Dissemination of IT for the Promotion of Materials Science (DoITPoMS)


Cooper pairs

In order for electrons to be able to move in some coherent manner and exhibit superconducting properties, there must be some type of interaction between them. Ordinarily, electrons repel each other due to the Coulombic interaction of the similar charge but for electrons to become coherent there must be some type of attraction between them. The breakthrough to describe how there could possibly be an attractive force between two electrons came as a result of experiments looking at the effect of nuclear mass on the critical temperature.

Different isotopes of the same element were found to have different critical temperatures which led scientists to consider the fact that the underlying lattice must have some contribution to the superconducting effect. It was Leon Cooper who came up with the idea that vibrations within the lattice could indeed interact with electrons and cause there to be an attraction between them. The animation below shows the basic mechanism by which this attraction occurs.

Often this pairing of electrons is visualised in terms of ball bearings (the “electrons”) resting on a rubber sheet (the “lattice”). Putting one ball bearing on the sheet will cause it to stretch creating a depression in which the ball sits. This lowers the gravitational potential energy of the ball by making it lower down. If another ball is placed on the sheet, it too will form a depression, but if it is placed near enough to the first the two will roll together and form a deeper depression. This lowers the overall gravitational potential energy of the two balls and causes there to be a coupling between them that would otherwise not be there without the rubber sheet. The animation below gives an idea of how this occurs.  In practice, this is only a schematic representation of the microscopics of the interaction within electron pairs.

Video of the movement of particles into a depression

This analogy can be taken further if we consider the balls to be moving. As the first electron moves it causes the lattice to distort and creates the depression in the rubber sheet. However, the motion of the ball and the relaxation of the rubber sheet occur on different time scales, with the ball moving much faster. This means that there is still a depression in the rubber sheet even after the ball has moved on. This allows the second ball to roll into the well and become effectively bound to the first ball. This is demonstrated by the next animation.

Video of the movement of particles into and out of a depression

Up to now we have considered pairs to be correlated over a fairly short distance. In fact the mean separation at which pair correlation becomes effective is between 100 and 1000 nm. This distance is referred to as the coherence length, ξCo, of the Cooper pair. This coherence length is large compared with the mean separation between conduction electrons in a metal. Thus Cooper pairs overlap greatly. In between one pair there may be up to 107 other electrons which are themselves bound as pairs.