Superelliptic Josephson Tunnel Junctions

The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic field dependence of its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second-order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study is made of their magnetic patterns with an emphasis on the rate of decay of the sidelobe amplitudes for large field amplitudes.