Arrays Of Ultrasmall Josephson Junctions Research Articles

Charge Glass in Two-Dimensional Arrays of Capacitively Coupled Grains with Random Offset Charges

We study the effect of random offset charges in the insulator to conductor transition in systems of capacitively coupled grains, as realized in two-dimensional arrays of ultrasmall Josephson junctions. In presence of disorder, the conductive transition and charge ordering at nonzero gate voltages are both destroyed for any degree of disorder $\sigma$ at finite temperatures $T$, in the thermodynamic limit, but crossover effects will dominate at length scales smaller than $\xi_{\sigma, T}=T^{-\nu} f(\sigma T^{-\nu})$, where $\nu $ is the thermal critical exponent of the zero-temperature charge glass transition. The conductance is linear and thermally activated but nonlinear behavior sets in at a crossover voltage which decreases as temperature decreases. For large disorder, the results are supported by Monte Carlo dynamics simulations of a Coulomb gas with offset charges and are consistent with the thermally activated behavior found in recent experiments.

Duality in Two Capacitively Coupled Layered Arrays of Ultrasmall Josephson Junctions

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on their physical parameter values. The former case is dominated by a Cooper-pair superfluid while the quantum one is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and Mean Field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one in the quantum fluctuations dominated regimes, we derive a duality transformation between the charged and vortex dominated arrays that involve a gauge vector field, which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.

Quantum phase diagrams in periodic and glassy arrays of ultra-small Josephson junctions

Recent advances in submicrometer technology have made it possible to fabricate relatively large arrays of ultra-small Josephson junctions. The areas of these junctions can vary from a few microns to submicron sizes. Under these circumstances the long-range phase coherent properties of the Josephson junction arrays crucially depend on the interplay between the Josephson and charging energies. In this paper we will present a brief review of some of our recent results on the relevance of ultra-small capacitances in periodic and disordered arrays as well as the evidence for or against a low-temperature quantum0fluctuation-induced phase transition (QUIT), both for zero and full frustration. We also discuss results from a study of a quantum superconducting glass model, obtained from using different approximate analytic techniques. We mention a direct comparison between our results and those obtained in periodic arrays.

Superconducting to normal state phase boundary in arrays of ultrasmall Josephson junctions

We study the competition between Josephson and charging energies in two-dimensional arrays of ultrasmall Josephson junctions, when the mutual capacitance is dominant over the self-capacitance. Our calculations involve a combination of an analytic WKB renormalization group approach plus nonperturbative Quantum Monte Carlo simulations. We consider the zero frustration case in detail and we are able to make a successful comparison between our results and those obtained experimentally.

Measurements of charge soliton motion in two-dimensional arrays of ultrasmall Josephson junctions.

We have measured two-dimensional arrays of Josephson junctions where the charging energy ${\mathit{E}}_{\mathit{c}}$ dominates the Josephson coupling energy ${\mathit{E}}_{\mathit{J}}$ by as much as a factor of 33. In this system, an added charge polarizes neighboring islands, creating a soliton. Instead of the predicted Kosterlitz-Thouless-Berezinskii phase transition for unbinding soliton-antisoliton pairs, we find that our linear conductance data are better described by a simple Arrhenius form, with an activation energy of \ensuremath{\sim}0.23${\mathit{E}}_{\mathit{c}}$ in the normal state and \ensuremath{\sim}0.23${\mathit{E}}_{\mathit{c}}$ plus the superconducting energy gap in the superconducting state.

Quantum fluctuations in the two-dimensional XY model: Variational approach.

Due to the small self-capacitance of individual junctions, two-dimensional arrays of ultrasmall Josephson junctions are sensitive to charging effects. Identifying the charging energy term with the kinetic part of a quantum Hamiltonian for a two-dimensional XY spin system, we study the effects of quantum fluctuations on the equilibrium thermodynamics of such a system. The study is based on a self-consistent evaluation of the free energy of the system, with both effective couplings K and angular thermal averages 〈\ensuremath{\theta}〉 as variational parameters. In the weakly fluctuating regime (high values of K), we use the self-consistent harmonic approximation for an array of coupled quantum harmonic oscillators. In the strong fluctuating regime (small values of K), the coupling term is treated as a perturbation of the free-planar-rotator system. The calculation is then performed to second order in the coupling constant K. When plotted versus K, this free energy shows a double-well structure that evolves with the temperature as well as the capacitance, leading to a first-order phase transition at low temperatures. Sensitivity to charging effects is found to be considerably enhanced in fully frustrated systems (i.e., when the array is placed in a transverse magnetic field with half a flux quantum per plaquette). Furthermore, in the fully frustrated case we found an unusual coherent phase at very low temperatures. Our results are in good qualitative agreement with those obtained by Jacobs et al. with quantum Monte Carlo simulations.

