Josephson junctions in a local inhomogeneous magnetic field

Abstract

A Josephson junction can be subjected to a local, strongly inhomogeneous magnetic field in various experimental situations. Here this problem is analyzed analytically and numerically. A modified sine-Gordon type equation in the presence of time-dependent local field is derived and solved numerically in static and dynamic cases. Two specific examples of local fields are considered: induced either by an Abrikosov vortex, or by a tip of a magnetic force microscope (MFM). It is demonstrated that time-dependent local field can induce a dynamic flux-flow state in the junction with shuttling, or unidirectional ratchet-like Josephson vortex motion. This provides a mechanism of detection and manipulation of Josephson vortices by an oscillating MFM tip. In a static case local field leads to a distortion of the critical current versus magnetic field, $I_c(H)$, modulation pattern. The distortion is sensitive to both the shape and the amplitude of the local field. Therefore, the $I_c(H)$ pattern carries information about the local field distribution within the junction. This opens a possibility for employing a single Josephson junction as a scanning probe sensor with spatial resolution not limited by its geometrical size, thus obviating a known problem of a trade-off between field sensitivity and spatial resolution of a sensor.

arXiv comment8 pages, 5 Figures

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• Supratransmission-induced travelling breathers in long Josephson junctions
• Word and bit line operation of a 1x1 μm2 superconducting vortex-based memory
• Accurate determination of the Josephson critical current by lock-in measurements
• Theory of scanning gate microscopy imaging of the supercurrent distribution in a planar Josephson junction
• Unconventional superconducting diode effects via antisymmetry and antisymmetry breaking
• A distributed, active patch antenna model of a Josephson oscillator
• Holographic reconstruction of magnetic field distribution in a Josephson junction from diffraction-like Ic(H) patterns
• Reduced decay in Josephson coupling across ferromagnetic junctions with spin-orbit coupling layers
• Long-time soliton dynamics via a coarse-grained space-time method
• Revealing Josephson vortex dynamics in proximity junctions below critical current
• Universal route towards field-free electrically polarity-reversible Josephson diode