Quantum phase transition in one-dimensional arrays of resistively shunted small Josephson junctions

We have observed a superconductor-insulator transition in one-dimensional (1D) arrays of small Josephson junctions by changing both the resistance R(S) of normal metal resistors shunting each junction and the ratio of the Josephson coupling energy E(J) to the charging energy E(C). The phase boundary lies at R(S) approximately R(Q) (R(Q) identical with h/4e(2)=6.45 kOmega) when E(J)/E(C) is smaller than about unity. We discuss the obtained phase diagram in terms of theoretical models of the dissipation-driven quantum phase transition, with particular attention to differences from 2D arrays.     

Gauge theories of Josephson junction arrays

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field.     

Anomalous finite-size effect in superconducting Josephson junction arrays

We show that a previously reported discrepancy between simulations of superconducting Josephson junction arrays and the theoretical analysis of Ambegaokar, Halperin, Nelson, and Siggia (AHNS) [Phys. Rev. Lett. 40, 783 (1978)] is rooted in a peculiar finite-size effect under periodic boundary conditions. Our simulation results for the largest array support the power-law I-V curves predicted by AHNS. Analysis of the vortex dynamics reveals two intrinsic length scales set by the applied current, which define three size regimes with distinctive I-V characteristics.     

Nonsinusoidal current-phase relation in SFS Josephson junctions

Various types of current-phase relation I(?) in superconductor-ferromagnet-superconductor (SFS) point contacts and planar double-barrier junctions are studied within the quasi-classical theory in the limit of thin diffusive ferromagnetic interlayers. The physical mechanisms leading to highly nontrivial I(?) dependence are identified by studying the spectral supercurrent density. These mechanisms are also responsible for the 0-π transition in SFS Josephson junctions.     

Josephson behavior in small normal one-dimensional rings

Small and strictly one-dimensional rings of normal metal, driven by an external magnetic flux, act like superconducting rings with a Josephson junction, except that 2e is replaced by e.     

Computer simulations of the anisotropic Josephson junction arrays

Using complementary methods, we numerically investigate the anisotropic Josephson junction arrays (AJJAs). For various anisotropic strengths (λ$\lambda$), the Monte Carlo simulation gives a precise measurement of specific heat, magnetization, and magnetic susceptibility; while the resistively shunted-junction dynamical simulation produces the current–voltage characteristics. The critical temperatures obtained from the two approaches are well consistent with each other. We find that, except for the anisotropic limit (λ=0)$(\lambda =0)$, the quasi-long-range order is always established at a finite temperature. Further, the algebraically decaying spin–spin correlations in the low-temperature region are analyzed in detail. Finally, the full phase diagram of the AJJAs, which sheds some lights to the crossover of the XY model from one dimension to two, is constructed. These predictions are to be confronted with future experiments.     

Magnetic properties of two-dimensional SNS-type Josephson junction arrays

JETP Letters - The field dependence of the magnetic moment of square (100×100) SNS-type Josephson junction arrays was studied by a SQUID magnetometer. A considerable difference in the behavior...     

Hall effect and geometric phases in Josephson junction arrays

Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect.     

Charging fluctuations and resistive transition in Josephson junction arrays

The density of a vortex plasma in a two-dimensional quantum planar model is calculated as a function of temperature. The results imply flux-flow resistance with tails extending down to T = 0 and allowing for the possibility of resistance minima.     

Two-point phase correlations of a one-dimensional bosonic Josephson junction

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows us to measure the coupling strength and temperature and hence a full characterization of the system.     

Reentrant behavior of the phase stiffness in Josephson junction arrays

The phase diagram of a 2D Josephson junction array with large substrate resistance, described by a quantum XY model, is studied by means of Fourier path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition is found up to a threshold value g( small star, filled ) of the quantum coupling, beyond which no phase coherence is established. Slightly below g( small star, filled ) the phase stiffness shows a reentrant behavior with temperature, in connection with a low-temperature disappearance of the superconducting phase, driven by strong nonlinear quantum fluctuations.     

Fabrication of 3D proximity coupled Josephson junction arrays

Experimentally realizable 3D arrays of Josephson junctions have been a goal of researchers since 2D Josephson junctions (JJ) arrays were first introduced. In the past, it has proven to be technically impossible to manufacture 3D proximity-coupled arrays. Recent advancements in etching technology have now made fabrication more feasible. In this paper, we present details of our fabrication process.     

Skewness in the current-phase relation of double-barrier Josephson junctions

The current-phase relations of a double-barrier Josephson junction with a thin intermediate electrode show deviations from the usual sinusoidal dependence of a single Josephson junction. The skewness of these curves can be analytically found for small values of the coupling between the two outer electrodes of the double-barrier Josephson junction.