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The secret weapon of superconductivity: Why do Cooper pairs prevent electrons from colliding?
In condensed matter physics, Cooper pairs, also known as BCS pairs (Badren-Cooper-Schriever pairs), were proposed by American physicist Leon Cooper in 1956 , refers to pairs of electrons that bind together in a specific way at low temperatures. This phenomenon reveals the basic principles for the operation of superconductors.
Cooper showed that even a small attractive force is enough to cause electrons in metals to pair up, and the energy of the pair will be lower than the Fermi energy, meaning that the pair is bound.
In traditional superconductors, this attraction mainly comes from the interaction between electrons and phonons. Cooper pair states are the origin of superconductivity, a theory developed by John Baderyan, Leon Cooper, and John Schriever, for which they won the Nobel Prize in 1972.
Although Cooper pairing is a quantum effect, its cause can be seen in a simplified classical explanation. Electrons in metals usually behave like free particles. Due to their negative charge, the electrons repel each other, but they also attract the positive ions that make up the metal's rigid crystal lattice. This attractive force can distort the ion lattice, causing the ions to move slightly toward the electrons, thereby increasing the density of positive charges nearby.
This positive charge attracts other electrons. At longer distances, the attraction between electrons caused by the moving ions may overcome the repulsive effects between them, resulting in electron pairing.
A rigorous quantum mechanical interpretation shows that this pairing effect is caused by the interaction between electrons and phonons. Although the energy of pairing interactions is quite weak, on the order of 10 The electrons are bound in Cooper pairs.
The electrons in a Cooper pair are not necessarily close to each other because the interaction is over long distances and the distance between paired electrons may be hundreds of nanometers apart. This distance is usually greater than the average electron spacing, so many Cooper pairs can occupy Same space.
Electrons have spin 1/2, so they are fermions; however, the total spin of a Cooper pair is an integer (0 or 1), meaning it is a combinatorial boson, which makes its wave function The exchange is symmetrical.
This means that unlike electrons, many Cooper pairs can be in the same quantum state at the same time, which is the root cause of superconductivity. BCS theory also applies to other fermion systems, such as helium-3. In fact, Cooper pairing also contributed to the superfluidity of helium-3 at low temperatures.
In 2008, scientists proposed that boson pairs in optical lattices may be similar to Cooper pairs. This new perspective opened up more research directions.
The relationship between Cooper pairs and superconductivity
The tendency of all Cooper pairs to "condensate" into the same ground state in an object is the source of the strange properties of superconductivity. Cooper originally considered only the formation of isolated pairs, but when more realistic multi-electron pairing states were investigated, as illustrated by BCS theory, pairing opens an energy gap in the continuum of allowable energy states for electrons, which This means that all system excitations must have some minimum energy.
This excitation energy gap enables superconductivity because small excitations such as electron scattering are prohibited.
The energy gap occurs due to the many-body effect caused by the perceived attraction between electrons. R.A. Ogg Jr. first proposed that electrons might act as pairs coupled by lattice vibrations of a material, a theory also confirmed by isotope effects in superconductors. This effect shows that materials with heavy ions (different nuclear isotopes) will have lower superconducting transition temperatures, which can be explained by Cooper pairing theory: heavy ions have more difficulty attracting and moving electrons, which leads to pair binding Energy decreases.
The theory of Cooper pairs is fairly general and does not rely on specific electron-phonon interactions. Currently, condensed matter physicists have proposed pairing mechanisms based on other attractive interactions, such as electron-exciton interactions or electron-plasma interactions, but these pairing interactions have not been observed in any material so far.
It is worth noting that Cooper pairing does not involve the pairing of individual electrons to form "quasi-bosons". Instead, the paired states are energetically optimized, and electrons tend to move in and out of these states. John Baderen emphasized:
“Although the concept of paired electrons is not completely accurate, it captures the essence of this phenomenon.”
With the deepening of research on Cooper pairs, there may be new breakthroughs in the future that will affect our understanding of superconducting phenomena. What conditions can most effectively promote the formation of Cooper pairs?
