Ambegaokar-Baratoff Relation Research Articles

Violation of the Ambegaokar–Baratoff Relation in Dirty S–I–S Junctions

It has been shown that the presence of narrow-gap quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator layer) superconductor–insulator–superconductor (S–I–S) junctions results in a significant deviation of the critical supercurrent (Josephson current) in the temperature range 0 ≤ T ≤ Tc (Tc is the superconducting transition temperature in the S shores of the junction) from the value given by the known Ambegaokar–Baratoff relation. It has been found that the character of this deviation changes at a certain nonzero temperature Tb < Tc: this deviation is negative at 0 ≤ T< Tb (deficiency of the supercurrent), whereas it is positive at Tb< T ≤ Tc (excess of the supercurrent). Estimates indicate that experimental manifestation of this effect can be detected.

Josephson Tunneling Behaviors in NbN/AlN/NbN Junctions with an Ultrathin NbN Film

We fabricated epitaxial NbN/AlN/NbN tunnel junctions with an ultrathin NbN film as the base layer on single-crystal MgO (100) substrates. The measured thickness of the base layer was 4.7 nm. By measuring the electrical characteristics of the junctions, we showed that the junction had excellent Josephson tunneling properties, with a large gap voltage, a small gap voltage width, and a quality factor Rsg/RN of 42 at 4.2 K. The temperature dependence of the critical current for the junctions agreed with a theoretical calculation using the Ambegaokar-Baratoff relation over the temperature range of 3-12 K. An ideal Fraunhofer diffraction pattern appeared for the Josephson critical current as a function of magnetic field. Fiske steps were observed in current-voltage characteristics of the Josephson junctions at different applied magnetic field.

Effect of Quantum Jumpers on the Critical Supercurrent in Dirty S–I–S Junctions

It has been shown that the presence of narrowband quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator (I) layer) S–I–S (S is a superconductor) junctions at the temperature T = 0 significantly reduces the critical supercurrent (Josephson current) as compared to the value given by the known the Ambegaokar–Baratoff relation. The performed estimates have shown the possibility of the experimental manifestation of this effect.

Effect of Deuterium Interactions with Lattice Defects on Superconducting PdDxSystem

Results are presented for the current–voltage characteristics of PdDx, which shows a partial superconducting (SC) transition at Tc ∼ 7 K. The temperature dependence of the critical current is well fitted by the Ambegaokar–Baratoff relation, suggesting the existence of Josephson junctions between the SC grains. The effect of deuterium interactions with defects on the SC state in the PdDx system is discussed.

Josephson current between topological and conventional superconductors

We study the stationary Josephson current in a junction between a topological and an ordinary (topologically trivial) superconductor. Such an S-TS junction hosts a Majorana zero mode that significantly influences the current-phase relation. The presence of the Majorana state is intimately related with the breaking of the time-reversal symmetry in the system. We derive a general expression for the supercurrent for a class of short topological junctions in terms of the normal state scattering matrix. The result is strongly asymmetric with respect to the superconducting gaps in the ordinary ($\Delta_0$) and topological ($\Delta_{\mathrm{top}}$) leads. We apply the general result to a simple model of a nanowire setup with strong spin-orbit coupling in an external magnetic field and proximity-induced superconductivity. The system shows parametrically strong suppression of the critical current $I_c \propto \Delta_{\mathrm{top}}/R_N^2$ in the tunneling limit ($R_N$ is the normal state resistance). This is in strong contrast with the Ambegaokar-Baratoff relation applicable to junctions with preserved time-reversal symmetry. We also consider the case of a generic junction with a random scattering matrix and obtain a more conventional scaling law $I_c \propto \Delta_{\mathrm{top}}/R_N$.

