Josephson critical current

It would be interesting to carry out experiments on S/F structures with non-collinear magnetization in order to observe this new type of superconductivity. As follows from a semiquantitative analysis, the best conditions to observe the Josephson critical current caused by the TC are high interface transparency (small y ) and low temperatures. These conditions are a bit beyond our quantitative study. Nevertheless, all qualitative features predicted here (angle dependence, etc) should remain in a general case when one has to deal with the non-linear Usadel equation. 

The first kind of approaches is to investigate the diiferential conductance (d//dF) spectrum with various geometries in SIN or SIS junctions. The other type is to measure the dependence of the Josephson critical current J), as a function of plied magnetic field. 

Fratonhofer-like. The Josephson critical current oscillates according to the following equation ... 

Wollman et al. (1993, 1995) reported detailed measurements of the magnetic field dependence of the Josephson critical current for Y123/Au/Pb junctions formed on Y123 crystals. The observed results of the dependences for the edge junction and the corner junction are as shown in fig. 28. Double peak stmetures were seen for the comer junction, as expected from equation (5), indicating that Y123 is a d-wave superconductor. 

Figure 30 shows the Josephson critical current measured under external fields along different directions. With the field perpendicular to the twin boundary (j> 90° in the figure), the plot of the critical current exhibited the same Fraunhofer pattern as observed in an ordinary junction, except for a lower peak current. With the field parallel to the boundary = 0), a dip rather than a peak appeared at zero field B = 0), and the maximum current occurred at a field value corresponding to half-integer quantum flux, These observations indicate that the flux cancels the phase difference between the two domains and causes a current flow in the same direction. These observations indicate that Y123 favors d-wave symmetry with some s-wave admixture. 

Figure 4 Dependence of Josephson critical current density on the thickness of the MgO tunnel barrier.

The limitation on critical currents has been discussed by J. Clem (49) as due to weak link or Josephson coupling between grains. 

The switching between states, a characteristic of Josephson junctions, is applicable to binary-based logic circuits there is no voltage across the junction for currents below the critical current 7C, but one appears for currents greater... 

In 2001, groups in Chemogolovka / Leiden and Orsay showed that with weak ferromagnets it is possible to make SFS- and SFIS-contacts (with I to be an insulating barrier) in which critical currents and density of states exhibit oscillations as a function of temperature or F layer thickness. Thus for the first time the existence of Josephson r-junctions had been confirmed experimentally [12,13]. This breakthrough led to a host of theoretical and experimental activities, and several new concepts [1-4]. 

In conclusions, we believe that a use of FNF multilayer as a building block of SF spin valves opens an opportunity for effective control of magnitude and sign of Josephson junction critical current. Utilization of FNF multilayers also opens a way to engineering non Josephson spin valve devices. 

Figure 9 Dependence of the critical current on the external magnetic field from 21 K to 33 K, for the sample of Fig. 8. A clear phase shift of ix is observed at the same threshold temperature for which a minimum of the Josephson current is achieved.

We now give a more quantitative discussion of the Josephson effect. Suppose that a Josephson junction is connected to a de current source (Figure 4.6.2), so that a constant current I >0 is driven through the junction. Using quantum mechanics, one can show that if this current is less than a certain critical current, no voltage will be developed across the junction that is, the junction acts as if it had zero resistance However, the phases of the two superconductors will be driven apart to a constant phase difference 0 = 0 - 0, where 0 satis-... 

Before analyzing (4), we mention some typical parameter values for Josephson junctions. The critical current is typically in the range I I /zA- 1 mA, and a typical voltage is I R 1 mV. Since le/h 4,83 x 10 " Hz/V, a typical frequency is on the orderof lO" Hz. Finally, a typical length scale for Josephson junctions is around 1 (im, but this depends on the geometry and the type of coupling used. 

It was possible to correlate the measured electrical properties of the films deposited on different types of steps with the value of the step angle [13.20, 13.21]. Optimum properties for the fabrication of Josephson devices require high-angle steps in the substrate. In contrast, low-angle steps allow the fabrication of electrical interconnects and crossovers where a reduction of the critical current density has to be avoided. 

Fig. 27. (a) Fraimhofar diffiaction pattern for the critical current vs magnetic flux threading the junction barrier that is characteristic of a single Josephson tunnel Junction, (b) Diffraction patterns expected for a single corner Junction with s-wave (isotropic or anisotropic) and dj,2 2 pairing symmetry. After Wollman et al. (1995, fig. 1). 

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