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The phonon’s attractive force has begun to entice other electrons to draw near. Once one of
these other electrons comes close enough, a Cooper Pair is formed. Despite their
electromagnetic repulsion, the two electrons are now indirectly attracted to one another by
the generated phonon and seem to behave as one singular particle: a Cooper Pair. In
conventional superconductors, Cooper Pairs can exist in two different states: the spin-singlet
state, and the spin-triplet state. The spin-singlet state is formed when two paired electrons –
electrons that must have opposite spins – form a Cooper Pair, so that one has a +1⁄2 spin and
the other has a -1⁄2 spin. Therefore the total spin of the spin-singlet Cooper Pair can only take
a single value: 0 (hence the name spin-singlet). The spin-triplet state is formed when two
unpaired electrons form a Cooper Pair. This means the two electrons do not necessarily need
to have opposite spins to one another. The total spin of a spin-triplet Cooper Pair can take
one of three values:
- +1⁄2 and +1⁄2 = 1
- + 1⁄2 and -1⁄2 = 0
- - 1⁄2 and - 1⁄2 = -1
Did you notice that regardless of what value of spin each individual electron had, the Cooper
Pair always had a total spin that took an integer value?* If you can recall from earlier in this
article, we knew that particles that took integer spin values were not fermions, but bosons.
Now we know that Cooper Pairs, which are made up of two fermions, are in fact, bosons.
Hooray! Now we know Cooper Pairs are bosons, so they don’t have to follow the Pauli
Exclusion Principle any longer.
* It
is a common misconception that the two electrons in a spin-
triplet Cooper Pair violate the Pauli Exclusion Principle; after
all, they make up the same composite particle and have the
same spin. However, the formation of a Cooper Pair relies on
electron-phonon-electron interactions over a specific distance.
To maintain this distance, the two electrons must always be at
different points in space, thus yielding different sets of
quantum numbers.