Fluxon Dynamics in Elliptic Annular Josephson Junctions

Abstract

We analyze the dynamics of a magnetic flux quantum (current vortex) trapped in a current-biased long planar elliptic annular Josephson tunnel junction. The system is modeled by a perturbed sine-Gordon equation that determines the spatial and temporal behavior of the phase difference across the tunnel barrier separating the two superconducting electrodes. In the absence of an external magnetic field the fluxon dynamics in an elliptic annulus does not differ from that of a circular annulus where the stationary fluxon speed merely is determined by the system losses. The interaction between the vortex magnetic moment and a spatially homogeneous inplane magnetic field gives rise to a tunable periodic non-sinusoidal potential which is strongly dependent on the annulus aspect ratio. We study the escape of the vortex from a well in the tilted potential when the bias current exceeds the depinning current. The smallest depinning current as well as the lowest sensitivity of the annulus to the external field is achieved when the eccentricity is equal to −1. The presented extensive numerical results are in good agreement with the findings of the perturbative approach. We also probe the rectifying properties of an asymmetric potential implemented with an egg-shaped annulus formed by two semi-elliptic arcs.

Confocal Annular Josephson Tunnel Junctions

“…The dashed line depicts the quasi-particle current γ/ α. The ZFS profile results to be quite different from the perturbative model expectation γ(û) = 4α/π √û −2 − 1 (solid line) appropriate to constant width long JTJs [2,25]. The main discrepancy is the appearance of a zero-voltage (zero velocity) current range; the hysteresis stems from the already mentioned width-dependent fluxon potential and is characterized by a trapping current, i.e., the minimum current at which a fluxon still moves along the system, not being trapped by the potential and a depinning current, i.e., the maximum current at which the fluxon is pinned in the potential well.…”

“…The static [1] and dynamic [2] properties were recently studied for Elliptic Annular Josephson Tunnel Junctions (EAJTJs) in the presence of a uniform in-plane magnetic field.…”

Development of a Josephson vortex two-state system based on a confocal annular Josephson junction

“…The dashed right pointing arrow at γ = 0.19 indicates the depinning current already discussed in the previous paragraph, while the dotted left pointing arrow γ = 0.08 denotes the re-trapping current, i.e., the minimum current at which the fluxon still moves along the system, not being trapped by the potential. The γ −ū plot is quite smooth and only moderately departs from the perturbative model expectation γ(ū) = 4α/π √ū −2 − 1 (solid line) valid for fluxon traveling in a flat potential and in the absence of collisions 39,44 , that is, for ρ = 1. The main discrepancy is observed for low bias currents, where the step profile is not smooth but shows some, not well resolved, fine structures 49 due to the resonance of the traveling fluxon with wavelets radiated by the fluxon itself subject to periodic accelerations and decelerations.…”

“…The MDPs of electrically small ( << 1) and intermediate-length ( = 4π) CAJTJs with ρ = 0.5 have been reported in, respectively, Ref. 44 and Ref. 22 .…”

Engineering double-well potentials with variable-width annular Josephson tunnel junctions

“…Very recently, the static and dynamic properties were investigated for constant 32,33 and variable 34 width elliptic annular JTLs in the presence of an in-plane magnetic field of arbitrary orientations. In both cases, the fluxon motion is characterized by a strong radial inward acceleration where the curvature radius is smallest.…”