Superconducting tunneling without the tunneling Hamiltonian. II. Subgap harmonic structure

The theory of superconducting tunneling without the tunneling Hamiltonian is extended to treat superconductor/insulator/superconductor junctions in which the transmission coefficient of the insulating barrier approaches unity. The solution for the current in such junctions is obtained by solving the problem of a particle hopping in a one-dimensional lattice of sites, with forward and reverse transfer integrals that depend on the site. The results are applied to the problem of subgap harmonic structure in superconducting tunneling. The time-dependent current at finite voltage through a junction exhibiting subgap structure is found to have terms that oscillate at all integer multiples of the Josephson frequency,n(2eV/). The amplitudes of these new, and as yet unmeasured, ac current contributions as a function of voltage are predicted.     

Theory of the AC Josephson effect in triplet superconducting junction

The quasiparticle and AC Josephson current in superconductor / insulator / superconductor (S/I/S) junctions including a triplet p-wave superconductor are calculated for arbitrary transmission of the junction. As a triplet pairing state we select one of the unitary pairing states which is a promising candidate for the superconducting state in Sr ₂ RuO ₄ . In p-wave superconductor / insulator /p-wave superconductor junction, both quasiparticle current and AC Josephson current are enhanced near zero-bias voltage due to the existence of zero energy state of p-wave superconductors. For the s-wave superconductor/ insulator / p-wave superconductor junction, the quasiparticle current at low voltage is suppressed due to the energy gap of s-wave superconductor. The first Fourier component of the AC Josephson current vanishes due to the difference of the parity between the two superconductors.     

Josephson Current Through Planar Pb–Cu–Pb Nanobridges

We report on the fabrication and characterization of coplanar Pb–Cu–Pb nanobridges. In such superconductor (S) – normal metal (N) – superconductor junctions the Josephson coupling is mediated via the proximity effect at the S–N interface. For a junction in the dirty limit (ℓ≪ ξ _N where ℓ is the mean free path and ξ _N is the coherence length in N) the Josephson current I _c is proportional to L/ξ _N ·exp(−L/ξ _N ). The relation defines an upper limit for the length L of the normal-metal bridge in order to observe Josephson coupling. A Josephson current of up to 750 μA at 1.5 K was observed in junctions with L/ξ _N = 0.82 which is only 1/8 of the theoretically expected value. The reduction might originate from oxide layers at the normal metal – superconductor interfaces.     

The dc Josephson effect for superconducting proximity Kondo alloys

We calculate the maximum dc Josephson current I _Mof S-I-NX/S tunnel junctions, where N is a normal metal containing a low concentration c of magnetic impurities X in proximity with a superconducting film S. Our calculation shows a reentrant behavior of I _Mvs temperature T. A three-dimensional representation of f(I_M; T; c) = 0 is given.Laboratoire associé au CNRS.Research fellow of the Belgian IIKW.     

Investigations onNb/Al-AlO x -Al/Nb proximity tunneling junctions for X-ray detection

A new Nb/Al-AlO_x-Al/Nb trilayer process using a movable mechanical slit for junction-detector applications is described. Best junctions have a quality factor of 42 mV with a Josephson current density of 1200 A/cm ² at 4.2 K. The temperature dependence of the sub-gap current in the range of 0.45 to 4.2 K has been measured. Deviations from the thermally activated behavior due to imperfections in the tunneling barrier are observed. We compare our simple method with the usual whole wafer processes and we discuss the influence of proximity effects in these junctions in terms of the models proposed by Golubov et al. and by McMillan.     

The Order Parameter Susceptibility and Collective Modes of Superconductors

The spectrum of order parameter fluctuations of superconductors can be determined through the measurement of the wave-vector and frequency-dependent generalized susceptibility, or pair-field susceptibility. The determination of the pair-field susceptibility is conceptually similar to other susceptibility measurements. In the case of paramagnets at temperatures above a ferromagnetic transition, the susceptibility is determined by the linear response to a magnetic field. Because the superconducting order parameter is off-diagonal in number space, for superconductors there is no classical field analogous to a laboratory magnetic field. However, an effective field can be applied to a fluctuating superconductor across a tunneling barrier through the Josephson coupling of the rigid order parameter of a second superconductor well below its transition temperature. This leads to an observable dc contribution to the tunneling current that is a higher order, “incoherent” Josephson current. The magnitude of this current determines the susceptibility. Its frequency and wave-vector dependence are determined by the dc voltage across the junction and the dc magnetic field applied in the plane of the junction, respectively. In conventional superconductors near, but above their transition temperatures, measurements of the pair-field susceptibility have revealed a diffusive dynamics that can be described by a simple time-dependent Ginzburg–Landau equation. Measurements of the pair-field susceptibility below the transition temperature have revealed the existence of a gapless, propagating order parameter collective mode that becomes quickly overdamped as the temperature is reduced below T _c. The physics of these phenomena and the existing experiments will be reviewed. Opportunities for the application of these techniques to contemporary problems of high-temperature superconductors will be presented. Of particular interest are the possibilities for characterizing the nature of the pseudogap regime.     

