Conventional Josephson Junctions Research Articles

Skewness and critical current behavior in a graphene Josephson junction

In this work, the DC Josephson effect is investigated for a superconductor-graphene-superconductor junction in both short- and long-junction regimes. The electric transport properties are calculated while taking into account the contribution of the discrete and continuous energy spectrum. In our approach, the phase dependence of the critical current is calculated at arbitrary temperature and doping level, which generalizes previous results. We show that critical current ${I}_{c}$ and skewness $S$ exhibit critical points as a function of graphene doping ${E}_{F}$, which can be explained by Klein resonances in graphene. We give a general characterization of $S$ vs ${I}_{c}$ curves while fixing temperature or doping level. When the temperature dependence of ${I}_{c}$ is analyzed, we find differences with respect to conventional Josephson junctions, given that there is a relevant doping effect. In the long-junction regime with ${E}_{F}$ far away from the Dirac point, the ${I}_{c}$ vs $T$ curve may exhibit an exponential decay law, which has been measured recently. We report the temperature dependence of $S$ in the whole range of temperature, and our approach allows us to account for skewness suppression in the vicinity of the Dirac point, which is in agreement with recent experiments. We mention some effects which can be attained in Josephson junctions with well-defined edges and for transparency values below unity of the graphene-superconductor interfaces.

Towards quantum phase slip based standard of electric current

An accurate standard of electric current is a long-standing challenge of modern metrology. It has been predicted that a superconducting nanowire in the regime of quantum fluctuations can be considered as the dynamic equivalent of a chain of conventional Josephson junctions. In full analogy with the quantum standard of electric voltage based on the Josephson effect, the quantum phase slip phenomenon in ultrathin superconducting nanowires could be used for building the quantum standard of electric current. This work presents advances toward this ultimate goal.

Tunable Nb Superconducting Resonator Based on a Constriction Nano-SQUID Fabricated with a Ne Focused Ion Beam

Hybrid superconducting--spin systems offer the potential to combine highly coherent atomic quantum systems with the scalability of superconducting circuits. To fully exploit this potential requires a high quality-factor microwave resonator, tunable in frequency and able to operate at magnetic fields optimal for the spin system. Such magnetic fields typically rule out conventional Al-based Josephson junction devices that have previously been used for tunable high-$Q$ microwave resonators. The larger critical field of niobium (Nb) allows microwave resonators with large field resilience to be fabricated. Here, we demonstrate how constriction-type weak links, patterned in parallel into the central conductor of a Nb coplanar resonator using a neon focused ion beam (FIB), can be used to implement a frequency-tunable resonator. We study transmission through two such devices and show how they realise high quality factor, tunable, field resilient devices which hold promise for future applications coupling to spin systems.

Chiral supercurrent through a quantum Hall weak link

We use a microscopic model to calculate properties of the supercurrent carried by chiral edge states of a quantum Hall weak link. This "chiral" supercurrent is qualitatively distinct from the usual Josephson supercurrent in that it cannot be mediated by a single edge alone, i.e., both right and left going edges are needed. Moreover, chiral supercurrent was previously shown to obey an unusual current-phase relation with period $2 \phi_0=h/e$, which is twice as large as the period of conventional Josephson junctions. We show that the "chiral" nature of this supercurrent is sharply defined, and is robust to interactions to infinite order in perturbation theory. We compare our results with recent experimental findings of Amet et al [Science, 352(6288)] and find that quantitative agreement in magnitude of the supercurrent can be attained by making reasonable but critical assumptions about the superconductor quantum Hall interface.

