Exotic Vortex Matter: Pancake Vortex Molecules and Fractional-Flux Molecules in Some Exotic and/or Two-Component Superconductors

The discovery of superconductivity in MgB₂ and, more recently, in iron pnictides, revived the interest in two-component and other exotic superconductors, including in the field of vortex matter, as was shown recently by the discovery of ??type 1.5?? superconductivity. However, even some ??older?? exotic cuprates grown by high-pressure techniques showed interesting anomalies related to the interplay between Josephson and magnetic coupling and/or two-gap superconductivity. Here, we will present two such examples of exotic vortex matter: magnetically-coupled pancake-vortex molecules in super-multilayered cuprates, and vortex molecules composed of fractional flux quanta glued by an interband phase difference soliton, and will discuss the major differences between MgB₂ and such multilayer cuprates in terms of the relative strength of the interband interaction and, respectively, in terms of the coherence and penetration lengths.