Cooper pair

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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

Leon Cooper predicted pairs in 1956, and John Bardeen, Leon Cooper, and John Schrieffer built the theory of superconductivity (BCS) based on them.

How it works

An electron passing ions slightly attracts them, creating a region of increased positive charge. A second electron feels this attraction and approaches, forming a pair.

💡 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.

In BCS theory, two electrons with energies near the Fermi surface exchange virtual phonons (quanta of lattice vibrations) and form a pair with zero net spin and momentum. The effective attraction overcomes Coulomb repulsion, creating a bound state with binding energy on the order of 1–10 meV. The condensate of Cooper pairs is described by a common wave function, leading to the superconducting effect: all pairs move coherently, and scattering by lattice imperfections becomes impossible without breaking pairs. In high-temperature superconductors, the pairing mechanism is likely not phonon-mediated but involves exchange of spin fluctuations.

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.

2\Delta = 3.53 k_B T_c

Δ — energy gap (J), k_B — Boltzmann constant (1.38×10⁻²³ J/K), T_c — critical temperature (K)

Open problems & fun facts

The pairing mechanism in high-temperature superconductors remains unclear.; Search for superconducting states without Cooper pairs (e.g., in topological materials).; Possibility of stabilizing Cooper pairs at room temperature.

💡 In superconducting qubits (quantum computers), Cooper pairs tunnel through Josephson junctions, creating artificial atoms with controllable energy levels.

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Cooper pair

History

How it works

History

How it works

History

How it works

Open problems & fun facts

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