We investigate the Josephson current between two superconductors (S) which are connected through a diffusive magnetic junction with a complex structure (F$_{c}$). Using the quantum circuit theory, we obtain the phase diagram of 0 and $π$ Josephson couplings for F$_{c}$ being a IFI (insulator-ferromagnet-insulator) double barrier junction or a IFNFI structure (where N indicates a normal metal layer). Compared to a simple SFS structure, we find that the width of the transition, defined by the interval of exchange fields in which a $0-π$ transition is possible, is increased by insulating barriers at the interfaces and also by the presence of the additional N layer. The widest transition is found for symmetric F$_{c}$ structures. The symmetric SIFNFIS presents the most favorable condition to detect the temperature induced $0-π$ transition with a relative width, which is five times larger than that of the corresponding simple SFS structure.
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between th…
We perform extensive analysis of graphene Josephson junctions embedded in microwave circuits. By comparing a diffusive junction at 15 mK with a ballistic one at 15 mK and 1 K, we are able to reconstruct the current-phase relation.
Josephson junctions and SQUIDs with graphene or other 2D materials as the weak link between superconductors have become a hot topic of research in recent years, with respect to both fundamental physics and potential applications. We have previously reported ultra-wide Josephson junctions (up to 80 μm wide) based on CVD graphene where the critical current was found to be uniformly distributed in the direction perpendicular to the current. In this paper, we demonstrate that the unusually large Josephson penetration depth λ_J that this corresponds to is enabled by the unique geometric structure o…
We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable i…
We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific mod…
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$π$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evid…
One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction, is $π$-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman effect induced 0-$π$ transitions in Bi$_{1-x}$Sb$_x$, 3D Dirac semimetal-based Josephson junctions. The large g-factor of the Zeeman effect from a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0- to $π$- regimes. This is revealed by sign changes …
We study the thermodynamic properties of topological Josephson junctions using a quantum spin Hall (QSH) insulator-based junction as an example. In particular, we propose that phase-dependent measurements of the heat capacity offer an alternative to Josephson-current measurements to demonstrate key topological features. Even in an equilibrium situation, where the fermion parity is not conserved, the heat capacity exhibits a pronounced double peak in its phase dependence as a signature of the protected zero-energy crossing in the Andreev spectrum. This double-peak feature is robust against chan…
Superconducting circuits incorporating Josephson tunnel junctions are widely used for fundamental research as well as for applications in fields such as quantum information and magnetometry. The quantum coherent nature of Josephson junctions makes them especially suitable for metrology applications. Josephson junctions suffice to form two sides of the quantum metrology triangle, relating frequency to either voltage or current, but not its base, which directly links voltage to current. We propose a five Josephson tunnel junction circuit in which simultaneous pumping of flux and charge results i…
We investigate the coupling between ferromagnet and superconducting phase dynamics in superconductor-ferromagnet-superconductor Josephson junction. The current-voltage characteristics of the junction demonstrate a pattern of subharmonic current steps which forms a devil's staircase structure. We show that a width of the steps becomes maximal at ferromagnetic resonance. Moreover, we demonstrate that the structure of the steps and their widths can be tuned by changing the frequency of the external magnetic field, ratio of Josephson to magnetic energy, Gilbert damping and the junction size.
Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the …
The $4π$ Josephson Effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. Here we numerically study the transient transport properties in a topological Josephson junction. We show that the $4π$ Josephson current can be sustained for a significant time (around several $μs$ with suitable conditions). Furthermore, we compare the behaviors of Josephson current in different conditions, identifying three main regimes: First, when both the superconducting wires of the Josephson junction lie in the topologically non…
We report an experimental study on the tuning of supercurrent in a ballistic graphene-based Josephson junction by applying a control voltage to a transverse normal channel. In this four-terminal geometry, the control voltage changes the occupation of Andreev states in the Josephson junction, thereby tuning the magnitude of the supercurrent. As a function of gate voltage, we find two different regimes characterized by a double-step distribution and a hot-electron distribution, respectively. Our work opens new opportunities to design highly controllable Josephson junctions for tunable supercondu…
We report on half-integer Shapiro steps observed in an InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found anomalous half-integer steps in addition to the conventional integer steps. The half-integer steps disappear as the temperature increases or transmission of the junction decreases. These experimental results agree closely with numerical calculation of the Shapiro response for the skewed current phase relation in a short ballistic Josephson junction.
The response of superconductor-normal-metal-superconductor junctions to magnetic field is complicated and non-universal because all trajectories contributing to supercurrent have a different effective area, and therefore acquire arbitrary magnetic phases. We design an hourglass-shaped Josephson junction where due to the junction symmetry the magnetic phase of every trajectory is approximately equal. By doing so we are able to increase a critical field of the Josephson junction to many flux quanta per junction area. We then analyse how breaking the symmetry condition increases the sensitivity o…
We theoretically study a Josephson junction formed by two finite-size $s$-wave SCs on a topological insulator under a magnetic field. At certain conditions, the junction hosts the chiral Majorana modes enclosing the two finite-size SCs. The interplay of the extended chiral Majorana modes and the states inside the junction can results in nontrivial topological effects such as the $2n π$ fractional AC Josephson effects predicted in Ref.~\cite{ChoiSim} We show that the $2n π$ fractional AC Josephson effects can occur in a realistic situation, such as the presence of the midgap states, without req…
The concept of coupled robust field induced Josephson junctions placed in complex electromagnetic environments is presented. Such structures are made by polarization of superconducting nanostructures by magnetic fields. The methodology of modeling of structures and possible implementations is introduced. The presented scheme is expected to implement and describe both classical and quantum computers with use of Josephson junction and artificial evolution. In such cases one can obtain unexpected new topologies of circuits that can contribute in enhancement of known and used circuit schemes. Furt…
We demonstrate the possibility to build stable Josephson $π$-junction stripes with exciton-polariton condensates. The stability of the $π$-junction between arbitrary long polariton stripes is achieved at low pumping by balancing the snaking instability with counter-propagating flows towards the junction. Not dissimilar from a dark soliton, the instability becomes relevant at high pumping leading to formation of vortex dipoles. The resulting structures can be stabilised to produce static lattices of Josephson vortices in straight and ring geometries. Our results build towards realization of qua…
