# Homework Help: Split Josephson Junction

1. Mar 16, 2014

### maximus123

Hello everyone, here is my problem
I'm not sure where to start with this problem, I suppose if the phase difference due to the circulating current is negligible then the total phase difference can be written
$\Delta\phi_{tot}=\Delta\phi_{a}+\Delta\phi_{b}+ \Delta \phi_{B}$​
In our notes we also have it that
$V=\frac{\Phi_{0}}{2\pi}\dot{\delta}$​
Where $\delta$ is the difference between the superconducting phase in the
two electrodes. Which seems like it must be relevant due to the similarity with the intended final result

#### Attached Files:

• ###### Untitled.png
File size:
15 KB
Views:
74
2. Mar 17, 2014

### tman12321

You must relate the phase to the vector potential A, where B = curl(A). This will include a factor of the flux quantum and 2 pi. Then you can do a line integral of A around the loop to get the total flux. Argue that the sum of the finite phase differences across the links must be zero mod 2 pi. You will find that the sum of the gauge-invariant phase differences is what you're looking for. A good reference is Tinkham's book on superconductivity, specifically chapter six section four. Your library should have it, or you can buy it for around \$15 I think.

3. Mar 17, 2014

### maximus123

Thank you, this helped.