Revised Theory of the Josephson Effects: Just published in Journal of Applied Physics, Vol. 103, 103902, (2008)

Highlighted in Virtual Journal of Applications of Superconductivity, Vol. 14, issue 11, June 1, 2008

    In 1962 B. Josephson predicted the Josephson effects. He won the Nobel Prize in Physics in 1973 for the contribution. Nevertheless, there are still some  unsolved fundamental problems, such as the sign problem in the AC Josephson effect, the threshold behavior in the DC Josephson effect, and etc. 

    This paper introduces a Cooper pair wavefunction approach to the Josephson effects. This method is more powerful and error-free, compared to the previous techniques. We have found that SIS junctions have a material-dependent threshold resistance, shown in the figure below,which explains why MgB2 SIS junctions don't show the supercurrent for the big gap! In addition we have found a more accurate formula for the temperature dependence of the supercurrent.

    This understanding may lead to the discovery of better materials for SIS junctions other than Nb and the optimum miniaturization of the SIS junctions for the petaflops superconducting supercomputers.

    The preliminary result has been published in the LT24 Proceedings: Threshold resistance in the DC Josephson effect.  



















    Copyright (2006) American Institute of Physics.

In 1998 I predicted this behavior in my booklet "Reinvestigation of Inhomogeneous and high
Tc Superconductors".
       cf. 5.5 Josephson effect
            The (insulator) thickness dependence of the supercurrents is not well understood! 

Around 1975 Testardi and coworkers found this correlation [3,4]. However, P. W. Anderson's theorem [5] does not allow this kind of correlation. Therefore, the experimetnal discovery was forgotten. Recently, we showed that Anderson's theorem breaks down when electrons are (weakly) localized [6], which led to the explanation of the correlation [1]. Furthermore, we noticed that this correlation can probe the phonon mechanism in superconductors [2]. In particular, the Testardi correlation provided definite proof of the phonon mechanism in the recently discovered 39K superconductor, MgB2 [2,7].  


                                                               















                                  
 
                            From Buzea and Yamashita [7]  


Advantage:  applicable to any superconductor, including d- and f- electron 
                               superconductors      
Limitation:   limited applicability in systems, such as
                   i) highly anisotropic systems where impurity scattering can reduce the Tc to 
                                   zero even before electrons are weakly localized
                   ii) high Tc cuprates where the Coulomb interactions are comparable to the 
                                   electron-phonon interaction even at room temperature       

                    => Nevertheless weak localization effect shows that the electron-phonon interaction is also crucial even in high Tc cuprates:  Using weak localization to probe the phonon-mechanism in high Tc superconductors.    

The Byers and C. N. Yang's theory [9] of flux quantization is not consistent with the 
observation of persistent current in normal metal rings [10]. Byers and Yang (BY) assumed 
that the normal state free energy Fn does not depend on the flux ÃŽÂ¦, i.e., Fn(Φ) = constant. 
However, the persistent current is given by I= -c ∂Fn(Φ)/ ∂Φ. Accordingly, the 
BY theory leads to the following: 





























 

                                                                                               No flux quantization!

New Interpretation [8] : flux dependence of the pairing interaction leads to flux quantization.

Comment by an expert: 
    " I do not think your finding is actually at odds with the way in which flux quantization 
     is understood by experts on superconductivity - it is at odds with the way it is often
    discussed in text books however."