# Impurities effects in Type II SCs

• Shiricon
In summary, this article discusses how the addition of impurities to a type II superconductor can affect its critical temperature. The theory behind this is explained in terms of the Abrikosov-Gorkov theory. The article also includes a formula for calculating the effect of a non-magnetic particle on Tc. This information is helpful in understanding how the addition of impurities to a superconductor can affect itsproperties.
Shiricon
Hello,

I have a question about how non-magnetic impurities affect the transition temperature in type II superconductors.

I know that the impurities introduce additional scattering and therefore act to reduce Tc, but is there a simple formula that would relate the effect on Tc due to particles of a particular size in relation to xi or lambda? Also, what about particle shape, as a sphere would cause scattering different from that of a long needle-like impurity?

Most of the papers I have found present experimental results showing the decrease of Tc, but I haven't found any that cite where I could find a theoretical estimation for the reduction of Tc with a specific impurity. I have found some very lengthy and complex formulas in a few papers, but it was not clear to me how the size or shape would factor into these formulas.

If you know a source or if you can guide me in the right direction, that would be helpful. Thank you!

"Particles of a particular size" doesn't really make much sense in this context, when we talk about impurities in SC we generally refer to atoms (well, ions); not particles. It is a microscopic effect. Also, "geometric size" is usually not very important, what matters is how well an impurities scatters electrons/pairs which in turn depends on its moment.

Particles will of course act affect vortex dynamics etc, but that won't affect Tc directly.
If you have a large number of particles dispersed in the solid one could of course imagine that this affects the phonon spectrum etc which might affect Tc somewhat; but that effect would presumably be very small.

Thank you for your input. I am trying to get the sense for this...

In a type II superconductor in the vortex state, impurities can act as pinning centers. However, with the addition of impurities/defects you reduce the mean free path by introducing additional scattering. As the Cooper pair is of the order of xi, I would naively think that a particle below the order of xi would have much less effect on scattering than a particle >xi. By particle I could mean ion; I am using the term generically to mean "something" of finite size, whether it be a single atom or collection of atoms.

But this is what I am trying to find out... "We" like to add impurities to help pin vortices, but what effect are we having on Tc (experimentally I know that the Tc will be reduced).

For magnetic impurities, the Abrikosov-Gorkov theory provides a pair breaking term alpha which takes into account the exchange energy between the electron spin and the magnetic impurity. This alpha is in terms of the concentration and contains a critical concentration for which superconductivity can not exist for any temperature. In this way, I can use the magnetic properties of the impurity with the concentration to calculate the effect on lowering Tc.

I would like a similar formula for a non-magnetic particle/impurity/ion. I would like a formula for which I can take the properties and concentration (and potentially the particle size) of the non-magnetic particle and roughly estimate the effect on Tc, whether that shift be .01, 1, or 10 degrees.

I suppose I should mention that I am interested in doing calculations for bulk samples, and not thin films or wires.

The point... If I am making a bulk superconductor, say like a pellet of MgB2, and I want to mix in a powder of non-magnetic impurities to increase pinning in the sample, but I also want to know how that would affect Tc. If I'm using a powder, what effect do I expect my choice of powder size (nano-powders versus micro-powders) to have on the reduction of Tc? I can look at the experimental results and see the Tc shifts will typically be small, but I assume there is a formula somewhere that estimates the relative shift in Tc, and that is what I am looking for.

I thought I would post this in case anyone comes across this post in the future and is looking for a similar result.

I found a paper that answers my question sufficiently.
Markowitz, D. and Kadanoff, L. P. (1963). Effects of impurities upon critical temperature of anisotropic superconductors. Physical Review, 131(2):563.

There is an appendix at the end of the article that contains a formulation for dTc if the scattering cross section and anisotropy interaction are known.

## 1. What are impurities and how do they affect Type II superconductors?

Impurities are foreign particles or defects present in a material. In Type II superconductors, impurities can disrupt the flow of electrons and decrease the critical temperature at which the material becomes superconducting. They can also create pinning sites, which can hinder the movement of magnetic flux lines and decrease the material's ability to carry current without resistance.

## 2. Can impurities be intentionally added to Type II superconductors to improve their properties?

Yes, impurities can be added in controlled amounts to Type II superconductors to enhance their properties. For example, adding small amounts of certain elements can increase the critical temperature and improve the material's ability to carry current.

## 3. How do impurities affect the critical current in Type II superconductors?

Impurities can decrease the critical current in Type II superconductors by creating pinning sites for magnetic flux lines. This makes it more difficult for the flux lines to move through the material, leading to a decrease in the maximum current that can be carried without resistance.

## 4. Are impurities the only factor that affects the critical temperature in Type II superconductors?

No, impurities are not the only factor that affects the critical temperature in Type II superconductors. Other factors such as crystal structure, composition, and external magnetic fields can also influence the critical temperature.

## 5. How do impurities affect the macroscopic properties of Type II superconductors?

Impurities can have a significant impact on the macroscopic properties of Type II superconductors. They can alter the electrical and magnetic properties, such as critical current, critical temperature, and magnetic field penetration depth. Impurities can also affect the mechanical properties, such as strength and ductility, of the material.

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