# BCS theory

1. Oct 6, 2009

### Petar Mali

In the theory of superconductivity BCS theory is given eigen - problem

$$-\frac{\hbar^2}{2m}(\Delta_{\vec{r}_1}+\Delta_{\vec{r}_2})\psi(\vec{r}_1-\vec{r}_1)=(E+2\frac{\hbar^2k^2_F}{2m})\psi(\vec{r}_1-\vec{r}_1)$$

Why $$E+2\frac{\hbar^2k^2_F}{2m}$$?

Maybe because is Fermi sphere is centered in origin?

2. Oct 8, 2009

### olgranpappy

This is just a convenient redefinition of the zero of energy. There are two electrons involved in the pair so it is convenient to measure energy with respect to *twice* the Fermi energy. Where the Fermi energy is supposed to be given in terms of the Fermi momentum $k_F$ by
$$E_F=\frac{k_F^2}{2m}$$

3. Nov 6, 2009

### Petar Mali

Is there a clear boundary between low temperature and high temperature superconductors? Is it maybe 40K? I ask because BCS theory is theory for low temperature superconductors. And from this theory we know that the energy of bond of Cooper pair is

$$E=-2\hbar\omega_De^{-\frac{1}{WN(0)}}$$

where $$WN(0)<<1$$

4. Nov 6, 2009

### sokrates

Yes, above 30K anything is considered high Tc superconductivity, because that's the predicted upper limit of BCS theory.

Müller and Bednorz received 1986 Nobel prize immediately after discovering a ceramic structure with Tc=35K.

5. Nov 6, 2009

### olgranpappy

In low temperature superconductors it is thought that phonons make up the "glue" for the Cooper pairs (hence the \omega_D in your formula, etc). In high temperature superconductors the "glue" is thought to be something else...