Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current–voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.     

Spatial AC Josephson effect

Investigating the current threshold in the mixed state of superconductors basing on the Ginzburg-Landau theory, we find that the threshold is determined by a mechanism analogous to the Josephson effect. An experimental evidence of this phenomenon is presented.     

Josephson effect in nuclear reactions

The transfer of Cooper pairs during the scattering of two superfluid nuclei just below the Coulomb barrier is discussed on a phenomenological and a microscopic level. This transfer is analogous to the Josephson current between two superconductors. Candidates for the observation of such an effect are heavy ions with a small difference in mass number. Numerical estimates are presented.     

Josephson effect in fulde-ferrell-larkin-ovchinnikov superconductors

Because of the difference in the momenta of the superconducting order parameters, the Josephson current in a Josephson junction between a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor and a conventional BCS superconductor is suppressed. We show that the Josephson current may be recovered by applying a magnetic field in the junction. The field strength and direction at which the supercurrent recovery occurs depend upon the momentum and structure of the order parameter in the FFLO state. Thus the Josephson effect provides an unambiguous way to detect the existence of an FFLO state, and to measure the momentum of the order parameter.     

Josephson effect in ferromagnetic superconductors

The DC Josephson effect in ferromagnetic superconductors is theoretically studied in the presence of external magnetic fields. In addition to the usual term for the Josephson tunneling current, a new term expressing the pair tunneling current induced by the magnetization appears. The amplitude and period of the Fraunhofer pattern of the maximum Josephson current drastically diminish near the phase transition temperature for the magnetization bound around the junction.     

Higher harmonics in the Josephson effect

In the low temperature regime where macroscopic flux tunneling allows a SQUID magnetometer to follow the stable thermodynamic free energy without hysteretic dissipation, it is possible to exhibit macroscopic quantum behaviour via higher Josephson harmonic oscillations in the thermal response. A simple theory is presented here; the experimental data will appear elsewhere.     

Josephson effect through a ferromagnetic layer

We report transport measurements on Superconductor/Ferromagnet/Superconductor (S/F/S) junctions: Nb/Al/Gd/Al/Nb where gadolinium (Gd) is a weakly polarized ferromagnet. A sizeable critical current I _c is observed in the I(V) characteristics. This current can be modulated by a weak magnetic field, as expected for a Josephson current. With these experiments, we establish that superconducting coherent transport survives across a small ferromagnetic layer. The penetration depth of Cooper pairs in Gd has been measured. An extensive study of the Josephson critical current in temperature for different thicknesses of magnetic compounds is presented. A comparison of transport measurements with S/N/S junction is given through measurements made on Nb/Al/Y/Al/Nb, where yttrium (Y) is used as non magnetic rare earth metal. Received 20 September 2000 and Received in final form 22 February 2001     

Josephson effect on YBCO break junctions

We have investigated dc and ac Josephson effects on YBa₂Cu₃O_7–x ceramic samples using the break junction technique. The critical current was measured as a function of external magnetic field and temperature. The field dependence shows superposition effects of junction and SQUID behavior. The critical current depends linearly on temperature like for SNS junctions. We observed Shapiro steps with microwave radiation with a frequency of 35 GHz at 4.2 K and 77 K, respectively. Deviations of the step height from Bessel behavior at low microwave power are explained within the Stewart-McCumber model using small capacitances of the junction in simulation calculations.     

Josephson effect in coherent roton aggregates

A localized microwave electromagnetic field in liquid helium behaves as a laser of rotons: it produces a coherent roton aggregate. We show that the whispering gallery mode of the dielectric resonator excites multiple coherent aggregates simultaneously and predict a Josephson effect between them. The superfluid velocity around the resonator acts as a “voltage across the weak link” in superconducting Josephson junctions. Josephson frequency-velocity relation agrees with existing experimental data.     

Novel Josephson effect in triplet-superconductor-ferromagnet-triplet-superconductor junctions

We predict a novel type of Josephson effect to occur in triplet-superconductor-ferromagnet-triplet-superconductor Josephson junctions. We show that the Josephson current, IJ, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional sign change of IJ with increasing temperature.     

Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.     

Magnetic-thermoelectric effect in Josephson SNS junction

A response of the Josephson SNS junction to a heat flow and to an electric current has been studied with the same junction. A non-monotonous dependence of a critical heat flow on the magnetic field B_e is discovered. This dependence is found to be completely identical with the measured function I_c(B_e).     

Josephson effect between nanoclusters in resonance conditions

A general expression is derived for the Josephson current between nanoclusters. It is shown that, in the resonance conditions between electron levels of clusters, the expression for the current obtained in the tunnel Hamiltonian model becomes invalid. In the case of degeneracy or close to degeneracy of energy levels in isolated clusters, the critical Josephson current may exceed the value obtained in the model of tunnel Hamiltonian in the large parameter, viz., the ratio of the order parameter |Δ| to the distance between the resonance level and the levels closest to it.     

Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(?) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.     

Strong-coupling topological Josephson effect in quantum wires

We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ～ ± cos(?/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value gc [Formula: see text]. At this point the Josephson energies have the principal values [Formula: see text], where m =- 1,0,1 and σ =± 1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with an odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels.     

Josephson effect through an isotropic magnetic molecule

We study the Josephson effect through a quantum dot magnet whose spin is isotropic and which is coupled to the dot electron spin via exchange coupling. We calculate the Andreev levels and the supercurrent and examine the intertwined effect of the exchange coupling, Kondo correlation, and superconductivity. The former suppresses Kondo correlations, which triggers phase transitions from the 0 to the pi state, but strong antiferromagnetic coupling restores the 0 state. The asymmetric phase diagram in the exchange coupling suggests that the coupling sign could be determined in experiments.