Quantum waveguide theory of the Josephson effect in multiband superconductors

We formulate a quantum waveguide theory of the Josephson effect in multiband superconductors, with special emphasis on iron-based materials. By generalizing the boundary conditions of the scattering problem, we first determine the Andreev levels spectrum and then derive an explicit expression for the Josephson current which generalizes the formula of the single band case. In deriving the results, we provide a second quantization field theory allowing to evaluate the current-phase relation and the Josephson current fluctuations in multiband systems. We present results for two different order parameter symmetries,namely $s_\pm$ and $s_{++}$, which are relevant in multiband systems. The obtained results show that the $s_\pm$ symmetry can support $\pi$ states which are absent in the $s_{++}$ case. We also argue a certain fragility of the Josephson current against phase fluctuations in the $s_{++}$ case. The temperature dependence of the Josephson critical current is also analyzed and we find, for both the order parameter symmetries, remarkable violations of the Ambegaokar-Baratoff relation. The results are relevant in view of possible experiments aimed at investigating the order parameter symmetry of multiband superconductors using mesoscopic Josephson junctions.

Superconducting Memristors

In his original work Josephson predicted that a phase-dependent conductance should be present in superconducting tunnel junctions, an effect difficult to detect, mainly because it is hard to single it out from the usual non-dissipative Josephson current. We propose a solution for this problem that consists in using different superconducting materials to realize the two junctions of a superconducting interferometer. According to the Ambegaokar-Baratoff relation the two junctions have different conductances if the critical currents are equal, thus the Josephson current can be suppressed by fixing the magnetic flux in the loop at half of a flux quantum without cancelling the phase-dependent conductance. Our proposal can be used to study the phase-dependent conductance, an effect present in principle in all superconducting weak links. From the standpoint of nonlinear circuit theory such a device is in fact an ideal memristor with possible applications to memories and neuromorphic computing in the framework of ultrafast and low energy consumption superconducting digital circuits.

Transport properties in FeSe0.5Te0.5 nanobridges

FeSeTe nanobridges of different widths have been fabricated on MgO substrates using focused ion beams. These nanobridges exhibit the Josephson effects. The current-voltage curves of junctions with 248–564 nm wide follow the resistively and capacitatively shunted junction model. Shapiro steps under microwave radiation were clearly observed in these nanobridges. The products of the critical current and normal state resistance (IcRn) are remarkably high. The temperature dependence of IcRn product followed the Ambegaokar-Baratoff (A-B) relation. The value of energy gap of FeSeTe calculated from the A-B relation is 3.5kBTc. The nanobridge junctions have a strong potential for high frequency applications.

Josephson effect in a CeCoIn5 microbridge

We report DC Josephson effects observed in a microbridge prepared from an individual crystalline growth domain of CeCoIn5 thin film. Josephson effects were observed by periodic voltage modulations under external magnetic field ΔV(B) with the expected periodicity and by the temperature dependence of the Josephson critical current Ic(T). The shape of ΔV(B) was found to be asymmetric, as it is expected for microbridges. The dependence Ic(T) follows the Ambegaokar–Baratoff relation, which is unexpected for microbridges. Features in the dynamical resistance curves were attributed to the periodic motion of Abricosov vortices within the microbridge.

Josephson effect in CeCoIn5microbridges as seen via quantum interferometry

A superconducting quantum interference device (SQUID) was prepared on a micron-sized single crystal using a selected growth domain of a thin film of $CeCoIn_5$ grown by molecular beam epitaxy. SQUID voltage oscillations of good quality were obtained as well as interference effects stemming from the individual Josephson microbridges. The transport characteristics in the superconducting state exhibited several peculiarities which we ascribe to the periodic motion of vortices in the microbridges. The temperature dependence of the Josephson critical current shows good correspondence to the Ambegaokar-Baratoff relation, expected for the ideal Josephson junction. The results indicate a promising pathway to identify the type of order parameter in $CeCoIn_5$ by means of phase-sensitive measurements on microbridges.

Ambegaokar-Baratoff relations for Josephson critical current in heterojunctions with multigap superconductors

An extension of the Ambegaokar-Baratoff relation to a superconductor-insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Appling the resultant relation to a SIS Josephson junction formed by an iron-based (five-band) and a single-band Bardeen-Cooper-Schrieffer (BCS) type superconductors, a theoretical bound of the Josephson critical current ($I_{\rm c}$) multiplied by the resistance of the junction ($R_{\rm n}$) is given. We reveal that such a bound is useful for identifying the pairing symmetry of iron-pnictide superconductors. One finds that if a measured value of $I_{\rm c}R_{\rm n}$ is smaller than the bound then the symmetry is $\pm s$-wave, and otherwise $s$-wave without any sign changes. In addition, we stress that temperature dependence of $I_{\rm c}R_{\rm n}$ is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.

