Ballistic Josephson Junctions Research Articles

Energy distribution controlled ballistic Josephson junction

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 superconducting quantum circuits.

Multiterminal ballistic Josephson junctions coupled to normal leads

Multiterminal Josephson junctions have aroused considerable theoretical interest recently and numerous works aim at putting the predictions of correlations among Coopers (i.e., the so-called quartets) and simulation of topological matter to the test of experiments. This paper is motivated by recent experimental investigation from the Harvard group reporting $h/4e$-periodic quartet signal in a four-terminal configuration containing a loop pierced by magnetic flux, together with inversion controlled by the bias voltage, i.e., the quartet signal can be larger at half-flux quantum than in zero magnetic field. Here, we theoretically focus on devices consisting of finite-size quantum dots connected to four superconducting leads and to a normal lead. In addition to presenting numerical calculations of the quartet signal within a simplified modeling, we reduce the device to a non-Hermitian Hamiltonian in the infinite-gap limit. Then, relaxation has the surprising effect of producing sharp peaks and log-normal variations in the voltage sensitivity of the quartet signal in spite of the expected moderate fluctuations in the two-terminal DC Josephson current. The phenomenon is reminiscent of a resonantly driven harmonic oscillator having amplitude inverse proportional to the damping rate, and of the thermal noise of a superconducting weak link, inverse proportional to the Dynes parameter. Perspectives involve quantum bath engineering multiterminal Josephson junctions in the circuits of cavity quantum electrodynamics.

Josephson junctions with chiral p-wave ferromagnetic superconductor reservoirs in presence of spin-orbit coupling interaction

The spin transfer torque (STT), is studied in new cases of Josephson junctions containing triplet p-wave chiral ferromagnetic superconductor (FS) reservoirs. To be more precise, FS1|spin orbit coupling layer (SOC1)|Normal metal (N)|SOC2|FS2 materials have been investigated. Specifically, FS1|N|FS2 structure with one layer of SOC at FS1|N interface and also two layers of SOC at both FS1|N and N|FS2 interfaces are investigated. For the structures including two SOC layers, both symmetric and asymmetric cases with respectively equal and different potential strengths are studied. The ballistic Josephson junctions are studied solving the Bogoliubov–de-Gennes equation. In particular, the cases with short normal metal contacts with thickness much smaller than the superconducting coherence length, ψ, are studied. It is obtained for the case with only one SOC layer, while the absolute value of the out-of-plane STT remains almost unchanged, its direction reverses for lower values of α, the angle between exchange fields of the two FSs. Also, the nanosystem in presence of two similar SOCs, exhibits lower out-of-plane STT. This is justified as the unit vector along the interface normal for the SOC1 is in the opposite direction of the second SOC2 layer. Hence, one can expect that these potentials fade the effect of each other. When the SOCs are not the same and have different values of potential strength, the out-of-plane STT reduces less which is attributed to slighter cancellation due to unequal potential strength. Moreover, the barrier strength is varied. It has been shown that the barrier strength increment changes the behavior of the STT. Particularly, it is found that it results in sign and value change of the STT. Further, the emergence of in-plane STTs in presence of SOC are confirmed and investigated for various systems.

Effect of Rashba and Dresselhaus spin–orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions

Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction (JJ) leads to a possible violation of the I(φ) = −I(−φ) equality for the current–phase relation. This is known as anomalous Josephson effect and it produces a phase shift φ 0 in sinusoidal current–phase relations. In ballistic JJs with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy (MCA) of Josephson inductance. In this work, we present measurements of both effects on arrays of JJs defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the MCA, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips.

Josephson Inductance as a Probe for Highly Ballistic Semiconductor-Superconductor Weak Links.

We present simultaneous measurements of Josephson inductance and dc transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency τ[over ¯] are extracted without need for phase bias, demonstrating, e.g., a near-unity value of τ[over ¯]=0.94. Our method allows us to probe the devices deeply in the nondissipative regime, where ordinary transport measurements are featureless. In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer pattern of the critical current, which is insensitive to the value of τ[over ¯]. In contrast, the signature of supercurrent interference in the inductance turns out to be extremely sensitive to τ[over ¯].

Evidence of half-integer Shapiro steps originated from nonsinusoidal current phase relation in a short ballistic InAs nanowire Josephson junction

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.

Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs

In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing the interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor (FS) materials are investigated. First, the diffusive FS1/Fc/FS2 structures with Fc being a junction consisting of ferromagnetic and normal metal parts as well as insulating barriers are investigated. Secondly, the ballistic Josephson junction containing the triplet chiral p/wave FS reservoirs is studied. Using the Nazarov quantum circuit theory for the diffusive structures, it is found that the antiparallel/parallel or vice versa parallel/antiparallel transition of the favorable exchange coupling takes place due to the appearance of the only out-of-plane STT. Furthermore, the analyze of the phase difference interval in which an interlayer length-induced antiparallel/parallel transition can be occurred, is performed. Afterward, the mentioned ballistic structure is dealt with solving the 16 16 Bogoliubov–de-Gennes equation. It is found that although the exchange fields of the FS are laid in the z and y direction, the STT interestingly exists in all three directions of x, y and z. This exciting finding suggests that the favorable equilibrium configuration concerning the least exchange coupling occurs in the relative exchange field direction different from 0 or .

