Josephson $\pi$-junctions and Andreev current-transport ‘engineering’ in S–N/F–S nanostructures

We present a review of studies of two types of Josephson $\pi$-junctions, i.e., Josephson structures with an inverse current–phase relation. In particular, we discuss the features of the transition to the $\pi$-state of Josephson superconductor–ferromagnet–superconductor sandwiches (Josephson SFS junctions). At the same time, much attention is devoted to the ‘Andreev’ coherent transport in planar superconductor–normal metal–superconductor structures (Josephson SNS junctions) and transitions to the $\pi$-state caused by a nonequilibrium electron distribution in a Josephson junction with a normal metal barrier. We also discuss in detail various types of nonequilibrium distributions arising in hybrid Josephson S–N/F–S structures upon injection of spin-polarized carriers into the Josephson barrier and the features of Andreev current transport due to contacts between a normal metal and a ferromagnet in the Josephson barrier. The review relies mainly on the works performed with the participation of the authors.