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 a time-dependent local field can induce a dynamic flux-flow state in the junction with shuttling or unidirectional ratchetlike Josephson vortex motion. This provides a mechanism for detection and manipulation of Josephson vortices by an oscillating MFM tip. In a static case, the local field leads to a distortion of the critical current versus magnetic field, Ic(H), pattern. The distortion is sensitive to both the shape and the amplitude of the local field. Therefore, the Ic(H) pattern carries information about the local field distribution within the junction. This opens the 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 the field sensitivity and the spatial resolution of a sensor.

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