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Cooper pairs and superfluidity: the quantum magic behind the helium-3 superfluid phenomenon!
In condensed matter physics, a Cooper pair is a pair formed by two electrons (or other fermions) combined in a specific way under low temperature conditions. The phenomenon was first described by American physicist Leon Cooper in 1956. Cooper showed that even a weak attractive force could cause electrons to form pairing states with energies lower than the Fermi energy. This means that the pairs that are formed exist due to this strong interaction.
In conventional superconductors, this attractive force arises primarily from electron-phonon interactions.
Cooper pairs are the cornerstone of superconductivity, a theory developed by John Bardeen, Leon Cooper and John Schrieffer, for which they shared the Nobel Prize in 1972. Although Cooper pairing is a quantum effect, the cause of the pairing can be understood using a simplified classical explanation.
In metals, electrons usually move around as free particles. The negative charges of electrons repel each other, but at the same time they also attract the cations that make up the metal lattice. This attraction causes a deformation of the cation lattice, moving the cations slightly near the electrons and thus increasing the positive charge density nearby. Such a positive charge can attract other electrons. Over long distances, this attractive force due to the displaced cations overcomes the repulsive forces between the electrons, causing them to pair up.
The energy of the pairing interaction is very weak, on the order of 10-3 eV, so thermal energy can easily destroy these pairs.
Thus, only at low temperatures, in metals and other matrices, do electrons exist in significant numbers as Cooper pairs. It is important to note that the paired electrons do not have to be very close to each other. Since the interaction is long-range, the paired electrons can still be hundreds of nanometers apart, which is usually larger than the average distance between electrons, so many Cooper pairs can occupy the same space.
Electrons have spin 1/2, so they are fermions, but Cooper pairs have a total spin of integer (0 or 1), so they are composite bosons. This means that under particle exchange, the wave function of the Cooper pair is symmetric. Therefore, unlike electrons, multiple Cooper pairs can coexist in the same quantum state, which is the fundamental reason for the phenomenon of superconductivity.
The BCS theory also applies to other fermion systems, such as helium-3. In fact, Cooper pairing is what makes helium-3 superfluid at low temperatures. As science progresses, many physicists have also proposed that bosonic pairs in optical lattices may be similar to Cooper pairs.
Relationship between Cooper pairs and superconductivity
The tendency of all Cooper pairs to condense into the same ground quantum state is the source of the strange properties of superconductivity. Cooper originally considered only the formation of lone pairs in metals, but in the more realistic case of multi-electron pair formation, the full BCS theory showed that pairing opens a gap in the continuum of allowed electronic energy states, meaning that all excited states must have some minimum energy.
The energy gap of this excitation makes small excitations, such as electron scattering, impossible.
This energy gap appears due to the many-body effect caused by the mutual attraction felt by electrons. R.A. Ogg Jr. first proposed that electrons might pair up through lattice vibrations, an idea reflected in the isotope effect observed in superconductors. The isotope effect shows that materials with heavier cations have lower superconducting transition temperatures, which can be explained by the Cooper pairing theory: heavy cations are more difficult to attract and move electrons, resulting in smaller pairing energy.
The Cooper pairing theory is quite general and does not rely on specific electron-phonon interactions. Condensed matter physicists have proposed pairing mechanisms based on other attractive interactions, such as electron-exciton interactions or electron-plasmon interactions, but no examples of these other pairing interactions have been observed in any material so far.
It is worth mentioning that Cooper pairing is not the pairing of single electrons to form "quasi-bosons", but rather a pairing state with more advantages and the priority of electrons entering and exiting these states.
This is particularly evident in John Bardeen's distinction, which was made by Young, who noted that "the concept of paired electrons, while not entirely precise, captures the essence of the phenomenon."
The discovery of Cooper pairs not only laid the foundation for superconductivity, but also opened a mysterious quantum window for our understanding of the superfluidity of helium-3. How will quantum physics further advance our understanding of the properties of materials in the future?
