How Does Superconductivity Change with Size?

There are many benefits of superconductors, including magnetic levitation trains, fast computers, more energy efficient electricity and larger data storage. They are mostly used in research and technological development, medical diagnosis in the form of MRI machines.

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In metals, electrical resistance occurs due to deviations, impurities and vibrations in the material which cause electrons to scatter. It is known that approximately 7% of electricity generated in the US is lost due to resistance of transmission lines, usually as thermal energy. However, in a superconductor, there is no resistance below the transition temperature as there is are no reasons for an electron to scatter. The current is carried by electrons known as ‘Cooper pairs’. Many physicists consider the distance between the two electrons in a Cooper pair to have equal correlation length. This is determined to be the size of the Cooper pair.

In 1959, theoretical physicist P.W. Anderson proposed a theory that there were limits on how small a superconductor could be created. In his conjecture, he predicted that an objects superconductivity is linked to its gap energy. He proposed that the superconducting gap energy must be larger than the materials electronic energy level spacing. It is known that if this spacing is increased then the magnitude decreases.

According to theory, this limits a superconductor’s volume at a minimum of approximately 100nm­­­3, the point at which the gap energy and electronic energy level spacing are equal to each other. This was known as the Anderson limit. Due to the scale in question, it was not until 2017, when it was possible to prove this theory experimentally. This was due to the difficulty in observing superconducting effects at this scale.

The research was published by Sergio Vliac who worked with researchers from the University Paris Sciences et Lettres as well as the French National Centre for Scientific Research. The team was able to accurately design a nano-system that proved the limitations set by Anderson, 50 years previously.

"Our experimental demonstration of the Anderson conjecture is also a demonstration of the validity of the Richardson-Gaudin models," stated Hervé Aubin, coauthor of the paper and researcher at the University Paris Sciences et Lettres. "The Richardson-Gaudin models are an important piece of theoretical works because they can be solved exactly and apply to a wide range of systems; not only to superconducting nanocrystals but also to atomic nuclei and cold fermionic atomic gas, where protons and neutrons, which are fermions like electrons, can also form Cooper pairs."

Conversely, there are many examples of extremely large superconductors being used around the world. Currently, the longest superconducting energy cable has been installed in the city of Essen, Germany and is 0.62 miles long. As of 2006, CERN has the largest operating superconductor magnet in the world, the Barrel Toroid. It consists of eight superconducting coils, 5m wide and 25m long. They have a weight of approximately 100 tones. The superconductor is now part of CERN’s Large Hadron Collider and is being used to provide a powerful magnetic field.

Works Cited

Amel Abdallah Ahmed Elfaki, M. D.-A. (2017). The Effect of Temperature on Conductivity of Conductors and Superconductors. American Journal of Physics and Applications Vol 5, 1-5.

CERN. (2006, November 20). World's Largest Superconducting Magnet Switches On. Retrieved from CERN: https://home.cern/news/press-release/cern/worlds-largest-superconducting-magnet-switches

Landgraf, M. (2014, May 12). Operation of longest superconducting cable worldwide started. Retrieved from phys.org: https://phys.org/news/2014-05-longest-superconducting-cable-worldwide.html

Oxford University. (2018). Superconductivity Explained. Retrieved from superconductors.org: http://www.superconductors.org/oxtheory.htm

Vlaic, S. (2017). Superconducting parity effect across the Anderson limit. Nature Communications.

Woodford, C. (2018, November 3). Superconductors. Retrieved from Explain That Stuff!: https://www.explainthatstuff.com/superconductors.html

Zyga, L. (2017, March 20). How small can superconductors be? Retrieved from phys.org: https://phys.org/news/2017-03-small-superconductors.html

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