We have investigated the critical temperature behavior in periodic superconductor/ ferromagnet (S/F) multilayers as a function of the ferromagnetic layer thickness d f and the interface transparency. The critical temperature Tc(d f ) exhibits a damped oscillatory behavior in these systems due to an exchange field in the ferromagnetic material. In this work we have performed Tc calculations using the self-consistent multimode approach, which is considered to be exact solving method. Using this approach we have derived the conditions of 0 or π state realization in periodic S/F multilayers. Moreover, we have presented the comparison between the single-mode and multimode approaches and established the limits of applicability of the single-mode approximation, frequently used by experimentalists.

Rapid development of micro- and nanofabrication methods have provoked interest and enabled experimental studies of electronic properties of a vast class of (sub)micrometer-size solid state systems. Mesoscopic-size hybrid structures, containing superconducting elements, have become interesting objects for basic research studies and various applications, ranging from medical and astrophysical sensors to quantum computing. One of the most important aspects of physics, governing the behavior of such systems, is the finite concentration of nonequilibrium quasiparticles, present in a superconductor even well below the temperature of superconducting transition. Those nonequilibrium excitations might limit the performance of a variety of superconducting devices, like superconducting qubits, single-electron turnstiles and microrefrigerators. On the contrary, in some applications, like detectors of electromagnetic radiation, the nonequilibrium state is essential for their operation. It is therefore of vital importance to study the mechanisms of nonequilibrium quasiparticle relaxation in superconductors of mesoscopic dimensions, where the whole structure can be considered as an 'interface'. At early stages of research the problem was mostly studied in relatively massive systems and at high temperatures close to the critical temperature of a superconductor. We review the recent progress in studies of nonequilibrium quasiparticle relaxation in superconductors including the low temperature limit. We also discuss the open physical questions and perspectives of development in the field.

In the following paper we investigate the critical temperature Tc behavior in the two-dimensional S/TI (S denotes superconductor and TI -topological insulator) junction with a proximity induced inplane helical magnetization in the TI surface. The calculations of Tc are performed using the general self-consistent approach based on the Usadel equations in Matsubara Green's functions technique. We show that the presence of the helical magnetization leads to the nonmonotonic behavior of the critical temperature as a function of the topological insulator layer thickness.

We present a quantitative study of the current-voltage characteristics (CVC) of SFIFS Josephson junctions (S denotes bulk superconductor, F -metallic ferromagnet, I -insulating barrier) with weak ferromagnetic interlayers in the diffusive limit. The problem is solved in the framework of the nonlinear Usadel equations. We consider the case of a strong tunnel barrier such that the left SF and the right FS bilayers are decoupled. We calculate the density of states (DOS) in SF bilayers using a self-consistent numerical method. Then we obtain the CVC of corresponding SFIFS junctions, and discuss their properties for different set of parameters including the thicknesses of ferromagnetic layers, the exchange field, and the magnetic scattering time. We observe the anomalous nonmonotonic CVC behavior in case of weak ferromagnetic interlayers, which we ascribe by DOS energy dependencies in case of small exchange fields in F layers.

It is well known that the ground state of homogeneous superconducting systems with spin-orbit coupling in the presence of the Zeeman field is the so-called helical state, which is characterized by the phase modulation of the order parameter, but zero supercurrent density. In this paper we investigate the realization of the helical state in a hybrid system with spatially separated superconductivity and exchange field by considering a superconductor/ferromagnet (S/F ) bilayer on top of a three-dimensional topological insulator. This system is characterized by strong spin-momentum locking and, consequently, provides the most favorable conditions for the helical state generation. The analysis is based on the microscopic theory in terms of the quasiclassical Green's functions. We demonstrate that in the bilayer the helical state survives if the exchange field has a nonzero component perpendicular to the S/F interface even in spite of the fact that the superconducting order parameter and the exchange field are spatially separated. At the same time, in this spatially inhomogeneous situation the helical state is accompanied by the spontaneous currents distributed over the bilayer in such a way that the net current vanishes. Further, we show that this hybrid helical state gives rise to nonreciprocity in the system. We demonstrate the realization of the nonreciprocity in the form of the superconducting diode effect and investigate its dependence on the parameters of the bilayer.