Macroscopic quantum tunneling in unshunted Josephson junctions

Macroscopic quantum tunneling (MQT) in a Josephson junction (JJ) is considered. The typical I–V curve of a JJ is used for the expressions of the tunneling and thermal activation rates of the phase of a JJ in order to help clarify the role of the dynamical resistance in MQT in Josephson junctions. The participating parameters in the expressions of the rates are experimentally independently measurable.Work at the Technion was supported by the Lidow Chair of Solid State Physics and the Oren Carmi Abraham and Laura and Irving Steinhorn Visiting Professorship.     

Resonant macroscopic quantum tunneling in Josephson junctions

Many theoretical studies and some experiments have shown the possibility of several new secondary quantum effects in small Josephson junctions at low temperatures. We show that, within the well-established quantum picture of the junction, it is possible to experimentally observe sharp voltalge peaks at certain current values. Such peaks are related to a resonant macroscopic quantum tunneling between levels in neighboring wells of the proper washboard potential having close energies. The proposed experiment, with respect to experiments on Coulomb blockade or Block oscillations, requires a larger junction area, reducing the technological difficulties in making the samples.     

Quasiparticle tunneling in HTS grain boundary Josephson junctions

The quasiparticle tunneling (QPT) in YBa₂Cu₃O_7−δ (YBCO), Bi₂Sr₂CaCu₂O_8+x (BSCCO), Nd_1.85Ce_0.15CuO_x (NCCO) and La_1.85Sr_0.15CuO_4−δ (LSCO) grain boundary Josephson junctions (GBJs) has been studied. At voltages above the gap voltage V₉, the measured conductance vs. voltage, G(V), curves show a temperature independent parabolic shape allowing the determination of the effective height and thickness of the insulating grain boundary barrier. At |V|<V_g, the G(V)-curves are well fitted by a BCS density of states and temperature dependence of the energy gap, if a large broadening parameter Γ is assumed for the gap. The large Γ value most likely is related to the high density of localized states within the grain boundary barrier. Furthermore, a zero-bias conductance anomaly is observed which can be analyzed in terms of spin-flip and Kondo-type scattering at the interface (Anderson-Appelbaum model).     

Single-electron and Cooper-pair tunneling in ultrasmall Josephson junctions. Coulomb and environmental effects

We study the I-V curve of a small capacitance Josephson tunnel junction with a zero subgap conductance. In the limit of large external impedance and at low temperature, single electron tunneling across the junction is suppressed for eV < 2 + E_c due to a combination of superconducting and Coulomb gaps and the process of Cooper pair tunneling (CPT) plays the main role. For E _c , 2 Coulomb interaction between electrons of a tunneling Cooper pair strongly modifies the effective Josephson coupling energy and the CPT current can substantially deviate from its standard value. Very close to the point eV - 2 the effective tunneling time of a Cooper pair becomes very large and the CPT process is not adiabatic.     

Theory of self-resonant modes with zero external magnetic field in Josephson tunneling junctions

The effect of self-resonant modes in the absence of external magnetic fields in Josephson junctions is investigated by solving the Josephson equation. The method is based on the assumption of no external magnetic field but includes a dc bias and open-ended cavity boundary conditions. One finds a series of even-mode current singularities in the dc current-voltage characteristics. The method also provides theoretical explanations of the Q-value dependence (Q is the quality value in the resonance cavity) of the current singularities, the behavior of the cutoff voltage, and the maximum height of the first even-mode current singularities as found experimentally.     

Inelastic tunneling of Cooper pairs in c-direction in BSCCO single Josephson junctions and stacks

A reproducible fine structure at subgap voltages in the I(U)-characteristics of BSCCO single Josephson junctions and stacks has been observed and investigated. The structure is detectable only in the presence of an AC Josephson current. The overall form of the fine structure is in good agreement with the Raman scattering spectra of the optical phonon modes in this material. We attribute this structure to an inelastic (phonon assisted) tunneling of Cooper pairs, which is accompanied by the emission of coherent Raman-active optical phonons at resonance voltages U _res = _phon/2e. The observed structure can be explained in terms of a theoretical model developed by Maksimov, Arseyev and Maslova.     

