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International audience; The results of recent theoretical studies of features of superconducting states in hybrid structures whose properties are significantly determined by the spin–orbit effects have been reported. The two main phenomena appearing in such systems in the presence of additional spin splitting caused either by the Zeeman effect in a magnetic field or by the exchange field: (i) the generation of spontaneous currents and (ii) the appearance of topologically nontrivial superconducting phases. It has been shown that the spin–orbit coupling can be a key mechanism that allows implementing new inhomogeneous phase structures, in particular, the so-called “phase batteries.” The effect of geometric factors on the properties of topologically nontrivial superconducting states has been analyzed. New types of topological transitions in vortex states of Majorana wires have been proposed.

Recent theoretical ideas concerning the mechanism of the electromagnetic proximity effect in hybrid superconducting structures with ferromagnetic layers, as well as the problem of Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) instability with the modulation of the superconducting order parameter in the plane of the layers forming the structure, are reviewed. It is shown that, near the transition to the FFLO phase, the electromagnetic proximity effect can be enhanced: the corresponding spontaneous current flowing along the superconducting layer of the hybrid superconductor–ferromagnet structure increases drastically when approaching the FFLO transition line on the phase diagram of the structure. The transition to the FFLO phase can thus be observed using experimental techniques involving the diagnostics of the arising spontaneous currents.

Features of a phase transition between 0 and π states in superconductor/ferromagnet/superconductor (SFS) Josephson structures with thin superconducting layers and a ferromagnetic barrier are studied experimentally and theoretically. The dependence of the critical temperature T c of a transition of the hybrid structure to a superconducting state on the thickness of superconducting layers d s is analyzed by a local method involving measurements of the nonlinear microwave response of the system by a near-field probe. An anomalous increase in the measured temperature T c at the reduction of the thickness d s is detected and is attributed to the 0-π transition.

The mechanisms of individual vortex pinning and stability of multivortex configurations in different super-conducting compounds and artificial structures are analyzed on the basis of microscopic theory, which allowed describing the corresponding modification of the anomalous spectral branches in the quasiparticle spectrum caused by the electron scattering at the defect. The individual pinning potentials and corresponding depinning currents are evaluated. The experimentally observable consequences for the scanning tunneling microscopy characteristics and high-frequency field response are discussed. The comparative study of the conventional and chiral superconductors allowed suggesting experimental tests probing the superconducting gap symmetry. The chiral superconductors are shown to reveal a strong dependence of the pinning characteristics on the mutual orientation of the magnetic field and internal angular momentum of the Cooper pair.

Experimental and theoretical studies of ferromagnet-superconductor hybrid systems consisting of a Josephson junction placed in the nonuniform field of submicron ferromagnetic particles are reviewed.