Josephson parameters of bicrystal junctions of a new type based on metal oxide semiconductors

We have studied symmetric bicrystal Josephson junctions of a new type based on metal oxide superconductors in which the base planes are misoriented relative to the [100] direction by an angle within 22°–28°. These junctions exhibit record high values of the critical parameters at T = 77 K: the critical current density reaches I _C = (2−5) × 10⁵ A/cm² and the characteristic voltage is V _C = I _C R _N = 0.6−0.9 mV. The properties of the new junctions have been determined for the first time under the influence of monochromatic microwave radiation in the millimeter wavelength range and have been studied as functions of the magnetic field and temperature. The observed dependences of the critical current and the Shapiro step height on the electromagnetic field amplitude agree well with the theoretical predictions according to the resistive shunted junction model of the Josephson junction. The new junctions can be used in real superconducting devices operating at liquid nitrogen temperatures.     

Properties of niobium-based Josephson tunneling elements in junction microstructures

We describe the fabrication and electrical characteristics of niobium oxide-barrier tunnel junctions with counterelectrodes of lead/lead alloy. Primary attention is directed to the experimental conditions necessary to obtain high-quality tunnel barriers as well as studies on characterizing the atomic structure of the barrier region. In order to study the tunnel barrier homogeneity in the tunneling region the magnetic field dependence of the critical Josephson current is investigated. TheI–V characteristics and dependence of the critical Josephson current on temperature are analyzed quantitatively by using a proximity effect model. Finally, we discuss experimental results on the improvement of junction quality by including traces of carbon in the rf argon plasma during the sputter cleaning of niobium base electrodes.     

Reentrant superconducting transport behavior of single grain boundary Josephson junction in BaPb1−xBixO3 Bicrystals

Critical current and resistance of a single grain boundary in bulk bicrystals of the oxide superconductor BaPb_1–x Bi _x 0₃ show a reentrant behavior in the temperature region below critical temperature of single crystal blocks. We established that the reentrant behavior is related to intrinsic properties of a barrier of single grain boundary Josephson junctions in the bicrystals. Origin and structure of the tunneling barrier in the bicrystals under study are discussed.     

Experimental Studies to Realize Josephson Junctions and Qubits in Cuprate and Fe-based Superconductors

Cuprate superconductors are very promising in terms of Josephson junction device because of the large energy scale of high-T _c superconductivity. In particular, fabrication of qubits attracts lots of attention because of its primary importance for future computer technology. We will present some of our recent activities pointing to this purpose. (1) We succeeded in fabricating Josephson junction of cuprate without making any extra oxide barrier layer, rather putting Fe islands on the small strip of cuprate superconductors. This is very promising, since the fabrication of good Josephson junction was unsuccessful so far. Together with the introduction of the data, we discuss the possible mechanism of the weak-link fabrication in this structure. (2) We investigated the switching events in the I–V characteristics of the intrinsic Josephson junctions of Bi-cuprate superconductor, where macroscopic quantum tunneling (MQT) observation is well established recently. In addition to confirm the MQT for the first switching at 1 K in the multiple-branched current–voltage characteristics, we found that the temperature independence of the switching distribution for the second switching up to higher temperatures (10 K) is not due to the trivial Joule heating. We discuss the mechanism of the phenomena, including the possibility of MQT. (3) New Fe-based superconductors are also promising in terms of the application of superconductivity, since the anisotropy looks rather weak, in contrast to cuprates. We will introduce our trial to fabricate epitaxial thin films as the initial step to fabricate Josephson junction of this material.     

Phase Diffusion and Suppression of the Supercurrent by Quantum-Mechanical Fluctuations of the Josephson Plasma at Small Superconducting Point Contacts

The RCSJ model of resistively and capacitively shunted Josephson junctions is used to describe superconducting point contacts over a wide range of resistances up to the metallic–tunneling transition. Their small dynamic capacitance of order C = 0.1 fF due to the point-contact geometry results in a huge plasma frequency. The critical current is then strongly suppressed and the contact resistance becomes finite because of quantum-mechanical zero-point fluctuations of the Josephson plasma and the rather large escape rate out of the zero-voltage state due to quantum tunneling. We test the predictions of the RCSJ model on the classical superconductors lead, indium, aluminum, and cadmium.     

In situ epitaxial MgB2 thin films for superconducting electronics

The newly discovered 39-K superconductor MgB2 holds great promise for superconducting electronics. Like the conventional superconductor Nb, MgB2 is a phonon-mediated superconductor, with a relatively long coherence length. These properties make the prospect of fabricating reproducible uniform Josephson junctions, the fundamental element of superconducting circuits, much more favourable for MgB2 than for high-temperature superconductors. The higher transition temperature and larger energy gap of MgB2 promise higher operating temperatures and potentially higher speeds than Nb-based integrated circuits. However, success in MgB2 Josephson junctions has been limited because of the lack of an adequate thin-film technology. Because a superconducting integrated circuit uses a multilayer of superconducting, insulating and resistive films, an in situ process in which MgB2 is formed directly on the substrate is desirable. Here we show that this can be achieved by hybrid physical-chemical vapour deposition. The epitaxially grown MgB2 films show a high transition temperature and low resistivity, comparable to the best bulk samples, and their surfaces are smooth. This advance removes a major barrier for superconducting electronics using MgB2.     

A new type of biepitaxialc-axis tilted YBCO Josephson junction

A novel fabrication procedure of high critical temperature superconductor Josephson junctions (HTCSJJ) has been developed by a 90° rotation of YBa₂Cu₃O_7–x c-axis around an in-plane direction, on the basis of concepts of the biepitaxial technique. YBa₂Cu₃O_7–x grows oriented along (001) direction on a MgO seed layer deposited on a (110) SrTiO₃ substrate and along (110) direction on the bare substrate. Josephson junctions of good quality were obtained exhibiting RSJ behavior and features characteristic of HTCSJJ phenomenology. Even if not uniform, in some samples, the nature of the critical currentI _c is completely Josephson, as resulting from theI _c dependence on the applied magnetic field. The maximum measuredI _c R _N value atT=4.2K is 2mV.     

Tunneling and Phase-Sensitive Studies of the Pairing Symmetry in Sr2RuO4

Results obtained from several tunneling experiments on the pairing symmetry in Sr₂RuO₄ are reported. A normal surface layer was found to be present on the ab face of single-crystalline Sr₂RuO₄ in the c-axis tunnel junctions. Measurements in the in-plane junctions, however, revealed features suggesting a suppressed, but non-zero superconducting gap and Andreev bound states (ABSs) associated only with an unconventional superconductor. Josephson coupling between a conventional s-wave superconductor and Sr₂RuO₄ has been used to probe the pairing symmetry in the latter, through both the selection rule and the phase sensitive experiments. All results indicate that Sr₂RuO₄ is unconventional, most likely spin-triplet superconductor. Finally, some recent studies of several newly-characterized ruthenates are reviewed.     

On‐Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb–In0.75Ga0.25As‐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–In_0.75Ga_0.25As‐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 In_0.75Ga_0.25As 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 In_0.75Ga_0.25As‐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 In_0.75Ga_0.25As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb–In_0.75Ga_0.25As–Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.     

Tunneling Conductance in Strained Graphene-Based Superconductor: Effect of Asymmetric Weyl–Dirac Fermions

Based on the BTK theory, we investigate the tunneling conductance in uniaxially strained graphene-based normal metal (NG)/barrier (I)/superconductor (SG) junctions. In the present model, we assume that by depositing the conventional superconductor on the top of the uniaxially strained graphene, normal graphene may turn to superconducting graphene with the Cooper pairs formed by the asymmetric Weyl–Dirac electrons, the massless fermions with direction-dependent velocity. The highly asymmetrical velocity, v _y /v _x ≫1, may be created by strain in the zigzag direction near the transition point between gapless and gapped graphene. In the case of highly asymmetrical velocity, we find that the Andreev reflection strongly depends on the direction of strain, and the current perpendicular to the direction of strain can flow through the junction as if there were no barrier. Also, the current parallel to the direction of strain anomalously oscillates as a function of the gate voltage with very high frequency. Our predicted result is quite different from the feature of the quasiparticle tunneling in the unstrained graphene-based NG/I/SG conventional junction. This is because of the presence of the direction-dependent-velocity quasiparticles in the highly strained graphene system.     

