``Moth-eaten effect" driven by Pauli blocking, revealed for Cooper pairs
W. V. Pogosov+*, M. Combescot+ 1)
+Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, CNRS, Campus Boucicaut, 75015 Paris, France
*Institute for Theoretical and Applied Electrodynamics RAS, 125412 Moscow, Russia
We extend the well-known Cooper's problem beyond one pair and
study how this dilute limit is connected to the many-pair BCS condensate. We
find that, all over from the dilute to the dense regime of pairs, Pauli
blocking induces the same ``moth-eaten effect" as the one existing for
composite boson excitons. This effect makes the average pair binding energy
decrease linearly with pair number, bringing it, in the standard BCS
configuration, to half the single-pair value. This proves that, at odds with
popular understanding, the BCS gap is far larger than the broken pair energy.
The increase comes from Pauli blocking between broken and unbroken pairs.
Possible link between our result and the BEC-BCS crossover is also discussed.