concept

Cooper pair

A Cooper pair is a bound state of two electrons that enables superconductivity through their correlated motion.
41 related articles · 3 formulas · 1 who worked here

Description

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.

History

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.

How it works

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.

In practice

Without Cooper pairs, MRI and maglev trains would not work; they are the foundation of all superconducting electronics.

Fun fact

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.

Concept graph →

Formulas

$$C = \frac{4g^2}{\kappa_1 \kappa_2}$$
Parameter quantifying coupling strength between two modes in cavity QED.
What is in the formula
gvariablecoupling strength between the two modes — coupling strength radian per second
κ₁variabledecay rate of the first mode — decay rate radian per second
κ₂variabledecay rate of the second mode — decay rate radian per second
c=\frac{4g_0^2n_p}{\kappa_o\kappa_m} · 2505.02057v4
$$U = E_{\text{pair}} < 0$$
Pairing energy must be negative for favorable pair formation.
What is in the formula
UvariablePairing energy — energy joule
E_{\text{pair}}variablePairing energy contribution — energy joule
u=e_2+e_0-e_1-e_{1'}<0 · 2607.03022
$$E_1 E_2 \ge m_e^2 c^4$$
Minimum photon energy product for electron-positron pair creation.
What is in the formula
E_1variableEnergy of first photon — energy joule
E_2variableEnergy of second photon — energy joule
m_evariableElectron rest mass — mass kilogram
cvariableSpeed of light in vacuum — speed of light metre per second
e_1e_2\gem_e^2c^4 · 2607.14276

Related articles · 123

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