-insulating islands, that also correlate with regions of suppressed $\kappa(\mathbf{r})$. We investigate the signatures of quantum fluctuations in the evolution of $\kappa(\mathbf{r})$ and $\chi(\mathbf{r})$ across the SIT, distinct from thermal fluctuations. We discuss the experimental implications of our results for scanning Josephson spectroscopy, compressibility, and scanning SQUID measurements.

Critical behavior of dynamic vortex Mott transition in superconducting arrays at fractional vortex densities

We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to $f$ flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of $f$. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near $f=1/2$ are consistent with the experimental observations. The same scaling behavior is observed near $f=1/3$. For a honeycomb array, although similar results are obtained for $f=1/3$, the transition is absent for $f=1/2$, consistent with an incommensurate vortex phase.

Magnetic flux disorder and superconductor-insulator transition in nanohole thin films

We study the superconductor-insulator transition in nanohole ultrathin films in a transverse magnetic field by numerical simulation of a Josephson-junction array model. Geometrical disorder due to the random location of nanoholes in the film corresponds to random flux in the array model. Monte Carlo simulation in the path-integral representation is used to determine the critical behavior and the universal resistivity at the transition as a function of disorder and average number of flux quanta per cell, $f_o$. The resistivity increases with disorder for noninteger $ f_o$ while it decreases for integer $ f_o$, and reaches a common constant value in a vortex-glass regime above a critical value of the flux disorder $D_f^c$. The estimate of $D_f^c$ and the resistivity increase for noninteger $ f_o$ are consistent with recent experiments on ultrathin superconducting films with positional disordered nanoholes.

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

We study the superconductor to insulator transition at zero temperature in a Josephson-junction array model on a honeycomb lattice with $f$ flux quantum per plaquette. The path integral representation of the model corresponds to a (2+1)-dimensional classical model, which is used to investigate the critical behavior by extensive Monte Carlo simulations on large system sizes. In contrast to the model on a square lattice, the transition is found to be first order for $f=1/3$ and continuous for $f=1/2$ but in a different universality class. The correlation-length critical exponent is estimated from finite-size scaling of vortex correlations. The estimated universal conductivity at the transition is approximately four times its value for $f=0$. The results are compared with experimental observations on ultrathin superconducting films with a triangular lattice of nanoholes in a transverse magnetic field.

Monte Carlo study of pseudo-gap temperature [formula omitted] within JJA model

We study pseudo-gap temperature T∗ of high-Tc superconductors by a Monte Carlo simulation of anisotropic 3D Josephson junction array (JJA) model based on the Ginzburg–Landau theory. We investigate T∗ both in the cases of zero external current and finite external current I in the JJA. It is found that, the external current I depresses only a little the pseudo-gap temperature T∗, while the superconducting critical temperature Tc is much affected by I.

Andreev reflection off a fluctuating superconductor in the absence of equilibrium

Andreev reflection between a normal metal and a superconductor whose order parameter exhibits quantum phase fluctuations is examined. The approach chosen is nonperturbative in the tunneling Hamiltonian and enables us to probe the whole range of voltage biases up to the gap amplitude. Results are illustrated using the one-dimensional Josephson junction array model previously introduced in the linear response regime. Phase fluctuations are shown to affect the differential conductance and are compared to the result of Blonder, Tinkham, and Klapwijk for a rigid BCS superconductor. The noise spectrum of the Andreev current is also obtained and its second derivative with respect to frequency is proposed as a direct tool to analyze the phase fluctuations.

Superfluid-insulator transition of the Josephson-junction array model with commensurate frustration

We have studied the rationally frustrated Josephson-junction array model in the square lattice through Monte Carlo simulations of $(2+1)$D XY-model. For frustration $f=1/4$, the model at zero temperature shows a continuous superfluid-insulator transition. From the measurement of the correlation function and the superfluid stiffness, we obtain the dynamical critical exponent $z=1.0$ and the correlation length critical exponent $\nu=0.4 \pm 0.05$. While the dynamical critical exponent is the same as that for cases $f=0$, 1/2, and 1/3, the correlation length critical exponent is surprisingly quite different. When $f=1/5$, we have the nature of a first-order transition.