Design methodology of single-flux-quantum flip-flops composed of both 0- and π-shifted Josephson junctions

A methodology for designing single-flux-quantum (SFQ) flip-flops composed of both conventional (0-) and π-shifted Josephson junctions is investigated. We investigated the implementation of a storage loop, which can store flux quantum and is indispensable to express binary logic states in superconductor logic circuits. As all SFQ flip-flops have storage loops, the investigated design methodology can be applied to their design. We designed several SFQ flip-flops composed of 0- and π-shifted Josephson junctions using the investigated design methodology. The performances of the designed SFQ flip-flops were quantitatively evaluated by using an analog circuit simulator which we developed. We confirmed the correct operation of various SFQ flip-flops composed of 0- and π-shifted Josephson junctions with wide operating margins. Moreover, we observed that the investigated design methodology is suitable for SFQ flip-flops with complementary outputs because a storage loop composed of both 0- and π-shifted Josephson junctions has a symmetric structure and the complementary output function can be realized by using the storage loop. Our investigation indicates that the number of Josephson junctions and static power consumption of a non-destructive read-out flip-flop with complementary outputs (NDROC) can be reduced to less than half of those of the conventional NDROC, which has two storage loops composed of 0-Josephson junctions, to realize the complementary output function. The investigated design methodology is expected to be applied to not only SFQ circuits but also other superconducting logic circuits and novel reconfigurable logic devices using programmable 0-π Josephson junctions.

Fabrication of Three-Dimensional Nanobridge Junction Arrays for SQIFs

Superconducting quantum interference filters (SQIFs) are arrays of superconducting quantum interference devices with various loop areas. In contrast to the SQIFs of conventional Josephson junctions, we propose a way for creating highly integrated SQIFs using 50 × 50 nm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> three-dimensional (3-D) nanobridge junctions. Here, we report the fabrication of arrays composed of a hundred 3-D nanobridge junctions. Current-voltage curves of single, 10, and 100 junctions in series were measured and analyzed. Measurements of single junctions revealed an average critical current of 104 μA with a standard deviation of 24 μA. Furthermore, the 10 junctions in series had randomly distributed switching events. The normal resistance as the function of the number of junctions in series showed a good linearity, indicating a good uniformity of the junctions. Therefore, we propose that the local differences in the thermal-dissipation conditions and random trapped vortices were likely responsible for the random switching of the nanobridge junctions in series.

Spin orbit interaction fingerprints of a ballistic graphene Josephson junction

In this study, we establish the universal characteristics of the contributions of the Rashba spin orbit interaction (RSOI) and the Dresselhaus spin orbit interaction (DSOI) to the supercurrent in a graphene Josephson junction. The most striking property of the skewness and the critical supercurrent, so far not unequivocally revealed, is the presence of a maximum value or a single singularity at the key point (the DSOI equates to half of the RSOI) in pristine case. This is in sharp contrast to that in conventional Josephson junction (the π junction) and its counterpart in heavily doped graphene case (monotonically decay). Using a general delta potential model, we determine the barrier effect on the quasilocalized Andreev level (π periodic) and the propagating Andreev mode (π/2 periodic). Moreover, we trace the pronounced critical supercurrent Fabry–Pérot oscillations patterns as a function of the doping level, and find that it shows a good qualitative agreement with the recent experiment of M. Ben Shalom et al. [Nat. Phys. 12, 318 (2016)]. Our results show that definitive signatures of specular Andreev reflection can be observed in the graphene material and suggest that the graphene Josephson junction can lead to a new possible application in quantum computing.

Dissipation in microwave quantum circuits with hybrid nanowire Josephson elements

Recent experiments on hybrid Josephson junctions have made the argument a topical subject. However, a quantity which remains still unknown is the tunneling (or response) time, which is strictly connected to the role that dissipation plays in the dynamics of the complete system. A simple way for evaluating dissipation in microwave circuits, previously developed for describing the dynamics of conventional Josephson junctions, is now presented as suitable for application even to non-conventional junctions. The method is based on a stochastic model, as derived from the telegrapher's equation, and is particularly devoted to the case of junctions loaded by real transmission lines. When the load is constituted by lumped-constant circuits, a connection with the stochastic model is also maintained. The theoretical model demonstrated its ability to analyze both classically-allowed and forbidden processes, and has found a wide field of applicability, namely in all cases in which dissipative effects cannot be ignored.

