Theory of scanning gate microscopy imaging of the supercurrent distribution in a planar Josephson junction

We theoretically investigate the mapping of supercurrent distribution in a planar superconductor-normal-superconductor junction presence perpendicular magnetic field via scanning gate microscopy technique. find that counterpropagating supercurrents aligned Josephson vortices can be mapped by change critical current induced tip probe if flux is set close to maxima Fraunhofer pattern. Instead, when drives minimum pattern, superconducting phase adapts, and always increases supercurrent. The leads formation vortices, whose extension for highly transparent junctions depends on circulation direction. show this an asymmetric revealed microscopy. explain our findings basis numerical calculations both short- long-junction limits provide phenomenological model observed phenomena.