Effect of Geometry on Fluxon Width in a Josephson Junction

Abstract

We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.

Exponentially tapered Josephson flux-flow oscillator

“…This is consistent with the fact that no static multifluxon solutions exist for decreasing width junctions, because as soon as a fluxon is created it tends to move in the direction of decreasing junction width in order to minimize its field energy. 12 The bias current b is applied on the left-hand end of the junction and we assume that the right-hand end is connected to a passive load of impedance z, which will absorb the fluxon chain. Then the boundary conditions at xϭ0 and xϭl are…”

Josephson flux-flow oscillator: The microscopic tunneling approach

“…A possible explanation could be the influence of the idle region [110][111][112][113][114][115][116][117][118] which may have a stabilizing effect on the dynamics of FFO and, presumably, affect the values of MFFCs. Influence of the idle region on the dynamics of FFO has been neglected in our theoretical treatment (except for the renormalization of Josephson penetration length on which it has an effect [115,116]). The proper account of the idle region requires upgrading the model (21) to the full 2D problem (15) coupled to the Maxwell equations inside the idle region.…”

Analysis of a Semilinear PDE for Modeling Static Solutions of Josephson Junctions

“…Although we are unable to prove their existence, such solutions have been observed in practice, and their physical justification is well established in the case where no extra fluxons have entered the interior of the window [4,5]. For this type of solution we are able to obtain the following estimations of its size.…”

“…Therefore, although these estimates seem to be very generous for the PDE problems considered in Table 7.1, they are sharp for large windows. Nevertheless, since many important physical properties of Josephson junctions depend on the size and the geometry of the window [4,5] new a priori estimates which sense the geometrical parameters of the window would be of importance.…”

“…In [4] we proposed a semilinear PDE problem which accurately and effectively modeled the static behavior of a window Josephson junction. This model enabled us to predict specific effects depending on the size of the cavity, such as the rescaling of λ j and the increase of the maximum current for zero magnetic field [5].…”