Impact of inhomogeneities on various properties of novel superconductors and magnetic oxides

Novel superconducting compounds such as cuprates and borocarbides are in the ``pseudogap state'' at T$>$Tc: they display anomalous diamagnetism, an energy gap, a ``giant'' proximity Josephson effect, etc. The compound is intrinsically inhomogeneous because of the effects of doping and pair-breaking. The phase diagram is characterized by three energy scales (T*$>$Tc*$>$Tc;res). When cooled below T*, the system begins to display phase separation, i.e., coexistence of metallic and insulating phases as well as other possible effects, e.g., a CDW gap.Below Tc* superconducting ``clusters'' embedded into the normal metallic matrix appear, leading to diamagnetism, pairing gap, a.c.losses, and the ``giant'' proximity effect. The Meissner and resistive transitions are split, and the ``intrinsic'' critical temperature (Tc*) greatly exceeds Tc;res. Further cooling towards Tc=Tc;res. increases the volume taken up by the superconducting ``islands'' and eventually results in a percolation transition at Tc, so that a macroscopic coherent dissipationless phase forms. The percolation transition is similar to that in manganites [L.Gor'kov, V.Kresin, Phys. Rep. 400, 149 (2004)].