Critical Temperature Tc and Charging Energy Ec between B–B Layers of Superconducting Diboride Materials MgB2 in 3D JJA Model

The diboride materials MB2 (M = Mg, Be, Pb, etc.) are discussed on the basis of the 3D Josephson junction array (JJA) model due to Kawabata-Shenoy-Bishop, in terms of the B-B layers in the diborides analogous to the Cu-O ones in the cuprates. We propose a possibility of superconducting materials with the MgB2-type structure which exhibit higher critical temperature Tc over 39K of MgB2. We point out a role of interstitial ionic atoms (e.g., Mg in MgB2) as capacitors between the B-B layers, which reduce the charging coupling energy in JJA.

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}

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.

Induced vortex dynamics in parallel Josephson junction arrays

As an attempt to understand many unusual characteristics of Josephson junctions between high-${\mathrm{T}}_{\mathrm{c}}$ Cu-oxide superconductors, we employed a parallel Josephson junction array model to study dynamical properties of the high-${\mathrm{T}}_{\mathrm{c}}$ superconducting single grain-boundary Josephson junction, where the relative scale of Josephson penetration depth ${\ensuremath{\lambda}}_{\mathrm{J}}$ is expected to play a crucial role in determination of its dynamics. Results of our numerical studies on the parallel Josephson junction arrays are presented for various values of Ginzburg-Landau parameters ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$=${\ensuremath{\lambda}}_{\mathrm{J}}$/a, where a represents the array spacing. For the calculations, we take into account the full long-range inductions between vortices and the effects of induced magnetic fields by external currents in the array. From the results, it is found that subharmonic Shapiro steps emerge even under the zero external magnetic field for ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\sim}1, while subharmonic Shapiro steps are suppressed in the limits of either ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\rightarrow}0 or ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\rightarrow}\ensuremath{\infty}. We conclude that, for the intermediate case of ${\mathrm{\ensuremath{\kappa}}}_{\mathrm{J}}$\ensuremath{\sim}1, the edge magnetic fields induced by external currents may be responsible for the existence of subharmonic Shapiro steps with no external magnetic field present.

Vortex structure and resistive transitions in high-Tc superconductors.

The nature of the resistive transition for a current applied parallel to the magnetic field in high-Tc materials is investigated by numerical simulation on the three dimensional Josephson junction array model. It is shown by using finite size scaling that for samples with disorder the critical temperature Tp for the c axis resistivity corresponds to a percolation phase transition of vortex lines perpendicularly to the applied field. The value of Tp is higher than the critical temperature for j perpendicular to H, but decreases with the thickness of the sample and with anisotropy. We predict that critical behavior around Tp should reflect in experimentally accessible quantities, as the I-V curves.

An inhomogeneous Josephson junction array model in HTSC granular bridges

Experimental and theoretical studies are reported of the electrodynamic behaviours, such as current - voltage characteristics (IVCs), microwave self-radiations and dynamic resistances, dV/dI, of granular high- superconducting (HTSC) (YBCO) and (BSCCO) film bridges. We show that the granular structure of bridges can be understood as series-connected independent and inhomogeneous resistively shunted junction (RSJ) arrays.

Single-electron tunneling and phase transitions in granular films

An overview is given on recent experiments on the transitions between insulating, resistive and superconducting phases in systems consisting of small tunnel junction lattices fabricated by electron beam lithography. Possible interpretations based on the Josephson junction array model are presented.

Low-field diamagnetic response of hollow cylindrical samples of sintered high-T c superconductors

Magnetization curves of hollow cylindrical samples of sintered high-Tc superconductors are derived both numerically, by means of a Josephson junction array model, and analytically, by a critical-state model. In both cases the field dependence of the critical current density Jc is assumed to have the following analytic form: Jc(h,T)=Jc0(T) H02(T)/[H0(T)2+h2]. The two descriptions are seen to be qualitatively equivalent.

Flux creep in Josephson junction arrays

In order to analyze the diamagnetic properties of weakly coupled structures in high-T/sub c/ ceramic superconductors , the Josephson junction array model is used. It is suggested that the coupling is strong enough to allow magnetic flux trapping inside nonsuperconducting regions surrounded by superconducting loops closed by Josephson junctions. It is noted that the presence of currents flowing through the junctions has to be taken explicitly into account in the Hamiltonian. This description leads to a creep model of the Josephson junctions array. As a result, one observes the following: (1) pinning centers generated by nonsuperconducting regions into the loops, (2) pinning potentials determined by fluxon motion barriers due to the Josephson junctions, (3) absence of degeneracy of the states corresponding to a different number of fluxons in the loops, and (4) a reduction of the barrier height due to measuring currents or to diamagnetic shielding currents. The last effect is equivalent to the Lorentz force effect in type-II semiconductors. Thus, it is believed that this picture greatly modifies the usual superconducting glass model.