Cooper Pairs

The behavior of superconductors suggests that electron pairs are coupling over a range of hundreds of nanometers, three orders of magnitude larger than the lattice spacing. Called Cooper pairs, these coupled electrons can take the character of a boson and condense into the ground state.

This pair condensation is the basis for the BCS theory of superconductivity. The effective net attraction between the normally repulsive electrons produces a pair binding energy on the order of milli-electron volts, enough to keep them paired at extremely low temperatures.

Further discussionModel of the attractive mechanism
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Superconductivity concepts

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Cooper Pairs

The transition of a metal from the normal to the superconducting state has the nature of a condensation of the electrons into a state which leaves a band gap above them. This kind of condensation is seen with superfluid helium, but helium is made up of bosons -- multiple electrons can't collect into a single state because of the Pauli exclusion principle. Froehlich was first to suggest that the electrons act as pairs coupled by lattice vibrations in the material. This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration energy. Experimental corroboration of an interaction with the lattice was provided by the isotope effect on the superconducting transition temperature. The boson-like behavior of such electron pairs was further investigated by Cooper and they are called "Cooper pairs". The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.

Resistance diagramPhase diagram
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Superconductivity concepts

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A passing electron attracts the lattice, causing a slight ripple toward its path.

A model of Cooper pair attraction

Another electron passing in the opposite direction is attracted to that displacement.
Further discussion of mechanism
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Superconductivity concepts

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Model of Pair Attraction




A visual model of the Cooper pair attraction has a passing electron which attracts the lattice, causing a slight ripple toward its path. Another electron passing in the opposite direction is attracted to that displacement. This constitutes a coupling between electrons which can be depicted in a Feynman diagram.
As strange as such an interaction seems, it is experimentally supported by the isotope effect and the evidence for a condensation to a boson -like state at the critical temperature for superconductivity.

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Superconductivity concepts

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Isotope Effect, Mercury

If electrical conduction in mercury were purely electronic, there should be no dependence upon the nuclear masses. This dependence of the critical temperature for superconductivity upon isotopic mass was the first direct evidence for interaction between the electrons and the lattice. This supported the BCS theory of lattice coupling of electron pairs.

It is quite remarkable that an electrical phenomenon like the transition to zero resistivity should involve a purely mechanical property of the lattice. Since a change in the critical temperature involves a change in the energy environment associated with the superconducting transition, this suggests that part of the energy is being used to move the atoms of the lattice since the energy depends upon the mass of the lattice. This indicates that lattice vibrations are a part of the superconducting process. This was an important clue in the process of developing the BCS theory because it suggested lattice coupling, and in the quantum treatment suggested that phonons were involved.

Index

Superconductivity concepts

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