Universal resistance capacitance crossover in current-voltage characteristics for unshunted array of overdamped Nb–AlOx–Nb Josephson junctions

We report on some unusual behavior of the measured current-voltage characteristics (CVC) in artificially prepared two-dimensional unshunted array of overdamped Nb–AlOx–Nb Josephson junctions. The obtained nonlinear CVC are found to exhibit a pronounced (and practically temperature independent) crossover at some current Icr=(1/2βC−1)IC from a resistance R dominated state with VR=RI2−IC2 below Icr to a capacitance C dominated state with VC=ℏ/4eCI−IC above Icr. The origin of the observed behavior is discussed within a single-plaquette approximation assuming the conventional resistively shunted junction model with a finite capacitance and the Ambegaokar–Baratoff relation for the critical current of the single junction.

Study of the Josephson Current of ${\rm MgB}_{2}/{\rm Insulator/Pb}$ Tunnel Junctions

We have fabricated MgB2/Insulator/Pb Josephson tunnel junctions on MgB2 films deposited by hybrid physical-chemical vapor deposition using native oxide as the tunnel barrier. For the critical current of the junction on MgB2 (0001) film, its temperature dependence follows the Ambegaokar-Baratoff relation and its magnetic field dependence exhibits a Fraunhofer pattern. From analysing the magnetic field dependence of the critical current of the junction on c-axis tilted MgB2 film, we find small contribution of the Josephson current from the ab-plane tunneling, which may suggest a pi phase difference between the order parameters of MgB2pi and sigma bands.

Resistance and current-voltage characteristics of individual superconductingNbSe2nanowires

Resistance and current-voltage characteristics of individual superconducting $\mathrm{Nb}{\mathrm{Se}}_{2}$ nanowires are investigated. In the current-voltage curves, a stairlike structure is observed, indicating the possible formation of phase-slip centers. A close examination of the current-voltage characteristic in a selected high quality $\mathrm{Nb}{\mathrm{Se}}_{2}$ nanowire with a diameter of $75\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ reveals that the characteristic voltages in the stairlike structure follow the BCS-like temperature dependence of superconducting gaps vanishing at ${T}_{C}$. While the phase-slip center mechanism remains to be a plausible explanation of the observed features, an alternative model involving multigap Josephson tunneling is proposed to account for the BCS-like temperature dependence. From the BCS fits, two distinct superconducting gaps are extracted. Moreover, the critical current of the $75\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanowire at low temperatures as well as near ${T}_{C}$ can also be described by the Ambegaokar-Baratoff relation for multigap Josephson junctions. Our data suggest the possible observation of multiband superconductivity in $\mathrm{Nb}{\mathrm{Se}}_{2}$ and are in good agreement with the predictions of recent band structure and Fermi surface calculations on $\mathrm{Nb}{\mathrm{Se}}_{2}$.

Fabrication of niobium tunneling junctions for X-ray detection with a magnetic barrier

We fabricated Nb-based superconducting tunneling junctions (STJs) with a structure of Nb/Al–AlOx/NiOx/AlOx/Al/Nb on silicon substrates, having NiOx as a magnetic barrier, for use in X-ray detectors. In the STJs with Ni deposited onto oxidized Al, the subgap leak current was observed to be large, which probably is the result of the island-growth of Ni on the AlOx. On the other hand, in the junctions with Ni deposited on the metallic Al layer and oxidized together with the Al layer below, the current–voltage characteristics of a sharp gap structure were obtained. The magnitude of dc Josephson current (Ic) for all these junctions was suppressed to ∼5% of the magnitude theoretically predicted by the Ambegaokar–Baratoff relation.

