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Why do Cooper pairs break the laws of physics? Discover how electron pairing creates resistance-free flow of electricity!
In condensed matter physics, Cooper pairs are pairs of particles bound together by electrons (or other fermions) at low temperatures. This phenomenon was first described by American physicist Leon Cooper as early as 1956. Cooper's work showed that even tiny attractive forces can cause electron pairs to bind together, and their total energy will be below the Fermi energy, suggesting that the pair is stable. In conventional superconductors, this attraction comes primarily from electron-phonon interactions.
"Cooper pairs are at the heart of superconductivity, and it is this state that gives materials the ability to carry electric current without resistance."
Although the behavior of Cooper pairs is a quantum effect, we can understand its cause through a simplified classical explanation. In metals, electrons are usually considered as free particles. Under normal circumstances, electrons repel each other because of their negative charge, but at the same time they also attract positive ions that form the metal's rigid lattice. This attraction distorts the ionic lattice, causing the ions to move slightly toward the electrons, increasing the positive charge density in that area. This positive charge attracts other electrons. Over long distances, the attractive force caused by the ions' deflection may overcome the repulsion between the electrons, causing them to pair up.
"The interaction energy of this pair is quite weak, about 10-3 eV."
Of course, this electron pairing only occurs significantly in metals or other substrates at low temperatures. In Cooper pairs, although the interactions of the electrons can be distant, this does not mean that they must be very close to each other. Paired electrons may still be hundreds of nanometers apart, a distance that is typically larger than the average electron spacing, so many Cooper pairs can occupy the same space. It is worth noting that the electron is a spin-1/2 fermion, while the Cooper pairs have an integer total spin (0 or 1), which makes them composite bosons, meaning that their wave function is The particles are symmetrical when they are interchanged.
Therefore, the existence of Cooper pairs makes it possible to have multiple Cooper pairs in the same quantum state, which is the key to the superconductivity phenomenon. In addition to superconductors, the BCS theory can also be applied to other fermion systems, such as superfluid helium-3. In fact, Cooper pairing also makes helium-3 superfluid at low temperatures. In 2008, scientists proposed the concept that boson pairs in optical lattices might be similar to Cooper pairs.
"The formation of Cooper pairs involves an amplification effect coupled by lattice vibrations."
The tendency of all Cooper pairs in a system to "condense" into the same ground state is the fundamental reason for the property of superconductivity. Cooper initially considered only the formation of lone electron pairs in metals. But in a more realistic scenario, when the formation of multiple electron pairs is considered, it is found that this pairing opens an energy gap in the continuum of allowed energy states for electrons, which means that all excitations of the system must have A certain amount of energy. This excitation gap leads to superconductivity because small excitations, such as the scattering of electrons, are forbidden. This gap appears as a result of the attractive forces felt between electrons and the many-body effect.
R. A. Ogg Jr. first proposed that electrons could couple in pairs through lattice vibrations in a material. This is demonstrated by the isotope effect observed in superconductors. This effect shows that materials with heavier ions (different nuclear isotopes) have lower superconducting transition temperatures. This can be explained by the theory of Cooper pairing: heavier ions create greater difficulties for the attraction and movement of electrons, which leads to a smaller pairing binding energy.
"The theory of Cooper pairing is quite general and does not depend on a specific electron-phonon interaction."
Condensed matter physicists have proposed pairing mechanisms based on other attractive interactions, such as electron-exciton interactions or electron-plasmon interactions, but these other pairing interactions have not yet been observed in any material. . It is worth mentioning that Cooper pairing does not involve the pairing of individual electrons to form "quasi-bosons". Paired states are energetically preferred, and electrons will preferentially enter and leave these states. This is a subtle distinction that John Bardeen emphasized: "While this is not a technically accurate description of the concept of electron pairing, it still captures the essence of it."
A deeper understanding of this system not only changes our understanding of the physics of materials, but also provides unlimited possibilities for future technological advances. Can humans discover the same superconductivity phenomenon in a higher temperature range, perhaps changing our energy future?