Light-modulated 0- π transition in a silicene-based Josephson junction

We investigate the Andreev bound states (ABSs) and Josephson current in a silicene-based superconductor-normal-superconductor junction modulated by a perpendicular electric field and an off-resonant circularly polarized light. Based on the Dirac--Bogoliubov--de Gennes equation, we analytically derive the ABS levels and show they have different phase-difference dependences, which will remarkably influence the velocity of Cooper pairs and then the Josephson current. In the pristine or gated silicene, the ABS levels always show negative slope, which means that the Josephson current is irreversible because of the time-reversal symmetry. When an off-resonant circularly polarized light is applied, whether or not there is a perpendicular electric field, the ABS levels will have positive slope, leading to the emergence of reversed Josephson current due to the nonzero center-of-mass wave vector of Cooper pairs. In this light-modulated silicene-based Josephson junction, valley polarization provides an alternative mechanism for 0-$\ensuremath{\pi}$ transition, very different from that for the conventional ferromagnetic Josephson junctions where the spin polarization is essential.

Landau-Zener-Stückelberg-Majorana lasing in circuit quantum electrodynamics

We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"{u}ckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"{u}ckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.

Dual approach to circuit quantization using loop charges

The conventional approach to circuit quantization is based on node fluxes and traces the motion of node charges on the islands of the circuit. However, for some devices, the relevant physics can be best described by the motion of polarization charges over the branches of the circuit that are in general related to the node charges in a highly nonlocal way. Here, we present a method, dual to the conventional approach, for quantizing planar circuits in terms of loop charges. In this way, the polarization charges are directly obtained as the differences of the two loop charges on the neighboring loops. The loop charges trace the motion of fluxes through the circuit loops. We show that loop charges yield a simple description of the flux transport across phase-slip junctions. We outline a concrete construction of circuits based on phase-slip junctions that are electromagnetically dual to arbitrary planar Josephson junction circuits. We argue that loop charges also yield a simple description of the flux transport in conventional Josephson junctions shunted by large impedances. We show that a mixed circuit description in terms of node fluxes and loop charges yields an insight into the flux decompactification of a Josephson junction shunted by an inductor. As an application, we show that the fluxonium qubit is well approximated as a phase-slip junction for the experimentally relevant parameters. Moreover, we argue that the $0$-$\pi$ qubit is effectively the dual of a Majorana Josephson junction.

Signatures of topological Josephson junctions

Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4\pi$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching current measurements.

Junctionless Cooper pair transistor

Quantum phase slip (QPS) is the topological singularity of the complex order parameter of a quasi-one-dimensional superconductor: momentary zeroing of the modulus and simultaneous 'slip' of the phase by ±2π. The QPS event(s) are the dynamic equivalent of tunneling through a conventional Josephson junction containing static in space and time weak link(s). Here we demonstrate the operation of a superconducting single electron transistor (Cooper pair transistor) without any tunnel junctions. Instead a pair of thin superconducting titanium wires in QPS regime was used. The current–voltage characteristics demonstrate the clear Coulomb blockade with magnitude of the Coulomb gap modulated by the gate potential. The Coulomb blockade disappears above the critical temperature, and at low temperatures can be suppressed by strong magnetic field.

The Quantum Phase Slip Phenomenon in Superconducting Nanowires with High-Impedance Environment

Quantum phase slip (QPS) is the particular manifestation of quantum fluctuations of the order parameter of a current-biased quasi-1D superconductor. The QPS event(s) can be considered a dynamic equivalent of tunneling through conventional Josephson junction containing static in space and time weak link(s). At low temperatures T<<Tc the QPS effect leads to finite resistivity of narrow superconducting channels and suppresses persistent currents in tiny nanorings. Here we demonstrate that the quantum tunneling of phase may result in Coulomb blockade: superconducting nanowire, imbedded in high-Ohmic environment, below a certain bias voltage behaves as an insulator.

Flux qubit in a dc SQUID with the 4π period Josephson effect

We propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero-energy Majorana bound states transport 4π period Josephson currents in the nanowire junction. The interplay between this 4π period Josephson effect and the convectional 2π period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a result, the two lowest-energy levels of the SQUID are isolated from the other levels. These two levels show counterpropagating supercurrents, thus can be used as a flux qubit. We reveal that this flux qubit has the merits of stability to external noises, tolerance to the deviation of system parameters, and scalability to large numbers. Furthermore, we demonstrate how to couple this flux qubit with the Majorana qubit by tuning the junction parameters, and how to use this coupling to manipulate the Majorana qubit.

