Static properties of classical Josephson junction arrays: models and experimental achievements

Abstract

This review deals with the static properties of classical Josephson arrays. We first comment on the model describing the system, both in the phase representation - the frustrated XY model - and in the vortex representation - the Coulomb gas model. Self-induced magnetic fields and disorder are added so as to faithfully reproduce physical systems. A review of scaling theory concerning the I-V curve - which provides relevant information about, for example, the proximity of a phase transition - is given in order to compare theoretical predictions with experimental results. Josephson arrays are characterized by an extremely rich phase diagram as a function of both external parameters (temperature, applied magnetic field) and inherent ones (disorder, self-inductance). Such a diagram is explored in the light of recent results. Questions such as those of the nature of the ground state and the stability of the static states, and the existence of a disordered vortex state due to disorder intrinsic to the array and/or to external influences arise.

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

“…That is, suppose that the bosons are in the superconducting state (this is a subtle issue in one dimension), the magnetic flux would possibly be quantized so as to form rigid vortex-lattice order along the ladder. This order is confirmed to develop in the preceding semi-classical analysis [18]. That is, the chiral order of our model has two-unit-cell periodicity.…”

“…Therefore, vortex-antivortex alignment gets favored. The semi-classical version S → ∞ of the model (4) has been studied extensively [14,15,16,17,18]: In the limit, spins are represented by rotators, and through pathintegral mapping, the system reduces to a two-dimensional classical rotator model. According to numerical-simulation studies [14,15,17], that rotator model appears to be in the KT critical phase.…”

Microwave photonics with Josephson junction arrays: Negative refraction index and entanglement through disorder

“…[38][39][40][41][42][43][44][45] In particular, we know that JJAs constitute a physical realization or the classical frustrated XY model, where frustration is similarly induced by the fluxes threaded through the 2D plaquettes.…”

“…Where ϕ ij are the phase differences along each branch and Φ ext + Φ ind is the sum of external and induced fluxes enclosed by C. The presence of these fluxes may forbid an equilibrium condition with all phases equal to zero. The physics of our two-dimensional crystals is intimately related to that of 2D Josephson junction arrays (JJAs), a system whose equilibrium and non-equilibrium properties have been thoroughly studied in the last twenty years [38][39][40][41][42][43][44][45] . In particular, we know that JJAs constitute a physical realizations or the classical frustrated XY model, where frustration is similarly induced by the fluxes threaded through the 2D plaquettes.…”