Cooper pair

Cooper pair
Name	Cooper pair
Composition	Two bound electrons
Statistics	Bosonic
Theorized	Leon Cooper (1956)
Discovered	Implied by BCS theory (1957)

Cooper pair. In condensed matter physics, a Cooper pair is a bound state of two electrons with opposite momentum and spin that forms in a superconductor at low temperatures. This pairing, mediated by an attractive interaction through the crystal lattice, allows the electrons to overcome their mutual Coulomb repulsion. The formation of these pairs is the fundamental mechanism underlying conventional superconductivity, as described by the BCS theory developed by John Bardeen, Leon Cooper, and John Robert Schrieffer.

Discovery and historical context

The concept was first introduced by Leon Cooper in 1956, providing a key breakthrough in understanding superconductivity, a phenomenon first observed in mercury by Heike Kamerlingh Onnes. Cooper's work demonstrated that even a weak attractive interaction between electrons, via exchange of virtual phonons, could lead to a bound state. This insight was directly incorporated into the comprehensive BCS theory, formulated at the University of Illinois Urbana-Champaign, which successfully explained the properties of conventional superconductors. The theory resolved long-standing puzzles from the earlier London equations and Ginzburg–Landau theory, earning John Bardeen, Leon Cooper, and John Robert Schrieffer the Nobel Prize in Physics in 1972.

Formation mechanism

The pairing mechanism arises from an effective attractive interaction between two electrons near the Fermi surface. As one electron moves through the crystal lattice, it distorts the positively charged ion cores, creating a region of enhanced positive charge. A second electron is attracted to this distortion. This interaction is mathematically described as an exchange of virtual phonons, the quanta of lattice vibration. The net attraction can overcome the natural Coulomb repulsion between electrons within a certain energy range, known as the Debye frequency. This process leads to the formation of a bound state where the paired electrons have opposite momentum and spin, forming a singlet state.

Properties and characteristics

A Cooper pair behaves as a composite boson, in contrast to its constituent fermionic electrons. This allows all pairs to condense into the same quantum state, a macroscopic wave function described by the Ginzburg–Landau theory. The pairs have a finite spatial extent, characterized by the coherence length, which is typically much larger than the inter-electron spacing in the material. The binding energy of a pair is relatively weak, on the order of millielectronvolts, corresponding to the superconducting gap observed in experiments. The pairs also carry charge, specifically a charge of 2e, which is central to the dissipationless supercurrent.

Role in superconductivity

The condensation of Cooper pairs into a single quantum state is responsible for the two defining properties of a superconductor: zero electrical resistance and the expulsion of magnetic fields, known as the Meissner effect. The collective motion of the pairs as a superfluid cannot be scattered by individual impurities or lattice vibrations, leading to perfect conductivity. This state is protected by the superconducting gap in the energy spectrum. The dynamics and phase coherence of the pairs' wave function are described by the Josephson effect, which is foundational for devices like SQUID magnetometers and forms the basis of superconducting quantum computing.

Experimental evidence and verification

The existence of Cooper pairs has been confirmed through numerous experiments. The superconducting gap was first directly observed in tunneling spectroscopy experiments by Ivar Giaever, for which he shared the Nobel Prize in Physics in 1973. The flux quantization observed in SQUID rings demonstrates that the magnetic flux is trapped in units of flux quantum, which depends on the charge 2e of the pair. Further confirmation comes from the Josephson effect, predicted by Brian Josephson, which shows supercurrents tunneling between two superconductors separated by an insulator. Observations of the Meissner effect and precise measurements of heat capacity also align perfectly with predictions from BCS theory.

Related theoretical concepts

The Cooper pair concept has been extended beyond conventional superconductivity. In unconventional superconductors like cuprates or iron-based superconductors, pairing may be mediated by mechanisms other than phonons, such as spin fluctuations. Theoretically, similar pairing occurs in other fermionic systems, such as in superfluid helium-3 and in nuclear matter. The Bose–Einstein condensate of tightly bound molecules in ultracold atomic gases is a direct analog. The idea of pairing also underpins the description of the quantum Hall effect and is central to theories of neutron star interiors.

Category:Condensed matter physics Category:Superconductivity Category:Quantum mechanics