Dissipation in a simple model of a topological Josephson junction.

The topological features of low-dimensional superconductors have created a lot of excitement recently because of their broad range of applications in quantum information and their potential to reveal novel phases of quantum matter. A potential problem for practical applications is the presence of phase slips that break phase coherence. Dissipation in nontopological superconductors suppresses phase slips and can restore long-range order. Here, we investigate the role of dissipation in a topological Josephson junction. We show that the combined effects of topology and dissipation keep phase and antiphase slips strongly correlated so that the device is superconducting even under conditions where a nontopological device would be resistive. The resistive transition occurs at a critical value of the dissipation that is 4 times smaller than that expected for a conventional Josephson junction. We propose that this difference could be employed as a robust experimental signature of topological superconductivity.

Light-superconducting interference devices

Recently, we have proposed the half-Josephson laser (HJL): a device that combines lasing with superconducting leads, providing a locking between the optical phase and the superconducting phase difference between the leads. In this work, we propose and investigate two setups derived from a superconducting quantum interference device (SQUID), where two conventional Josephson junctions are replaced by two HJLs. In the first setup, the HJLs share the same resonant mode, while in the second setup two separate resonant modes of the two lasers are coupled optically. We dub the setup ``light-superconducting interference device'' (LSID). In both setups, we find the operating regimes similar to those of a single HJL. Importantly, the steady lasing field is significantly affected by the magnetic flux penetrating the SQUID loop, with respect to both amplitude and phase. This provides opportunities to tune or even quench the lasing by varying a small magnetic field. For the second setup, we find a parameter range where the evolution equation for the laser fields supports periodic cycles. The fields are thus modulated with the frequency of the cycle resulting in an emission spectrum consisting of a set of discrete modes. From this spectrum, two modes dominate in the limit of strong optical coupling. Therefore, the LSID can be also used to generate such modulated light.

Complete gate control of supercurrent in graphene p–n junctions

In a conventional Josephson junction of graphene, the supercurrent is not turned off even at the charge neutrality point, impeding further development of superconducting quantum information devices based on graphene. Here we fabricate bipolar Josephson junctions of graphene, in which a p-n potential barrier is formed in graphene with two closely spaced superconducting contacts, and realize supercurrent ON/OFF states using electrostatic gating only. The bipolar Josephson junctions of graphene also show fully gate-driven macroscopic quantum tunnelling behaviour of Josephson phase particles in a potential well, where the confinement energy is gate tuneable. We suggest that the supercurrent OFF state is mainly caused by a supercurrent dephasing mechanism due to a random pseudomagnetic field generated by ripples in graphene, in sharp contrast to other nanohybrid Josephson junctions. Our study may pave the way for the development of new gate-tuneable superconducting quantum information devices.

Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

The current–phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case in which the junction length is finite and magnetic impurity exists. The similarities and differences with respect to a conventional Josephson junction are discussed. Both the 2π- and 4π-period current–phase relations (I2π(ϕ),I4π(ϕ)) are studied. There is a sharp jump at ϕ = π and ϕ = 2π for I2π and I4π, respectively, in the clean junction. For I2π, the sharp jump is robust against the impurity strength and distribution. However, for I4π, an impurity makes the jump at ϕ = 2π smooth. The critical (maximum) current Ic,2π of I2π is given and we find it will be increased by an asymmetrical distribution of the impurity.

Current-phase relation of double-barrier Josephson junctions with a two-gap superconductor as intermediate electrode

The current-phase (I-ϕ) relation of a double-barrier Josephson junction with a two-gap superconductor as intermediate electrode is derived by means of a simplified version of Ohta’s model. As in conventional double-barrier Josephson junctions, a marked skewness in the I-ϕ curves is present. Moreover, as in heterotic Josephson devices, a reduction of the maximum Josephson current is predicted. An appropriate experiment to verify the rich behavior of this type of Josephson device is suggested.