This review provides a theoretical basis for understanding the current-phase relation (CΦR) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CΦR from the standard sinusoidal form. A new experimental tool for measuring the CΦR is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the CΦR measurements for both fundamental physics and applications.

The predictions of Moore’s law are considered by experts to be valid until 2020 giving rise to “post-Moore’s” technologies afterwards. Energy efficiency is one of the major challenges in high-performance computing that should be answered. Superconductor digital technology is a promising post-Moore’s alternative for the development of supercomputers. In this paper, we consider operation principles of an energy-efficient superconductor logic and memory circuits with a short retrospective review of their evolution. We analyze their shortcomings in respect to computer circuits design. Possible ways of further research are outlined.

We have measured the current-phase relationship $I\left(\varphi \right)$ of symmetric 45° ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature $T$, a local minimum at a temperature $T^{*}$. (ii) At $T\approx T^{*}$, the first harmonic of $I\left(\varphi \right)$ changes sign. (iii) For $T<\mathrm{}{T}^{*}$, the second harmonic of $I\left(\varphi \right)$ is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between $d$-wave superconductors.

We investigate a Magnetic Josephson Junction (MJJ) - a superconducting device with ferromagnetic barrier for a scalable high-density cryogenic memory compatible with energy-efficient single flux quantum (SFQ) circuits. The superconductor-insulator-superconductor-ferromagnet-superconductor (SIS^'FS) MJJs are analyzed both experimentally and theoretically. We found that the properties of SIS^'FS junctions fall into two distinct classes based on the thickness of S^' layer. We fabricate Nb-Al/AlOx-Nb-PdFe-Nb SIS^'FS MJJs using a co-processing approach with a combination of HYPRES and ISSP fabrication processes. The resultant SIS ^'FS structure with thin superconducting S^'-layer is substantially affected by the ferromagnetic layer as a whole. We fabricate these type of junctions to reach the device compatibility with conventional SIS junctions used for superconducting SFQ electronics to ensure a seamless integration of MJJ-based circuits and SIS JJ-based ultra-fast digital SFQ circuits. We report experimental results for MJJs, demonstrating their applicability for superconducting memory and digital circuits. These MJJs exhibit I_cR_n product only ~ 30% lower than that of conventional SIS junctions co-produced in the same fabrication. Analytical calculations for these SIS ^'FS structures are in a good agreement with the experiment. We discuss application of MJJ devices for memory and programmable logic circuits.

We study the critical temperature T _c of FSF trilayers (F is a ferromagnet, S is a singlet superconductor), where the triplet superconducting component is generated at noncollinear magnetizations of the F layers. An exact numerical method is employed to calculate T _c as a function of the trilayer parameters, in particular, mutual orientation of magnetizations. Analytically, we consider limiting cases. Our results determine the conditions necessary for the existence of recently investigated odd triplet superconductivity in SF multilayers.

The ultrastrong photon-to-magnon coupling is reached with an on-chip hybrid system using superconducting phenomena.