Cooper pair Definition and 19 Threads

In the Jellium model, it is customary to evaluate the exchange term of the Hartree-Fock equation for plane waves ##\varphi_{\mathbf{k}_i}## as a correction to the energy of the non-interacting electron gas obtaining $$\hat{U}^{ex} \varphi_{\mathbf{k}_i}=-e^2 \left( \int \dfrac{\mathrm{d}^3k}{2...

How do one get the electrons to move inside a superconductor? Since I have understood superconductors repel magnetic fields due to the Meissner effect, or is that when the charges already are moving within the superconductor? If so how did we get them o move from the beginning? Can you make...

We have a one dimensional lattice with a lattice constant equal to a (I'm omitting vector notation because we are in 1D). The reciprocal lattice vector is k_n=n\frac{2 \pi}{a}. So to get the nearest neighbour approximation I need to sum over k = -\frac{2 \pi}{a}, 0, \frac{2 \pi}{a}. If I...

This question is for those familiar with the BCS theory of superconductivity or familiar with R.D. Mattuck's book “A Guide to Feynman Diagrams in the Many-Body Problem.” I am working my way through the book, and I am stumped by some of the problems at the end of chapter 15 (superconductivity)...

One of the first starting points of introducing BCS theory in a superconductor is applying a theorem stating that the ground-state of a quantum system has an expectation value for its momentum of zero. You then use this to say that an electron must pair with another electron of equal and...

Is it possible to calculate the average number of Cooper-pairs, existing at any given moment, per cubic centimeter of niobium (or YBCO), at their critical temperatures? I realize that Cooper pairs form and dissolve continuously, and constantly change partners, so perhaps its not easy to...

Can Cooper pairs have any spatial orientation within a superconductor? In most graphical depictions of a Cooper pair they are both on the same axis (moving through the same channel within the lattice), and parallel with the current direction. Is there any reason the pair cannot be at a right...

Hello, This problem is about cooper pair formation and what happens with the calculations if there is an attractive potential between electrons but it is not in the presence of a filled fermi surface. 1. Homework Statement Two electrons just above the filled Fermi Surface of a material can...

So i came to know that electrons residing across a tiny shell around fermi momentum takes part into the game of forming cooper pair but this phenomenon in real space is actually different. here all the electrons are taking part into this. what does it mean. i am not able to comprehend this...

Hello, In my problem I need to We are advised to create the Cooper pair box Hamiltonian in a matrix form in the charge basis for charge states from 0 to 5. Here is the Hamiltonian we are given H=E_C(n-n_g)^2 \left|n\right\rangle\left\langle...

I am trying to understand the pairing mechanism in the Cooper pair in real space. When I googled the image of the Cooper pair, there are two different pictures explaining the pairing. While one describe the second electron moving in the same direction, other describe it as moving along the same...

Does the cooper pairs spins (up and down) cancelling out have anything to do with anything? Is the current spin polarized in a superconductor?

Can anyone help me, I am some what unclear on the reason why "conventional" superconductors have cooper pairs only in the singlet state. Is it something to do with the expectation values given for the separate states calculated from their spatial and spin wave functions? For example does the...

Hello, Would it be possible for an electron and positron to form a cooper pair if an electron is brought into the neighborhood of the positron who is anchored in a penning trap (or in some other fashion)? If normal cooper pairs form by using the the attractive force of the lattice...

It seems to me that the Ginzburg-Landau equations are derived from considering the particle of superconduction to be behaving in a superfluid way. This required the particle of superconduction to be a boson so that B-E statistics might apply. The use of Bose's presumptions surely tell us that...

What holds a :smile::smile: pair together?

I am trying to understand the cooper pair in a box. They don't seem to behave like normal particles. Can someone point me to a good intro. Especially on that focuses on how they are not like a quantum well. Some questions: 1) Does the cooper pair in the box see anything of the geometric shape...

Hi guys I hope you can help. The other day I tried to explain to someone the mechanism behind 'stripes' in lightly doped cuprates that gives rise to the Mott insulator/ anti-ferromagnetic stuff. It quickly became clear that my understanding of super-conductivity differs considerably from the...

How far apart in space are these electrons? Are the spins truly up and down or do they have the same spins (parallel)? If they are up and down paired, then what causes that orientation?