Theory of the cos ø term in the Josephson tunneling current

The current-phase relation for the Josephson tunnel junction is investigated by using the time-dependent Ginzburg-Landau (TDGL) equations. The cos ø term is shown to have a negative coefficient and the same order of magnitude as the phase-independent term. The effect of the tunneling barrier is taken into account in terms of the boundary conditions of the order parameter and the electric potential at the junction; the new boundary conditions are derived by generalizing de Gennes' discussions for the dc Josephson effect to the time-dependent phenomena. The TDGL equations are solved on the assumption that the transmission coefficient across the junction is small enough and that the processes involved are quasi-stationary. It is concluded that the spatial and temporal variations of various quantities are of vital importance to an understanding of the nonequilibrium characteristics in the tunnel junction.     

Approximate analysis for stationary current flow in two-dimensional Josephson tunnel junctions

The stationary current distribution in Josephson tunnel junctions is discussed within the framework of an approximate linear analysis. It is shown that such an approach can provide very useful information also on the behavior of two-dimensional junctions. Self-limiting effects and the magnetic field dependence of the critical current for various geometries are discussed in some detail. The special case of a square junction is analyzed extensively.     

Spatial distribution of the maximum Josephson current in superconducting tunnel junctions

The distribution of the maximum Josephson current in two-dimensional tunnel junctions is investigated both theoretically and experimentally. Measurements of the Josephson current density are performed using low-temperature scanning electron microscopy. Josephson current densities are calculated by means of a numerical iteration procedure, which is presented in detail. These theoretical calculations are found to be essential for the correct interpretation of the measured Josephson current densities. Combining these experimental and theoretical methods, we investigate trapped transverse vortices. Further, the strength of the elementary pinning centers acting upon the trapped flux quanta is measured by recording the shift of the vortex position as a function of an applied Lorentz force. Ringlike vortices are also observed, and the influence of different current feed configurations on the Josephson current distribution is investigated.     

Critical current 0-pi transition in designed Josephson Quantum Dot junctions

We report on quantum dot based Josephson junctions designed specifically for measuring the supercurrent. From high-accuracy fitting of the current-voltage characteristics, we determine the full magnitude of the supercurrent (critical current). Strong gate modulation of the critical current is observed through several consecutive Coulomb blockade oscillations. The critical current crosses zero close to, but not at, resonance due to the so-called 0-pi transition in agreement with a simple theoretical model.     

Dynamics and phase transitions of Josephson junctions with dissipation due to quasiparticle tunneling

We investigate the dynamics and the phase diagram of Josephson junctions where the dissipation is due to quasiparticle tunneling. This system is formally equivalent to a one-dimensional X-Y model with easy axis and long-range interaction. It has a phase transition at a critical strength of the dissipation, which differs in several respects from the one encountered if the dissipation is Ohmic. Quantum effects are reduced, though not destroyed, above this transition. We discuss the response of a junction to an imposed current. In the linear regime Coulomb blockade is important; in the nonlinear regime under suitable conditions Bloch oscillations can occur.     

Spin-filter Josephson junctions

Josephson junctions with ferromagnetic barriers have been intensively investigated in recent years. Of particular interest has been the realization of so called π-junctions with a built-in phase difference, and induced triplet pairing. Such experiments have so far been limited to systems containing metallic ferromagnets. Although junctions incorporating a ferromagnetic insulator (I(F)) have been predicted to show a range of unique properties including π-shifts with intrinsically low dissipation and an unconventional temperature dependence of the critical current I(c), difficulties with the few known I(F) materials have prevented experimental tests. Here we report supercurrents through magnetic GdN barriers and show that the field and temperature dependence of I(c)is strongly modified by the I(F). In particular we show that the strong suppression of Cooper pair tunnelling by the spin filtering of the I(F) barrier can be modified by magnetic inhomogeneity in the barrier.     

