We review our results on the investigation of the breakpoint phenomena in the stacks with finite number of INTRINSIC JOSEPHSON JUNCTIONS in high temperature superconductors. New ideas concerning the breakpoint region structure are discussed as well.

We study numerically the electronic heat capacity, spin and charge current in a diffusive Superconductor-Ferromagnetic-Superconductor systems، with singlet superconducting leads and non-uniform ferromagnetic layer. Specially, we focus on ferromagnetic layer with domain wall and conical structures incorporation the spin-active interfaces. We investigate, how the 0-p transition is influenced by non-uniform magnetization texture and also the appearance of spin-current in such structures. We find that for ferromagnetic layer with domain wall structure, only the one component of spin-current is non-zero and for conical structure, three components of spin-current are non-zero. Also we find that specific heat of such JUNCTIONS can be tuned by changing the superconducting phase difference. Interestingly, spin-current shows a discontinuous jump at the 0-p transition points of the critical charge current.

Charge creation in superconductor layers affects current–voltage characteristics (CVC) of the JOSEPHSON junction array and creates a breakpoint region in CVC. This charge may oscillate in the form of longitudinal plasma wave, (LPW), or nonregularity. In this paper we intend to distinguish the region with LPW from the nonregular region.

he JOSEPHSON Fluxonic Diode is a long JOSEPHSON Junction that uses oppositely directed magnetic flux quanta, associated with current votrices and antivortices, as its basis operation. the movement of the vortices creates a changing phase. this in turn creates a voltage drop. in this paper, discrete JJ is proposed instead of continues JJ in JFD. Also, by numerical calculation of the discrete sine-Gordon equation, the manner of the carriers is discussed in discrete JJ. Numerically study of the dynamics of JFD based on discrete JJ shows a rectification. Because of it is easy to adjust the value of the junction parammeters, and it is possible to have single flux quantum stuffed in a small area by adjusting the discreetness parameter, it is expected that the useful and practical JOSEPHSON fluxonic devices can be made by discrete JJs.

A tight binding approach based on the Bogoliubov de-Genes approach has been used to calculate the DC JOSEPHSON current for short JUNCTIONS with respect to the superconducting coherence length with a lattice model for SGNR-S JUNCTIONS. We calculate the phase, length, width, and chemical potential dependence at the JOSEPHSON junction and discuss the similarities and differences with regard to the theoretical and experimental results obtained for graphene. Regarding the calculations on graphene, using a lattice model, we convert the graphene honeycomb structure to a brick lattice structure that does not change the lattice topology. Then, by removing several atoms from the lattice, we create the simple vacancy defects in the brick lattice. Also we calculate the JOSEPHSON current with these vacancies.

In this paper, we model an entangled system of two identical superconducting qubits in which JOSEPHSON JUNCTIONS are coupled by a fixed capacitor. This coupling of the capacitor with JOSEPHSON JUNCTIONS is added due to increase the coherence and neutralize the effects of decoherence in the system. To better understand the state of the system, using the theory of quantum computing, the qualitative behaviors of entanglement, coherence, and comparison between them are numerically investigated. It was observed that there is a limit for increasing the mutual coupling energy between two qubits, and beyond that, it will weaken the system performance. It was also seen that the behaviors of the entanglement and the coherence are almost similar and they can be maintained at high temperatures under some conditions. A remarkable point was is that, as the JOSEPHSON energy of the qubits increases, the coherence and entanglement increase even at high temperatures. Also, by increasing the mutual coupling energy between qubits, coherence and entanglement are maintained at high temperatures, which can be considered in the construction of entanglement sources. In addition, the difference between an identical and a dissimilar two-qubit system is also stated.

In this work, we consider a topological JOSEPHSON junction that contains conventional superconductors and ferromagnet leads on the surface of three-dimensional topological insulators. We use Bogoliubov-deGennes formalism to show in-plane magnetization with a component perpendicular to the superconductor interface that alters the Andreev bound states and creates an Andreev zone. This effect reduces the magnitude of the supercurrent. Also, magnetization changes the spin arrangement of surface states and creates spin-polarized supercurrent. Because of strong spin-momentum interaction on topological insulators, the spin-polarized supercurrent has in-plane components with maximum value in m_x~Δ_0⁄2. On the other hand, the parallel component of in-plane magnetization creates an anomalous supercurrent that flows in the absence of a superconducting phase difference. The dissipation-less spin-polarized supercurrent has great importance from the application point of view in designing spintronics devices.