We investigate the physics of planar annular Josephson tunnel junctions
quenched through their transition temperature in the presence of an external
magnetic field. Experiments carried out with long Nb/Al-AlOx/Nb annular
junctions showed that the magnetic flux trapped in the high-quality
doubly-connected superconducting electrodes forming the junction generates a
persistent current whose associated magnetic field affects the both the static
and dynamics properties of the junctions. More specifically, the field trapped
in the hole of one electrode combined with a d.c. bias current induces a
viscous flow of dense trains of Josephson vortices which manifests itself
through the sequential appearance of displaced linear slopes, Fiske step
staircases and Eck steps in the junction's current-voltage characteristic.
Furthermore, a field shift is observed in the first lobe of the magnetic
diffraction pattern. The effects of the persistent current can be mitigated or
even canceled by an external magnetic field perpendicular to the junction
plane. The radial field associated with the persistent current can be
accurately modeled with the classical phenomenological sine-Gordon model for
extended one-dimensional Josephson junctions. Extensive numerical simulations
were carried out to disclose the basic flux-flow mechanism responsible for the
appearance of the magnetically induced steps and to elucidate the role of
geometrical parameters. It was found that the imprint of the field cooling is
enhanced in confocal annular junctions which are the natural generalization of
the well studied circular annular junctions.Comment: 26 pages, 10 figures. Supercond. Sci. Technol (2020
