a Cooper pair
/ KOO-per /
A Cooper pair is a pair of electrons that, against all naive expectation, bind together even though two electrons repel one another. Leon Cooper showed that in the presence of the lattice, an arbitrarily weak attraction is enough to make the calm sea of electrons in a metal unstable: two electrons just above the Fermi surface will bind into a pair. These paired electrons, not single ones, are the true carriers of a supercurrent.
The attraction is mediated by phonons, the quanta of lattice vibration. One electron, sweeping past, tugs the positive ions of the lattice inward and leaves behind a fleeting region of extra positive charge; a second electron is drawn toward that overdensity. The net effect is a weak, retarded attraction that can overcome the screened Coulomb repulsion. The two electrons pair with equal and opposite momenta and opposite spins, the state (k up, -k down), giving the pair zero net momentum and total spin zero, a spin singlet. Being a composite of two fermions, the pair behaves as a boson and can join a macroscopic condensate. Its size, the coherence length, is typically hundreds of nanometres, vastly larger than the spacing between atoms.
The Cooper pair is the microscopic object that carries current without resistance, and the energy needed to break one apart, 2 Delta, is exactly the superconducting energy gap. The essential caveat is that a Cooper pair is nothing like a tightly bound molecule of two electrons stuck together. Because its coherence length is so large, each pair overlaps with millions of others; the pairs are not discrete objects but a single, mutually interpenetrating, coherent quantum fluid.
In a typical superconductor the coherence length is around 100 nm to 1000 nm, so a single Cooper pair spans roughly a thousand lattice spacings and overlaps with millions of other pairs at once.
Two electrons of opposite momentum and spin, glued by phonons into a boson-like pair.
A Cooper pair is not a compact two-electron molecule; its members are separated by hundreds of atoms and its wavefunction overlaps millions of other pairs.