# Josephson Effect Class Presentation

1. Oct 9, 2015

### kq6up

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

2. Oct 12, 2015

### DrDu

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. Oct 12, 2015

### f95toli

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. Oct 12, 2015

### kq6up

Thanks, yes I just found Feynman's derivation, and it seems pretty straight forward. I will be delving into those tomorrow.

Regards,
Chris