Josephson Effect Class Presentation

In summary, Chris is working on a class presentation on the Josephson effect for his solid state physics class. He is struggling to understand the concept and is wondering if he can grasp it in a few days without understanding perturbation theory. He is also looking for a reference that explains it in more detail. The Josephson effect is a general phenomenon and there are various ways to derive the equations. Feynman's derivation seems to be the most straightforward and Chris plans to study it tomorrow.
  • #1
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I am working on a class presentation for my solid state physics class. I picked the topic of the Josephson effect. I would like to explain this phenomena in specific detail. However, the original paper and other material I have found quickly goes over my head as I have not been as far as perturbation theory in QM. I have a very solid grasp of basic QM, and I am wondering if it is possible to get at least a basic understanding of the Josephson effect in a day or so. Do I have to understand it in terms of perturbation? I was thinking it was a simple potential barrier when I picked the project. My rough draft is due next Wednesday. My professor said not to worry about the finer details, but I really want to wrestle with it. Is this possible for me to grasp in a couple of days? If so, could someone point me to a reference that unpacks it a little better than the general papers that I pull up using google.

Thanks,
Chris
 
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  • #2
I don't think that the Josephson effect has anything to do with perturbation theory at all.
The basic characteristic of a superconductor is the appearance of non- vanishing long range correlations of the form ##\langle c^+(x) c^+(x') c(y) c(y') \rangle## where ##x\approx x'## and ##y' \approx y## but x and y may be separated by a large distance. The wording behind this correlation function is the correlation between the destruction of a Cooper pair ( ie. two electrons) at y and the creation of a cooper pair at x. This is most easily realized by bending the superconductor into a ring and giving the electron the chance to tunnel through a small barrier.
 
  • #3
Have a look at the section on the Josephson effect in the Feynman lectures. The derivation is based on making a a couple of assumptions (which are easy to justify in the case of a superconductor) and then uses the Schroedinger equation to derive the Josephson effect formulas.

There are two things that is worth keeping in mind: The first is that Josephson effect is a very general phenomenon and is not limited to superconductors (it can also be observed in e,.g. Bose-Einstein condensates), the second (which sort of follows from the first) is that there are many different ways of the deriving the equations (the derivation used by Brian Josephson is actually rarely used) and which derivation is the most "physical" depends on which system you are studying (although all derivation will of course end up with the same result).
Josephson's original derivation was only valid for S-I-S junctions, if you are studying e.g. S-N-S junctions it might be better to think about is in terms of say Andreev states/reflections, or if you want to be less stringent BTK-formalism etc
 
  • #4
Thanks, yes I just found Feynman's derivation, and it seems pretty straight forward. I will be delving into those tomorrow.

Regards,
Chris
 

What is the Josephson Effect?

The Josephson Effect is a phenomenon in quantum physics where an electrical current flows between two superconductors that are separated by a thin insulating barrier.

Who discovered the Josephson Effect?

The Josephson Effect was discovered by British physicist Brian David Josephson in 1962, for which he was awarded the Nobel Prize in Physics in 1973.

What are the applications of the Josephson Effect?

The Josephson Effect has a wide range of applications, including in superconducting quantum interference devices (SQUIDs) used for highly sensitive measurements of magnetic fields, and in the development of superconducting qubits for quantum computers.

What are the two types of Josephson junctions?

The two types of Josephson junctions are the superconducting-insulating-superconducting (SIS) junction and the superconducting-normal-superconducting (SNS) junction. The SIS junction has two superconducting layers separated by an insulating barrier, while the SNS junction has a normal metal layer between the two superconducting layers.

What is the relationship between the Josephson Effect and the superconducting phase difference?

The Josephson Effect is directly related to the superconducting phase difference between the two superconductors in a Josephson junction. The electrical current flowing through the junction is directly proportional to the rate of change of the superconducting phase difference.

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