# Superconductor coherence length and penetration depth

• leroyjenkens
Does it vary from material to material? How would I find out this value?In summary, the conversation discusses the need to calculate the coherence length and London penetration depth for two different superconductor materials, indium and lead. The equations for these values are given, but there is uncertainty about the value of alpha and which equation to use for the London 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.

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.

## 1. What is the coherence length of a superconductor?

The coherence length of a superconductor is the average distance over which pairs of electrons remain correlated in their motion, and is a measure of how well a material can maintain its superconducting state. It is typically on the order of nanometers for conventional superconductors, and can vary greatly for different materials.

## 2. How is the coherence length related to critical temperature?

The coherence length is inversely proportional to the critical temperature of a superconductor. This means that materials with longer coherence lengths will have higher critical temperatures, allowing them to maintain their superconducting state at higher temperatures.

## 3. What is the significance of the penetration depth in superconductors?

The penetration depth, also known as the London penetration depth, is a measure of how far magnetic fields can penetrate into a superconductor. It is closely related to the coherence length and critical temperature, and plays a crucial role in determining the properties of superconductors, such as their ability to expel magnetic fields and their critical current density.

## 4. How does the coherence length and penetration depth affect superconducting applications?

The coherence length and penetration depth are important factors in determining the practicality and efficiency of superconductors in various applications. Materials with longer coherence lengths and smaller penetration depths are generally more desirable, as they can maintain their superconducting state over larger distances and are less affected by external magnetic fields.

## 5. Can the coherence length and penetration depth be altered in superconductors?

Yes, the coherence length and penetration depth can be altered through various methods such as doping, alloying, and applying external pressure or magnetic fields. These changes can affect the superconducting properties of the material, and are actively researched in order to improve the performance of superconductors in different applications.

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