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The Miracle of Electron Pairing: Why Can Tiny Attractions Cause Superconductivity?
In the field of condensed matter physics, a Cooper pair or BCS pair (Bardeen-Cooper-Schriver pair) is a pair of electrons that combine in a specific way at low temperatures. This concept was first proposed by American physicist Leon Cooper in 1956. Cooper showed that even with only a weak attraction, electrons inside a metal can form a pair state with an energy lower than the Fermi energy, suggesting that the pair is bound. In traditional superconductors, this attraction arises from the interaction between electrons and phonons.
The state of Cooper pairs is the origin of the phenomenon of superconductivity, as described by the BCS theory proposed by John Bardeen, Leon Cooper and John Shriver. The three scientists therefore shared the 1972 Nobel Prize. Bell Prize.
Although Cooper pairing is a quantum effect, the basic concept of its pairing mechanism can be explained with a simplified classical explanation. Normally, electrons within a metal appear to move freely, but are repelled by the negative charges between them; however, they also attract the positive ions that make up the metal's crystal lattice. This attraction will deform the ions in the crystal lattice, thereby increasing the positive charge density in the area close to the electrons, thereby attracting other electrons. At larger distances, this attraction between electrons due to displaced ions has the potential to overcome the repulsion between electrons, prompting them to pair up.
An in-depth explanation of quantum mechanics shows that this effect arises from the interaction between electrons and phonons, which are the collective movement of positive charges in the crystal lattice. The energy of pairing interactions is quite small, on the order of 0.001 eV, so thermal energy can easily break these pairs. This is why in metals or other substrates, Cooper pairs can only be formed when there are more electrons at low temperatures.
Paired electrons do not necessarily need to be close together, because this interaction is long-range. The paired electrons may be hundreds of nanometers apart, and this distance is usually greater than the average electron spacing, which allows many Cooper pairs to occupy the same space.
Electrons have spin 1/2, so they are fermions, but Cooper pairs have an integer spin (0 or 1), so they form composite bosons. This means that their wave functions are symmetric in particle interchange. Therefore, unlike electrons, multiple Cooper pairs can be in the same quantum state, which is the main reason for superconductivity.
BCS theory is also applicable to other fermion systems, such as the superfluidity of ^3He. Cooper pairing is also considered to be the reason why ^3He is superfluid at low temperatures. Furthermore, in 2008, it was suggested that boson pairs in the optical lattice might be similar to Cooper pairs. This suggests that Cooper pairs are not limited to interactions between electrons, but may also extend to other particle systems.
The formation of Cooper pairs causes all Cooper pairs to "condensate" to the same ground state within the material, which is a peculiar property exhibited by superconductivity.
Cooper initially considered only the formation of isolated pairs within the metal, then explored the more realistic formation of multiple pairs in BCS theory and found that pairing creates an energy gap in the continuous spectrum of allowed energy states of electrons. This means that all excitations of the system need to have a certain minimum energy. This energy gap for excitations leads to superconductivity because small excitations such as electron scattering are prohibited. This energy gap comes from the many-body effect caused by the mutual attraction between electrons.
R.A. Ogg Jr. first suggested that electrons might behave as pairs coupled by lattice vibrations, a notion supported by isotope effects observed in superconductors. This effect shows that materials with heavier ions (different nuclear isotopes) have lower superconducting transition temperatures, which can be explained by the Cooper pairing theory: heavier ions have a weaker ability to attract and move electrons, which results in The binding energy of the right pair is smaller.
Although current theories do not rely on specific electron-phonon interactions, condensed matter theorists have proposed pairing mechanisms based on other attractive interactions, such as electron-exciton interactions or electron-plasma interactions . As of now, these other pairing interactions have not been observed in any material.
It is worth noting that Cooper pairing does not involve the pairing of individual electrons to form "quasi-bosons". Its paired state is the energetically dominant electronic state, and electrons will preferentially move in and out of these states.
As the core of Cooper's pairing theory, the quadratic coherence involved in the mathematical description has been proposed by Yang. With the potential contribution of superconductivity phenomena to the development of science and technology, how will future research illuminate the path to understanding superconductivity and the formation of Cooper pairs?
