Semifluxons in long Josephson 0-π-junctions

We investigate analytically long Josephson junctions with phase π-discontinuity points. Such junctions are usually fabricated as a ramp between a superconductor such as YBa₂Cu₃O₇ with d-wave symmetry of the order parameter and an s-wave superconductor such as Nb. From the top, they look like zigzags with π jumps of the Josephson phase at the corners. These π jumps, at certain conditions, lead to the formation of half integer flux quanta, which we call semifluxons, pinned at the corners. We derive a version of sine-Gordon equation which describes the dynamics of the Josephson phase in such structures, and obtain an explicit formula that describes the shape of a semifluxon. Some properties of semifluxons are discussed. We propose a way to construct artificial 0-π-junctions using only s-wave superconductors.