Josephson current

The property of the spin-triplet components fi,2,z un) = — /i,2,3(—w ) means that their presence is not easy to observe. For example, the order parameter A is related to the sum X n=-oo /(wn) in which all contributions of the odd functions f 1,2,3 cancel. However, there are phenomena where the presence of the spin-triplet pairing plays a crucial role. One of them is the effect of the Tc dependence on the mutual orientation of magnetizations in the F/S/F structure. Another one is the predicted long-range proximity effect based on the spin-triplet component, which should lead to a Josephson current in F/S/F/S structures with anomalously thick F-layers.[10] The latter is relevant for experimental results of Ref. [5]. 

Summary. We consider the Josephson effect in a ballistic Superconductor/ Quantum Wire/ Superconductor junction. It is shown that the interplay of chiral symmetry breaking generated by Rashba spin-orbit interaction and Zeeman splitting results in the appearance of a Josephson current even in the absence of any phase difference between the superconductors. 

The Josephson current, being an equilibrium supercurrent between two superconductors, can be calculated from the general thermodynamical relation... 

Knowing explicitly the energy spectrum Eq. (5), it is straightforward to evaluate the Josephson current. It takes the form... 

At a given A ( controlled e.g. by an external local magnetic field) two (rj = 1) Andreev levels contribute to the resonance Josephson current Jr, which can be represented in the form... 

We have considered here the influence of dispersion asymmetry and Zee-man splitting on the Josephson current through a superconductor/quantum wire/superconductor junction. We showed that the violation of chiral symmetry in a quantum wire results in qualitatively new effects in a weak superconductivity. In particularly, the interplay of Zeeman and Rashba interactions induces a Josephson current through the hybrid ID structure even in the absence of any phase difference between the superconductors. At low temperatures (T critical Josephson current. For a transparent junction with small or moderate dispersion asymmetry (characterized by the dimensionless parameter Aa = (vif — v2f)/(vif + V2f)) it appears, as a function of the Zeeman splitting Az, abruptly at Az hvp/L. In a low transparency (D zero magnetic field the anomalous supercurrent disappears (as it should) since the spin-orbit interaction itself respects T-symmetry. However, the influence of the spin-orbit interaction on the critical Josephson current through a quasi-ID structure is still anomalous. Contrary to what holds... 

In this section we calculate the Josephson current between the S layers of a FSFSF structure. We assume again that the thickness of the F layers dp is much larger than In this case the Josephson coupling between the S layers is due to the long range part of the TC. Therefore the supercurrent in the transverse direction is unusual, since it is caused by the triplet component of the condensate that is odd in frequency and even in momentum. 

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.

The Josephson current is obtained by multiplying Eq. 50 by the conjugated wave function and integrating by parts. This yields the flow of the charged Bose gas with the current... 

It is worthwhile to note that the charged Bose gas trapped in the double well potential Ua of Eq. 50 behaves as an inverted Josephson junction (N-S-S-N). The super-current, which accompanies the matter wave coherence, is induced between the degenerate resonance states of the adjacent wells at the frequency of the tunnel splitting A response time, as is typical of tunnel junctions (whose frequency cutoff is much smaller than the vibrational frequency even for nano junctions). The coherent oscillations of the Josephson current can be observed by virtue of their slow frequency A V which is robustly controlled by the bias voltage. 

All components of the front-end chip have been tested. For the LO/SIS mixer strucure, the current-voltage characteristic (I-V curve) of the LO, when a 7 mA current is applied through the control line, exhibited a pronounced flux-flow step at 0.75 mV. At the same time, the I-V curve of the SIS mixer irradiated by the LO, while its Josephson current is suppressed by current through control line and when LO is biased at flux-flow step, exhibits the photo-assisted tunneling step at hfpj/e below the gap. 

Here dm is the effective magnetic thickness of the junction, 0o the magnetic flux quantum, and My) the maximum Josephson current density. A complete oscillation of the pair current density is called a Josephson vortex and contains one magnetic flux quantum. This behavior is shown schematically in Fig. 5.10... 

During electron beam scanning the maximum Josephson current density... 

T cO superconducting transition temperature in the undoped material x singlet-singlet, singlet-triplet and triplet-triplet components of the Josephson current 1 ... 

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