Intrinsic Josephson junctions in c-axis-oriented La1.85Sr0.15CuO4 thin films

We investigated current–voltage characteristics (IVCs) of intrinsic Josephson junctions (IJJs) for c-axis oriented La1.85Sr0.15CuO4 thin films. We fabricated IJJs with two kinds of structures. One was a mesa structure with a junction area of 22–194 μm2 fabricated by using conventional photolithography and Ar-ion milling, and the other was a microbridge structure with a junction area of 1.1–3.6 μm2 fabricated by using a focused-ion-beam technique. The mesa-type IJJs exhibited resistively-shunted-junction-like IVCs with no hysteresis. The temperature dependence of their critical current followed the Ambegaokar–Baratoff relation. IVCs of the microbridge-type IJJs, on the other hand, exhibited voltage jump and clear hysteresis. The different behaviors between the mesa-type and the microbridge-type IJJs were explained by the different numbers of grain boundaries involved in the IJJs.

Josephson Effect in d-Wave Superconductor Junctions in a Lattice Model

Josephson current between two d-wave superconductors is calculated by using a lattice model. Here we consider two types of junctions, $i.e.$, the parallel junction and the mirror-type junction. The maximum Josephson current $(J_{c})$ shows a wide variety of temperature ($T$) dependence depending on the misorientation angles and the types of junctions. When the misorientation angles are not zero, the Josephson current shows the low-temperature anomaly because of a zero energy state (ZES) at the interfaces. In the case of mirror-type junctions, $J_c$ has a non monotonic temperature dependence. These results are consistent with the previous results based on the quasiclassical theory. [Y. Tanaka and S. Kashiwaya: Phys. Rev. B \textbf{56} (1997) 892.] On the other hand, we find that the ZES disappears in several junctions because of the Freidel oscillations of the wave function, which is peculiar to the lattice model. In such junctions, the temperature dependence of $J_{c}$ is close to the Ambegaokar-Baratoff relation.

Structures and intrinsic Josephson tunnel junctions of (Bi 1 - xPb x) 2Sr 2CaCu 2O y single crystals

The effect of Pb-substitution on the crystal structures and current-voltage characteristics in the c-direction of Bi 2Sr 2CaCu 2O y (BSCCO) and (Bi 1 - x Pb x ) 2Sr 2CaCu 2O y (BPSCCO) (with x ≤ ∼ 0.25) single crystals is investigated. The Bi-type incommensurate modulation structure of the BSCCO single crystal is confirmed, and the modification and then disappearance of this structure with an increase in Pb content in the BPSCCO single crystlas are observed. For mesas of these single crystals which exhibit multiple branching in their I− V characteristics, and hence are composed of stacked intrinsic Josephson tunnel junctions, the critical current densities J c are discussed with respect to the structural modulation, suppressed energy gaps Δ and normal resistances R n on the basis of the Ambegaokar-Baratoff relation.

Microscopic theory of the dc Josephson effect in clean superconductor/insulator and superconductor/semiconductor multilayers

We have constructed a fully microscopic self-consistent theory of the dc Josephson effect in clean periodic superconducting multilayers with realistic finite-size repulsive barriers, at arbitrary temperatures. We have derived an explicit analytical expression for the critical Josephson current j{sub c} as a function of the superconductor-layer thickness a. In the limit a{lt}{xi}{sub 0}, we have found fundamental differences with the Ambegaokar-Baratoff relation: a strong reduction of j{sub c} and an unusual temperature dependence. In this limit, we also predict an exponential decrease of the critical temperature and the gap parameter due to the depairing effect of the Josephson current. {copyright} {ital 1997} {ital The American Physical Society}

Intrinsic Josephson effect devices of TI-2212 thin films

Intrinsic Josephson effect devices from Tl2Ba2CaCu2O8 (Tl-2212) thin films were investigated. The device was produced by epitaxially growing a Tl-2212 thin film on a LaAlO3 substrate with the surface cut at a small angle to the LaAlO3(001) plane, and by patterning a microbridge in the proper direction. The I–V characteristics of the microbridges exhibit large hysteresis at low temperatures, and the temperature dependence of the critical current Ic(T) is in good agreement with the theoretical Ambegaokar–Baratoff relation for superconductor–insulator–superconductor (SIS) junctions. The I–V curves also show multibranches for longer microbridges.