Electron-optical phase shift of a Josephson vortex

The possibility of directly observing Josephson vortices in a superconducting material by transmission electron microscopy is here investigated. First, the anisotropic London equation for the magnetic field of a Josephson vortex is solved in Fourier space. Then, from the knowledge of the magnetic field, the vector potential and the Aharonov-Bohm phase shift are derived. Finally, phase contrast image simulations are presented. It will be shown that, with current technology, the direct observation of a Josephson vortex is possible.