Experimental investigation of two-dimensional arrays of ultrasmall Josephson junctions

We have measured Current-Voltage (I-V) characteristics of a large number of two-dimensional arrays of small area Al-AlOx-Al junctions down to temperatures of 40 mK, recording the temperature dependence of the zero bias resistance R0(T). The normal state resistance of the junctions RN varies from 2 kΩ to 270 kΩ and the junction capacitance C from 0.2f F to 2.2f F. The arrays are classified into different types according to the EJ/Ec and the RQ/RN ratios, and mapped onto a parameter diagram. EJ is the Josephson coupling energy, Ec = e2/2C is the charging energy, and RQ = h/4e2 = 6.5 kΩ is the quantum resistance. For low resistance arrays, RQ/RN >> 1 with EJ/Ec > 1, the Josephson current prevails and the arrays are superconducting. When RQ/RN << 1 and EJ/Ec < 1, the I-V characteristics show typical Coulomb blockade features. In an intermediate region where RQ/RN similar 0.4, EJ/Ec similar 0.2, we find a "back-bending" I-V curve with negative differential resistance. The behavior of R0(T) also falls into three categories which can be correlated with the type of I-V characteristic. At the lowest temperature the arrays appear to be either insulating (dR0/dT < 0) or superconducting (dR0/dT > 0) depending on whether RN is greater than RQ or less than RQ respectively.

Charge-fluctuation effect on the critical temperature of layered high-Tcsuperconductors

The value of the superconducting critical temperature (${\mathit{T}}_{\mathit{c}}$) of artificially layered superconductors made out of alternating Y-Ba-Cu-O and Pr-Ba-Cu-O layers is calculated as a function of both the number of layers of pure Y-Ba-Cu-O within a unit cell of the superlattice and the thickness of the insulating (Pr-Ba-Cu-O) layer. The calculation is performed within a model of electrostatically coupled two-dimensional (2D) arrays of ultrasmall Josephson junctions. The underlying mechanism is assumed to be the depression of the Beresinskii-Kosterlitz-Thouless transition temperature (${\mathit{T}}_{\mathrm{BKT}}$) by quantum phase fluctuations due to charging effects. The ${\mathit{T}}_{\mathit{c}}$ value of the entire structure can then be tuned by varying the charging energy that depends on the average neighborhood of a typical site in Cu-O planes of Y-Ba-Cu-O layers. Recent experiments on such structures are described very accurately by the model. Furthermore, the ratio (${\mathit{T}}_{\mathit{c}}^{(\mathit{n})}$-${\mathit{T}}_{\mathit{c}}^{(1)}$)/(${\mathit{T}}_{\mathit{c}}^{(2)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$), where ${\mathit{T}}_{\mathit{c}}^{(\mathit{n})}$ is the critical temperature of a thin film made up of n Y-Ba-Cu-O unit cells, is found to be independent of the fitting parameters. This prediction is well confirmed by available experimental data. Furthermore, the model also applies for the series of Bi- and Tl-based cuprates of general formulas ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{y}}$ and ${\mathrm{Tl}}_{2}$ (1)${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{\mathit{n}\mathrm{\ensuremath{-}}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{y}}$ containing n Cu-O planes per unit cell, for which the observed values of the ratio \ensuremath{\rho}=(${\mathit{T}}_{\mathit{c}}^{(3)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$)/(${\mathit{T}}_{\mathit{c}}^{(2)}$-${\mathit{T}}_{\mathit{c}}^{(1)}$) agree within 10% with the predicted ones.

Influence on the electrical characteristics of the—NH radicals incorporated into PECVD silicon nitride films : O. Sanchez, C. Gomez-Aleixandre, M. Fernandez and J. M. Albella. Vacuum39(7/8), 727 (1989)

We study the competition between Josephson and charging energies in two-dimensional arrays of ultrasmall Josephson junctions, when the mutual capacitance is dominant over the self-capacitance. Our calculations involve a combination of an analytic WKB renormalization group approach plus nonperturbative Quantum Monte Carlo simulations. We consider the zero frustration case in detail and we are able to make a successful comparison between our results and those obtained experimentally.

New coherent states in periodic arrays of ultrasmall Josephson junctions.

An extensive study of the thermodynamics of a two-dimensional periodic array of ultrasmall Josephson junctions with and without a transverse magnetic field is presented. A quantum Monte Carlo algorithm is introduced to study a model that includes the Josephson energy, ${E}_{J}$, as well as the charging energy, ${E}_{c}$, contributions. The superfluid density, internal energy, and specific heat for different lattice sizes and numbers of Monte Carlo simulation sweeps are studied as a function of the ratio \ensuremath{\alpha}=${E}_{c}$/${E}_{J}$, the temperature and the magnitude of the magnetic field. When \ensuremath{\alpha}\ensuremath{\ne}0, it is found that as the temperature is lowered the model has two phase transitions. First, a second-order Berezinskii-Kosterlitz-Thouless (BKT) transition renormalized by the quantum fluctuations represented by a finite \ensuremath{\alpha}. Below this BKT transition the system has long-range phase coherence; thus it is a state with zero resistance. At lower temperatures, a first-order phase transition appears which is entirely due to the quantum fluctuations that nucleate vortex excitations. Below this ``quantum induced transition'' (QUIT) the model still has a finite but diminished superfluid density, thus indicating that the QUIT is between two different zero-resistance states, one dominated by thermal fluctuations and the other by quantum fluctuations. A QUIT is found to be more pronounced in the case where there is a magnetic field. The case studied here corresponds in the classical limit to the fully frustrated state. Finally, we discuss the physical properties of this new low-temperature phase as well as the necessary conditions to test this prediction experimentally.