First-principles study of metal-graphene edge contact for ballistic Josephson junction

Edge-contacted superconductor-graphene-superconductor Josephson junction have been utilized to realize topological superconductivity, which have shown superconducting signatures in the quantum Hall regime. We perform the first-principles calculations to interpret electronic couplings at the superconductor-graphene edge contacts by investigating various aspects in hybridization of molybdenum d orbitals and graphene $\pi$ orbitals. We also reveal that interfacial oxygen defects play an important role in determining the doping type of graphene near the interface.

Current phase relation from graphs and diagrams and application to thick ferromagnetic Josephson junctions

In this work we present a method of representing terms in the current-phase-relation of a ballistic Josephson junction by combinations of diagrams, used in previous work to represent an equivalent of the matching condition determinant of the junction. This is accomplished by the expansion of the logarithm of this determinant in Taylor series and keeping track of surviving terms, i.e. terms that do not annihilate each other. The types of the surviving terms are represented by connected graphs, whose points represent diagrammatic terms of the determinant expansion. Then the theory is applied to obtain approximations of the current-phase relation of relatively thick ballistic ferromagnetic Josephson junctions with non-collinear magnetizations. This demonstrates the versatility of the method in developing approximations schemes and providing physical insight into the nature of contributions to the supercurrent from the available particle excitations in the junction. We also discuss the strong second harmonic contribution to the supercurrent in junctions with three mutually orthogonal magnetization vectors and a weak intermediate ferromagnet.

Ballistic Josephson junctions based on CVD graphene

Josephson junctions with graphene as the weak link between superconductors have been intensely studied in recent years, with respect to both fundamental physics and potential applications. However, most of the previous work was based on mechanically exfoliated graphene, which is not compatible with wafer-scale production. To overcome this limitation, we have used graphene grown by chemical vapour deposition (CVD) as the weak link of Josephson junctions. We demonstrate that very short, wide CVD-graphene-based Josephson junctions with Nb electrodes can work without any undesirable hysteresis in their electrical characteristics from 1.5 K down to a base temperature of 320 mK, and their gate-tuneable critical current shows an ideal Fraunhofer-like interference pattern in a perpendicular magnetic field. Furthermore, for our shortest junctions (50 nm in length), we find that the normal state resistance oscillates with the gate voltage, consistent with the junctions being in the ballistic regime, a feature not previously observed in CVD-graphene-based Josephson junctions.

On-Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb-In0.75 Ga0.25 As-Quantum-Well-Nb Josephson Junctions.

A superconducting hard gap in hybrid superconductor-semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non-Abelian excitation). This requires the formation of homogeneous and barrier-free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb-In0.75 Ga0.25 As-quantum-well-Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high-quality and transparent contacts to the In0.75 Ga0.25 As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity-induced superconductivity in the In0.75 Ga0.25 As-quantum-well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g-factor and Rashba spin-orbit coupling in In0.75 Ga0.25 As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb-In0.75 Ga0.25 As-Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.

Graphene-based tunable SQUIDs

The superconducting proximity effect in graphene can be used to create Josephson junctions with critical currents that can be tuned using local field-effect gates. These junctions have the potential to add functionality to existing technologies; for example, superconducting quantum interference device (SQUID) magnetometers with adaptive dynamic range and superconducting qubits with fast electrical control. Here, we present measurements of graphene-based superconducting quantum interference devices incorporating ballistic Josephson junctions that can be controlled individually. We investigate the magnetic field response of the SQUIDs as the junctions are gated and as the device is tuned between symmetric and asymmetric configurations. We find a highest transfer function ≈ 300 μV/Φ0, which compares favorably with conventional, low temperature DC SQUIDs. With low noise readout electronics and optimised geometries, devices based on ballistic graphene Josephson junctions have the potential to match the sensitivity of traditional SQUIDs while also providing additional functionality.

Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes.

We investigate the critical current I_{C} of ballistic Josephson junctions made of encapsulated graphene-boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I_{C} is found to scale as ∝exp(-k_{B}T/δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity. As T→0 the critical current of a long (or short) junction saturates at a level determined by the product of δE (or Δ) and the number of the junction's transversal modes.

