Superconductor coherence length and penetration depth

[leroyjenkens]

Homework Statement

I have a lot of information about 2 different superconductor materials; indium and lead. The indium is pretty much 100% indium with no impurities, and the lead is unknown purity.
I have the temperatures and magnetic fields at which they are superconducting and the temperatures and magnetic fields at which they're in the transition between the superconducting state and the vortex state.

What I need to do is calculate the coherence length and London penetration depth of both of these materials.

Homework Equations

The two equations I've found are...

coherence length = \sqrt{\frac{\hbar^{2}}{2m|\alpha|}}

Where m is the mass of a cooper pair (2 times e), but I don't know what alpha is. Does it vary from material to material? How would I find out this value?

And the london penetration depth = \sqrt{\frac{mc^{2}\epsilon}{ne^{2}}}

Where epsilon is epsilon naught, the permittivity of free space, and n is superconducting electron density.

I also found another equation for london penetration depth.

(\frac{m}{q^{2}n\mu})^{\frac{1}{2}}

Where mu is mu naught, the permeability of free space.
I'm not sure which of these equations to use.

The Attempt at a Solution

It looks like I can solve for the london penetration depth. I think I have all of that information. But for the coherence length, I need to know what alpha is. Anyone know?

Thanks.

 

[mfb]

The two formulas for the london penetration depth look equivalent, as q²=e² and c can be expressed in terms of $\epsilon_0$ and $\mu_0$.

I don't know what α is.