Ginzberg-Landau and the Cooper Pair

[ZapperZ]

You were given the BCS ground state wavefunction somewhere in this thread. Look at all the available momentum for each fermion pair and look how they are summed in that series! If you have "understood" the current theory, you would have noticed this. So it is puzzling why you still continue to ask this question.

There is nothing "wrong" with the observation of Josephson tunneling, especially when the phenomena was PREDICTED by Josephson based on what was understood to be the supercurrrent.

And here's something to consider. The CODATA standard for the accepted values of "e" and "h" were ALL derived out of measurement in the superconducting state. In fact, the value of "e" came out of the VERY certain measurement of "2e" in a superconducting flux quanta. If "cooper pair is wrong", so will a lot of our electronics, AND, many precise measurement will not make sense. In fact, you probably should never get out of the house, because we use SQUID detectors in making many non-destructive tests on materials.

There are many aspects of science that has varying degree of certainty. Superconductivity in conventional material AND the formation of Cooper Pair has one of, if not THE, highest degree of certainty as far as knowledge is concerned.

Your next "objection" must contain quantitative values to show where theory doesn't match observation. These hand-waving objection is no longer sufficient or accepted.

Zz.

 

[Zymandia]

You have not answered the question.
How do high k short-wavelength constituents of a Cooper Pair tunnel over > 1000 wave-lengths without the barrier potential attenuating them to nothing. Simple basic quantum mechanics is all that is needed for a v. low k single wave-function.

 

[ZapperZ]

You have not answered the question.
How do high k short-wavelength constituents of a Cooper Pair tunnel over > 1000 wave-lengths without the barrier potential attenuating them to nothing. Simple basic quantum mechanics is all that is needed for a v. low k single wave-function.

It depends on the barrier widths!

The supercurrent has a WHOLE RANGE OF k! That was how I answered your question, but you didn't have a clue what that meant, obviously. The BCS ground state summed up all the plane wave states from 0 to the Fermi momentum! The tunneling current doesn't involved ALL of the Cooper Pairs! If they do, the tunneling current would be identical to the supercurrent, which we do NOT see. All the cooper pairs do not have the same probability of tunneling!

So here's your turn to answer MY question. http://arxiv.org/PS_cache/cond-mat/pdf/0410/0410184v1.pdf" , without any Cooper pair tunneling, show me a detailed theoretical explanation for the energy gap formation at 2Delta in the tunneling conductance, AND the presence of the Josephson current, even at zero bias. Remember, there have been ZERO other explanation for this other than the current conventional explanation which has worked very well, AND, what was predicted by Josephson using the BCS formulation. This is the non-handwaving argument that I'm expecting and it will be the last time I will ask this.

Zz.

 

[f95toli]

"Direct" tunnelling of Cooper pairs is quite rare in real junctions; in most cases the Josephson current is mediated by Andreev states in the barrier; i.e there is no tunnelling over "long distances" involved.
All you need in order to get a Josephson current (i.e. a NET transport of Cooper pairs) is two electrodes connected via a weak link of some sort. The SIS junction is just one extreme, at the other end you have SNS junctions and everything in-between (usually specified using the BTK parameter, 0 being an insulating barrier and 1 a normal metal) not to mention junctions that do not really fit that classification such as SS'S, ScS, SFS etc.
In junctions made from hight-Tc superconductors the situation becomes even more complicated due to the d-wave symmetry and the nature of the interfaces.

The original papers by Josephson just deal with a special case; the Josephson effect is much more general than even he ever realized.

 

[Zymandia]

"The supercurrent has a WHOLE RANGE OF k! That was how I answered your question, but you didn't have a clue what that meant, obviously."

No I don't have a clue, and attempts to find-out just finds high-phalutin' physicists giving hand-waving explanations of the 'super-current'.
So let's use logic. A low k long-wavelength 'supercurrent' is required to tunnel the distances observed, but it can't be a low-energy electron because that would be forbidden by Pauli. However we know that current flows across the gap so mass and charge are transferred.
No, I give up. What has an extremely long wavelength so presumably low kinetic energy, yet carries charge and mass in the ratio of the electron, what type of wave is a 'supercurrent'?

 

[ZapperZ]

"The supercurrent has a WHOLE RANGE OF k! That was how I answered your question, but you didn't have a clue what that meant, obviously."

No I don't have a clue, and attempts to find-out just finds high-phalutin' physicists giving hand-waving explanations of the 'super-current'.
So let's use logic. A low k long-wavelength 'supercurrent' is required to tunnel the distances observed, but it can't be a low-energy electron because that would be forbidden by Pauli. However we know that current flows across the gap so mass and charge are transferred.
No, I give up. What has an extremely long wavelength so presumably low kinetic energy, yet carries charge and mass in the ratio of the electron, what type of wave is a 'supercurrent'?

You didn't answer MY question.

And you are more than welcome to look at Josephson's original theory. See if THAT is "hand-waving". This thread is done.

Zz.