Properties of superconducting materials, especially those with a complex structure of the order parameter, differ greatly from the bulk properties when the size of the sample is small. Moreover, current transport properties of superconductors are of great interest when they are put in contact with normally conducting metals or ferromagnets (proximity effect). Particularly interesting is the regime when the size of the non-superconducting region is small enough that the current transport is fully coherent.
We investigate properties of unconventional novel superconducting materials, such as the high-Tc cuprates and Sr2RuO4 in restricted geometries. We also studied the unconventional ordering induced in nanoscale superconductor-ferromagnet heterostructures. Long-range order in these materials is affected either by the physical size of a sample or by contact to other materials. This gives rise to new physics that governs Josephson transport, current-voltage characteristics, heat conduction, and, in the case of superconductor-ferromagnet structures, local spin polarization. To have a proper description of ultra-small superconducting systems, one needs to know the quasi-particle density of states, which is usually strongly modified compared to its bulk-material value due to quantum interference effects. These interference effects occur when the size of the system is comparable to the superconducting coherence length (approximately 1-100 nm). Moreover, in unconventional superconductors with an anisotropic pairing state of the Cooper pairs, these interference effects are intrinsic and always present because of non-homogeneities, such as surfaces, interfaces, or impurities.