• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

136 submissions , 114 unreviewed
3,844 questions , 1,360 unanswered
4,805 answers , 20,346 comments
1,470 users with positive rep
489 active unimported users
More ...

How to understand the equivalence between Andreev reflection and Cooper pair injection?

+ 5 like - 0 dislike

  It is well know that Andreev reflection dominates the subgap transport at the normal metal-superconductor interface. An incident electron can be reflected as a hole in the Nambu space, which effectively describes two electrons transmit into the superconductor and form a Cooper pair. It seems reasonable and intuitive that the two pictures are equivalent to each other at first glance. However, it is not so easy for me to understand this fact.

  In the electron-hole picture, an electron in \(|+k\rangle\) state is incident from the normal side. Then it will transmit into the superconductor by pulling another electron in \(|-k\rangle\) state to form a Cooper pair. The empty state in \(|-k\rangle\) is called a hole, and the moving direction of the hole is opposite to the incident electron, so that this phenomenon is called Andreev "reflection". Based on this picture, the incident electron and reflected hole possess nearly the same momentum \(+k\) (note that the empty state in \(|-k\rangle\) has a momentum of \(+k\)). Therefore, the whole Andreev process is momentum conserved.

  Now let's turn to the two-electron picture. In this picture, two electron incident from the normal side both transmit into the superconductor, and they possess nonzero total momentum. So when they form a Cooper pair in the superconductor, their total momentum must be changed, for the Cooper pair has zero momentum.

  Based on the argument above, we see that the Andreev reflection is a process with the momentum conservation, while the two-electron injection process breaks the momentum conservation. I believe that, if the two pictures are equivalent, then the momentum of the two physical processes——Andreev reflection and two-electron injection, must be equal to each other. In my opinion, using the Andreev reflection picture to study the transport problems is always right. However, the Andreev picture can not deal with all relevant problems. For example, when we are interested in the two electron entanglement, then the single particle process described by Andreev reflection is powerless. Therefore, to find good equivalence between the two pictures are highly nontrivial.

asked Jun 2, 2014 in Theoretical Physics by pchenweis (40 points) [ no revision ]
retagged Jun 2, 2014

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights