Cooper Pairs
A Cooper pair is a loosely bound pair of electrons, formed through an effective attractive interaction mediated by vibrations of the crystal lattice (phonons), that together behave as a composite boson rather than as two individual fermions — the fundamental charge-carrying entity underlying conventional (BCS) superconductivity.
Curious
Electrons carry the same negative electric charge, so they should always repel each other directly. Leon Cooper showed in 1956 that, remarkably, an indirect attractive interaction can nonetheless arise between electrons in a metal at low temperature: one electron passing through the crystal lattice slightly attracts nearby positive ions, creating a fleeting, localised region of enhanced positive charge; a second electron passing through shortly afterward can be attracted to that residual distortion, producing a net effective attraction between the two electrons, mediated by the lattice's vibrations (phonons) rather than by any direct electron-electron force.
This attraction, though weak, is enough at sufficiently low temperature to bind electrons into loosely associated pairs. Crucially, a pair of electrons (each an individual fermion) combines to form a composite particle with integer total spin — a boson — and bosons, unlike fermions, can condense collectively into the same quantum state, which is precisely what allows the resulting Cooper pairs to flow through the superconductor collectively and coherently, without scattering and without resistance.
Exploring
| Property | Cooper pair |
|---|---|
| Constituents | 2 electrons, typically with opposite momentum and opposite spin |
| Binding mechanism | Phonon-mediated (lattice vibration) attraction |
| Statistics | Composite boson (integer total spin) |
| Typical pair size | Hundreds to thousands of nanometres — much larger than the average spacing between electrons |
Deep Dive
Leon Cooper's 1956 paper showed the surprising result that, in a Fermi gas of electrons (like those in a metal), an arbitrarily weak attractive interaction between electrons near the Fermi surface is enough to produce a bound pair state with lower energy than the unpaired configuration — a result that held even for the weak, phonon-mediated attraction available in real metals, and that provided the crucial missing physical mechanism enabling Bardeen, Cooper, and Schrieffer to complete the full BCS theory of superconductivity the following year, in 1957.
The energy gap: Formation of Cooper pairs opens an energy gap in the material's electronic spectrum — a minimum energy required to break a Cooper pair apart into two separate, unpaired electrons. This gap is directly responsible for several distinctive superconducting properties, including zero electrical resistance itself (since breaking apart the collectively flowing Cooper pair condensate to create resistive scattering requires overcoming this energy gap, which is unavailable at sufficiently low temperatures and currents) and characteristic features observed in tunnelling and spectroscopic experiments, providing some of the most direct experimental confirmations of BCS theory.
Cooper pairing is specific to conventional superconductors well-described by BCS theory; unconventional and high-temperature superconductors (discovered in 1986, well after BCS theory) are now understood to also involve electron pairing, but the precise pairing mechanism in these materials — whether phonon-mediated or something else entirely, such as magnetic interactions — remains an active area of theoretical and experimental research, unresolved nearly four decades after their discovery.
Concept Relationship Map
Requires: superconductivity, Fermi energy
Enables: BCS theory [PENDING FULL ENTRY]
Commonly confused with: imagining Cooper pairs as tightly bound, localised particle pairs (they're highly delocalised, spanning far more space than the electron spacing)
Sources
- Cooper, L.N. (1956). Physical Review, 104(4), 1189–1190.
- Bardeen, J., Cooper, L.N., Schrieffer, J.R. (1957). Physical Review, 108(5), 1175–1204.