
A Cooper pair is a bound state of two electrons that enables superconductivity through their correlated motion.A Cooper pair is a bound state of two electrons with opposite spins (intrinsic angular momenta) and momenta, arising from phonon-mediated attraction in the lattice. The pairs behave as bosons (particles with integer spin) and condense into a single quantum state, giving rise to superconductivity.
In 1956, Leon Cooper showed that in a degenerate Fermi gas, arbitrarily weak electron-electron attraction leads to the formation of a bound state of two electrons — a Cooper pair. In 1957, John Bardeen, Leon Cooper, and John Schrieffer generalized this to a many-body system, creating the microscopic theory of superconductivity (BCS). The existence of pairs was experimentally confirmed through tunneling effects (Ivar Giaever, 1960) and direct observation of the superconducting gap in the spectrum.
A conduction electron moves in the crystal lattice and polarizes it, displacing positive ions from equilibrium. This creates a local excess of positive charge, which attracts a second electron. Due to the inertia of ions, the interaction is retarded, avoiding instantaneous Coulomb repulsion. In momentum space, the attraction is maximal for electrons with opposite wave vectors (k and –k) and antiparallel spins. According to the Pauli principle, two fermions cannot occupy the same state, but a pair with integer spin acts as a boson, obeying Bose-Einstein statistics. The spin-statistics theorem guarantees that Cooper pairs can accumulate in the ground state, forming a macroscopic quantum condensate. The binding energy of the pair determines the magnitude of the superconducting gap Δ, which protects the current from dissipation.
Without Cooper pairs, MRI and maglev trains would not work; they are the foundation of all superconducting electronics.
The size of a Cooper pair in classical superconductors is about 1000 interatomic distances; the electrons in a pair can be separated by hundreds of nanometers, interacting at a distance.
| g | variable | coupling strength between the two modes — coupling strength radian per second |
| κ₁ | variable | decay rate of the first mode — decay rate radian per second |
| κ₂ | variable | decay rate of the second mode — decay rate radian per second |
| U | variable | Pairing energy — energy joule |
| E_{\text{pair}} | variable | Pairing energy contribution — energy joule |
| E_1 | variable | Energy of first photon — energy joule |
| E_2 | variable | Energy of second photon — energy joule |
| m_e | variable | Electron rest mass — mass kilogram |
| c | variable | Speed of light in vacuum — speed of light metre per second |


















