7. Superconductivity - University of Liverpool

The bound pair is called a Cooper pair. The electrons would
have opposite spin, so the resultant spin is zero - the pair is a
boson. Since the electrons have equal and opposite
momentum, the resultant momentum is also zero. As Cooper
pairs are bosons, they can all occupy the same zero momentum
state, and form a condensate. This is the beginning of the
explanation for the zero resistance.
So a gap ∆ opens up in the dispersion relation of the free
electrons, when the metal becomes superconducting.
∆ would be the excitation energy that breaks the Cooper pair.
This gives a Landau critical velocity of ∆/p F . If electrons flow
below this velocity, the Cooper pairs would be superconducting.
Above this critical current, the Cooper pairs would be broken.
Superconductivity 63