Low Temperature Properties and Superconductivity of LuB12

We have investigated the low temperature properties of LuB₁₂ by measuring its magnetic susceptibility, heat capacity, and electrical resistivity, as well as by point-contact spectroscopy using both the spear-anvil type technique and mechanically controllable break junctions. Our specific heat measurements and point - contact spectroscopy results indicate that LuB₁₂ is a simple weak-coupling BCS-type superconductor with T_C ≈ 0.4 K, a superconducting energy gap of 2 Δ ≈ 0.12 meV, and a very small critical field B_C ≈ 1 mT. From the dU/dI(U) characteristics in the superconducting state, the energy gap 2Δ, the critical current I_C and the Andreev-reflection excess current I_ex as a function of normal-state point contact resistance R_N have been determined. At low R_N all three parameters are strongly suppressed, possibly due to the self-magnetic field. At contacts with large R_N the model of resistively and capacitively shunted Josephson junctions (RCSJ) allowed us to estimate the superconducting current plasma frequency and the Josephson coupling energy. Moreover, from the d²U/d I²(U) spectra in the normal state the (point-contact) electron-phonon interaction function and the characteristic phonon energies of LuB₁₂ have been determined.     

Macroscopic Quantum Phenomena in High Critical Temperature Superconducting Josephson Junctions

YBa₂Cu₃O_7?δ grain boundary bi-epitaxial Josepshon junctions (JJs) allow a very clear demonstration of Josephson current variation with the misorientation angle, consistent with the d-wave symmetry of the superconducting order parameter in cuprate, high temperature superconductors. Our bi-epitaxial junctions show a strong suppression of the first harmonic, I ₁ sin ø, of the current phase relation when tunneling from a lobe into a node of the superconducting gap function. In these configurations, the contribution of the second harmonic, I ₂ sin 2ø, becomes of the same magnitude as the first one, giving rise to a characteristic two-well Josephson potential as a function of phase ø instead of the usual single well. This characteristic intrinsic property has suggested proposals of a new class of qu-bit named “quiet” because of the existence a spontaneously degenerate fundamental state without the need of applying an external field. Our experiments probe the macroscopic quantum properties in a d-wave Josephson junction by measuring macroscopic quantum tunneling and energy level quantization. The switching current out of the zero voltage state is measured as a function of temperature down to 20 mK. The temperature variation of the width of an ensemble of switching events goes over from one, which is characteristic of a thermal activation of phase fluctuations to a temperature independent width which is a token of quantum tunneling of the phase. The transition regime is affected by the two-well potential in a 45^° misorientation junction as the second harmonic term gives rise to additional thermal transitions. The difference between quantized energy levels in the harmonic potential was determined by microwave spectroscopy. From the broadening of energy levels, it was possible to extract a Q-value of about 40 for the phase oscillations. The relatively high Q indicates quantum coherence over a sizeable time in d-wave junctions and gives hopes for a realization of a “quiet” high-T _c qu-bit. The contributions of V. L. Ginzburg to several different fields of physics are impressive and long standing. In superconductivity the Ginzburg–Landau theory, for instance, still represents a very powerful approach to model a huge number of different physical systems. High Temperature Superconductors (HTS) have strongly influenced research of the last 20 years and their d-wave order parameter symmetry represents one of the most intriguing features from both the fundamental point of view and some types of innovative long-term applications.     

A new type of biepitaxialc-axis tilted YBCO Josephson junction

A novel fabrication procedure of high critical temperature superconductor Josephson junctions (HTCSJJ) has been developed by a 90° rotation of YBa₂Cu₃O_7?x c-axis around an in-plane direction, on the basis of concepts of the biepitaxial technique. YBa₂Cu₃O_7?x grows oriented along (001) direction on a MgO seed layer deposited on a (110) SrTiO₃ substrate and along (110) direction on the bare substrate. Josephson junctions of good quality were obtained exhibiting RSJ behavior and features characteristic of HTCSJJ phenomenology. Even if not uniform, in some samples, the nature of the critical currentI _c is completely Josephson, as resulting from theI _c dependence on the applied magnetic field. The maximum measuredI _c R _N value atT=4.2K is 2mV.     

Superconducting Energy Gap Features of FeSe Investigated by Tunneling Spectroscopy on Planar Junctions

Planar tunneling junctions of the presumably unconventional superconductor FeSe were prepared and investigated. The junctions consisted of rf-sputtered FeSe/AlO _x /Ag multilayers patterned lithographically into mesa structures. Bias voltage-dependent differential conductivities dI/dV(V) of junctions in the tunneling, intermediate barrier strength, and metallic regimes were investigated. Depending on the barrier type between two to four features of the conductivity were obtained, which are discussed in the framework of multiple superconducting energy gaps. Specifically, we reproduced with all barrier types two established energy gaps and identified another feature as presumably originating from an additional large superconducting gap. A further conductivity feature could be associated with a resonant state.