Two mechanisms of Josephson phase shift generation by an Abrikosov vortex

Abstract

Abrikosov vortex contains magnetic field and circulating currents that decay at a short range λ ∼ 100 nm. However, the vortex can induce a long range Josephson phase shift at distances r ∼ µm λ. The mechanism of this puzzling phenomenon is not clearly understood. Here we present a systematic study of vortex-induced phase shift in planar Josephson junctions. We make two key observations: (i) The cutoff effect: although vortexinduce phase shift is a long-range phenomenon, it is terminated by the junction and does not persists beyond it. (ii) A crossover from linear to superlinear dependence of the phase shift on the vortex polar angle occurs upon approaching of the vortex to the junction. The crossover occurs at a distance comparable with the penetration depth. This, together with theoretical and numerical analysis of the problem, allows unambiguous identification of two distinct and independent mechanisms. The short range mechanism is due to circulating vortex currents inside superconducting electrodes without involvement of magnetic field. The long range mechanism is due to stray magnetic fields outside electrodes without circulating vortex currents. We argue that understanding of controlling parameters of vortex-induced Josephson phase shift can be used for development of compact and fast electronic devices with low dissipation power.

Josephson junctions in a local inhomogeneous magnetic field

“…Note that the sign of the stray field is opposite to that in the vortex, leading to the minus sign in Eq. (15) [25]. [28] that spatial resolution of a scanning probe sensor based on a single planar junction is potentially not limited by its size.…”

“…However, in many experimental situations JJ's are subjected to a local, strongly inhomogeneous magnetic field. For example, it can originate from a self-induced flux in JJ's with a sign-reversal order parameter [7][8][9]; appear in JJ's containing ferromagnetic interlayers with spatially inhomogeneous thicknesses [10][11][12][13], nanoparticles or domain walls [14][15][16][17][18][19]; in JJ's with a local current injection [20,21]; can be induced by a nearby Abrikosov vortex [22][23][24][25], by a sharp tip of a Magnetic Force Microscope (MFM) [26,27], etc. Although such a situation has been considered previously, often this has been done without proper substantiation.…”

Reconfigurable Josephson Phase Shifter

“…They create two mechanisms of JPS generation. 44 The vortex-induced JPS, φ v , depends on the distance to the junction, z v , and the position, x v , along the junction. As shown in ref ( 44 ), it is well described by a steplike function: …”

“…The blue line shows the case without the vortex. (c) Measured JPS from a single vortex as a function of vortex polar angle (data from ref ( 44 )). (d) SEM image of a device with one planar junction and a single vortex trap at z v ≃ 0.1 L .…”

“… 14 , 15 Recently it was shown that an Abrikosov vortex can induce a JPS in nearby JJs in the full [−2π, + 2π] range. 23 , 43 , 44 Since vortices can be easily manipulated (displaced, introduced, or removed) by magnetic field, H , 23 , 45 − 47 current, I , 20 , 48 , 49 and light, 50 , 51 they can be used for creation of memory cells 20 and tunable phase shifters.…”