BCS Theory and Cooper Pairing

The microscopic theory of superconductivity shows that a tiny phonon-mediated attraction binds electrons into Cooper pairs that condense into a single coherent state with an energy gap.

Definition

BCS theory is the microscopic theory of conventional superconductivity in which a weak phonon-mediated attraction binds electrons of opposite momentum and spin near the Fermi surface into Cooper pairs that condense into a coherent ground state separated from excitations by an energy gap.

Scope

This topic covers the Bardeen-Cooper-Schrieffer theory: Cooper's demonstration that any attraction destabilizes the Fermi sea by forming bound pairs, the phonon-mediated origin of that attraction, the BCS ground state of condensed Cooper pairs, the superconducting energy gap and its temperature dependence, and the predictions for the critical temperature, specific-heat jump, and isotope effect. It is the microscopic foundation that the London and Ginzburg-Landau phenomenologies anticipated.

Core questions

• Why does an arbitrarily weak attraction make the normal Fermi sea unstable toward pairing?
• How do lattice vibrations mediate an effective attraction between electrons?
• What is the superconducting energy gap, and how does it relate to the critical temperature?
• Which experimental facts, such as the isotope effect and specific-heat jump, does BCS theory explain?

Key concepts

• Cooper pairs and the Cooper instability
• Phonon-mediated attraction
• BCS ground state and condensate
• Superconducting energy gap
• Isotope effect and the critical temperature

Key theories

Cooper instability

Cooper showed that two electrons just above a filled Fermi sea form a bound pair for any attractive interaction, however weak, so the normal metallic state is unstable toward pairing and a new ground state must form.

BCS ground state

Bardeen, Cooper, and Schrieffer built a coherent many-body wavefunction of condensed Cooper pairs that opens an energy gap at the Fermi surface and quantitatively predicts the critical temperature, the specific-heat jump, and the isotope effect.

Clinical relevance

BCS theory explains and predicts the properties of conventional superconductors used in magnets, sensors, and accelerators, and its concepts of pairing and condensation recur across physics, from superfluid helium-3 to neutron stars and the Higgs mechanism analogy in particle physics.

History

After Fröhlich identified the electron-phonon interaction and the isotope effect pointed to phonons, Cooper showed in 1956 that paired electrons bind, and in 1957 Bardeen, Cooper, and Schrieffer completed the microscopic theory, work that earned the 1972 Nobel Prize in Physics.

Key figures

• John Bardeen
• Leon Cooper
• John Robert Schrieffer

Seminal works

• bardeen1957
• cooper1956

Frequently asked questions

How can two negatively charged electrons attract each other?

One electron distorts the lattice of positive ions, drawing them inward; the resulting transient excess of positive charge attracts a second electron. This retarded, phonon-mediated interaction can outweigh the screened Coulomb repulsion and bind a Cooper pair.

What is the role of the energy gap?

The condensed Cooper pairs are separated from any excited state by an energy gap, so low-energy scattering that would dissipate current is forbidden; this gap is what gives a conventional superconductor its zero resistance and its exponential thermal properties.