Ballistic Josephson junctions in the presence of generic spin dependent fields

Ballistic Josephson junctions are studied in the presence of a spin-splitting field and spin-orbit coupling. A generic expression for the quasiclassical Green's function is obtained and with its help we analyze several aspects of the proximity effect between a spin-textured normal metal (N) and singlet superconductors (S). In particular, we show that the density of states may show a zero-energy peak which is a generic consequence of the spin dependent couplings in heterostructures. In addition, we also obtain the spin current and the induced magnetic moment in a SNS structure and discuss possible coherent manipulation of the magnetization which results from the coupling between the superconducting phase and the spin degree of freedom. Our theory predicts a spin accumulation at the S/N interfaces, and transverse spin currents flowing perpendicular to the junction interfaces. Some of these findings can be understood in the light of a non-Abelian electrostatics.

Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions.

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position-particle-hole-spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials.

Charge and spin currents in ferromagnetic Josephson junctions

We determine, using a self consistent method, the charge and spin currents in ballistic Josephson junctions consisting of ferromagnetic ($F$) layers sandwiched between superconducting ($S$) electrodes ($SFS$-type junctions). When there are two $F$ layers, we also consider the experimentally relevant configuration where a normal ($N$) nonmagnetic spacer layer separates them. We study the current-phase relationships as functions of geometrical parameters that are accessible experimentally including the angles that characterize the relative orientation of the magnetization in the $F$ layers. Our self-consistent method ensures that the proper charge conservation laws are satisfied. As we vary the phase difference $\Delta\varphi$ between the two outer $S$ electrodes, multiple harmonics in the current phase relations emerge, their extent depends on the interface scattering strength and the relative $F$ layer widths and magnetization orientations. By manipulating the relative $F$ layer magnetization orientations, we find that the charge supercurrent can reverse directions or vanish altogether. These findings are discussed in the context of the generation and long-range nature of triplet pair correlation. We also investigate the spin currents and associated spin transfer torques throughout the junction. For noncollinear relative magnetizations, the non-conserved spin currents in a given $F$ region gives rise to net torques that can switch directions at particular magnetic configurations or $\Delta\varphi$ values. The details of the spin current behavior are shown to depend strongly on the degree of magnetic inhomogeneity in the system.

Ballistic Josephson junctions in edge-contacted graphene.

Hybrid graphene-superconductor devices have attracted much attention since the early days of graphene research. So far, these studies have been limited to the case of diffusive transport through graphene with poorly defined and modest-quality graphene/superconductor interfaces, usually combined with small critical magnetic fields of the superconducting electrodes. Here, we report graphene-based Josephson junctions with one-dimensional edge contacts of molybdenum rhenium. The contacts exhibit a well-defined, transparent interface to the graphene, have a critical magnetic field of 8 T at 4 K, and the graphene has a high quality due to its encapsulation in hexagonal boron nitride. This allows us to study and exploit graphene Josephson junctions in a new regime, characterized by ballistic transport. We find that the critical current oscillates with the carrier density due to phase-coherent interference of the electrons and holes that carry the supercurrent caused by the formation of a Fabry-Pérot cavity. Furthermore, relatively large supercurrents are observed over unprecedented long distances of up to 1.5 μm. Finally, in the quantum Hall regime we observe broken symmetry states while the contacts remain superconducting. These achievements open up new avenues to exploit the Dirac nature of graphene in interaction with the superconducting state.

Electrostatic tailoring of magnetic interference in quantum point contact ballistic Josephson junctions

The magnetoelectrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads, and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, continuous modification of the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity $h/2e$, whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent tunable structures that might lead to the study of the elusive Majorana fermions.

Resonant effects in ballistic Josephson junctions

We study the Josephson effect in ballistic double-barrier SINIS planar junctions, consisting of bulk superconductors (S), a clean normal metal or semiconductor (N), and insulating interfaces (I) modeled as a δ-function potential-energy barriers. We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency, the Fermi wave vectors mismatch, and for different effective band masses. The effect of transmission resonances on the Josephson current and on the normal conductance is analyzed for short junctions. Curvature of the temperature dependence of the critical Josephson current is related to the presence of resonances at the Fermi level and to the interfacial transparency. For thin semiconductor layers with negative effective masses of the carriers, finite interfacial transparency and large Fermi wave vectors mismatch we find that an unusual and significant enhancement of both the normal conductance and the critical Josephson current occurs at low temperatures due to the presence of an evanescent mode localized at interfaces.

Anomalous Josephson Current in Junctions with Spin Polarizing Quantum Point Contacts

We consider a ballistic Josephson junction with a quantum point contact in a two-dimensional electron gas with Rashba spin-orbit coupling. The point contact acts as a spin filter when embedded in a circuit with normal electrodes. We show that with an in-plane external magnetic field an anomalous supercurrent appears even for zero phase difference between the superconducting electrodes. In addition, the external field induces large critical current asymmetries between the two flow directions, leading to supercurrent rectifying effects.