Temperature dependence of the maximum Josephson current in Nb-NbO x -Sn junctions

The measured temperature variation of the maximum zero-field dc Josephson current for small Nb-NbO _x -Sn junctions falls slightly under the Ambegaokar-Baratoff theoretical curve for temperatures nearT _c(Sn). This is consistent with measurements on Nb-NbO _x -Pb junctions and may be due to proximity effects at the Nb surface.Work supported in part by the Gruppo Nazionale di Struttura della Materia.     

Quasiparticle trapping,excitation, and tunneling times in Josephson junctions with spatially inhomogeneous electrodes

On the basis of a microscopic model of the proximity effect in an SS'-sandwich we have calculated effective trapping, excitation, and tunneling rates of the reduced gap region in an SSISS junction as a function of temperature, voltage over the junction and strength of the proximity effect. We developed a simple model to describe the effect of magnetic fields on the gap of the superconductor, and calculated the trapping rate as function of the field. The experimentally determined gap reduction and quasiparticle loss times as function of the field were described in terms of this model.     

Strong coupling theory and the Josephson current into proximity high-T c junctions

The correlation between the order parameter and the energy gap is studied. Josephson junctions containing proximity systems are described within the framework of the strong coupling theory. The value of the current is affected by the difference between the order parameter at zero frequency and the energy gap. The proximity effect leads to depression of the Josephson current for the high-critical-temperature junctions.     

Magnetic field patterns in Josephson junctions

The critical currents of Pb/Ag/Pb Josephson junctions have been measured as a function of magnetic field and temperature in order to study the types of magnetic field distributions that occur in superconductor-normal metal-super-conductor (SNS) junctions. A study is made of the quantum interference regime near the critical temperature where the junction is filled with vortices and the crossover to Meissner-like behavior at low temperature occurs. Special emphasis is placed on the changes in effective area of the junction as the London and Josephson penetration depths change with temperature. A mapping of the crossover regime in the temperature-magnetic field plane is given.This work was supported by the office of Basic Energy Sciences of the Department of Energy.     

Measurement of the spatial distribution of the maximum Josephson current in superconducting tunnel junctions

The spatial distribution of the maximum Josephson current densityJ _max is imaged in quasi-one-dimensional in-line tunnel junctions by scanning the junction surface with an electron beam and by recording the beam-induced change ofI _max as a function of the coordinates of the beam focus. In addition to the modulation of the Josephson current density for the different vortex states, the nonlocal effect resulting from the beam-induced change of the phase-difference function is observed. The results are in good agreement with the theoretical predictions. The electron beam scanning technique also serves well for imaging inhomogeneities in the barrier or in the electrodes of the junction.     

Half-harmonic parametric oscillations in Josephson junctions

Half-harmonic generation in Josephson tunnel junctions and microbridges is investigated theoretically, numerically, and experimentally. It is found that such generation may take place both at zero voltage and on rf-induced steps in tunnel junctions, but not in microbridges. A simplified theory, which leads to the definition of a plasma resonance on rf-induced steps, is presented. The experiments are made on junctions with different current densities and with pump frequencies at 18 and 70 GHz.This work was supported by The Danish Natural Science Research Council, grants 511-8048, 511-10098, 511-10279, and 511-15059.     

Phase dependence of the superconducting current in YBCO Josephson junctions on a bicrystal substrate

Dependences of the amplitudes of the harmonic and subharmonic Shapiro steps on an external monochromatic signal were used to study the current-phase dependence of high-temperature superconducting junctions on a bicrystal substrate. It is shown that for a symmetric definition of the transport current across the junction with an edge transparency of the order of and a mirror-symmetric bicrystal interface, the current-phase dependence is close to sinusoidal which differs from the theoretical predictions and is most likely caused by twinning of the high-temperature superconducting films of the electrodes forming the junction. A departure from symmetry in the definition of the transport current across the junction causes the current-phase dependence to deviate from sinusoidal, which increases with increasing degree of asymmetry. This change in the current-phase dependence is accurately described by a model which takes into account the formation of coupled Andreev states in junctions of superconductors with a type of superconducting wave function. Pis’ma Zh. Tekh. Fiz. 25, 65–72 (November 26, 1999)