Question

Inorganic Chemistry Semiconductors

Why does a breakdown of the Pauli exclusion principle from the formation ofCooper pairs result in superconductivity?

Answer 1

According to BCS (Bardeen, Cooper and Schrieffer) theory as temperature is lowered, an attractive interaction between conduction electrons near the surface of the fermi sea binds them into "Cooper pairs". The attractive interaction results instead from collective motions of the lattice positive ions, whose modes of oscillations are called
phonons. Superconductivity does not result merely from the formation of cooper pairs, but rather from getting a significant fraction of them to occupy a single quantum state, a phenomenon known as Bose condensation. By themselves, electrons are forbidden from bose condensing because they are fermions, not bosons - the Pauli exclusion principle states that no two of them can occupy the same state. In effect, the exclusion principle holds up the fermi sea. (In an atom, it similarly explains why the electrons don't all collapse onto lowest energy atomic orbital). On the otherhand, a cooper pair is a boson and the Pauli exclusion principle does not apply to bosons. The formation of cooper pair is thought to result from electron-phonon (lattice vibration) coupling. That is, an electron moving through the lattice attracts the positively charged nuclei of the lattice atoms, causing them to be distorted from their original position. This creates a small attractive force toward another electron of opposite spin, whose motion becomes correlated with that of the original electron. The concept of phonon facilitated cooper pair formation is known as the "isotope effect". Whereas individual electrons are fermions (1/2 spin) and must obey the Pauli exclusion principle, Cooper pairs exhibit boson-like properties and hence are able to condense into the same energy level.