Cooper pairs of electrons

Cooper pairs of electrons with equal and opposite momenta attract each other in a metal, a rectangular lattice of positive ions (cations) is shown, with a free electron with momentum p that (1) has just traveled upwards and (2) has attracted some cations toward itself. Then a second free electron (3) with equal and opposite momentum -p is attracted to electron (1) because the cations, being much more massive, have not yet relaxed back to their original unperturbed positions. 

The problematic nature of the melting transition can be illustrated by comparison with other well-known first-order phase transitions, for instance the normal metal-(low T ) superconductor transition. The normal metal-superconductor and melting transitions have similar symptomatic definitions, the former being a loss of resistance to current flow, and the latter being a loss of resistance to shear. However, superconductivity can also be neatly described as a phonon-mediated (Cooper) pairing of electrons and condensation of Cooper pairs into a coherent ground state wave function. This mechanistic description of the normal metal-super-conductor transition has required considerable theoretical effort for its development, but nevertheless boils down to a simple statement, indicat-... 

The theory includes Cooper pairs of electrons but does not explain the high critical transition temperatures of the newer ceramic superconductors. 

The basic mechanism of superconductivity was accounted for in considerable detail by the theory of Bardeen, Cooper, and Schrieffer (BCS theory), which discusses the phenomenon in terms of the formation of Cooper pairs of electrons through an attractive interaction mediated by the lattice. Unlike individual electrons. 

Some years later a more thorough discussion of the motion of pairs of electrons in a metal was given by Cooper,7 as well as by Abrikosov8 and Gor kov,9 who emphasized that the effective charge in superconductivity is 2e, rather than e. The quantization of flux in units hc/2e in superconducting metals has been verified by direct experimental measurement of the magnetic moments induced in thin films.10 Cooper s discussion of the motion of electron pairs in interaction with phonons led to the development of the Bardeen-Cooper-Schrieffer (BCS) theory, which has introduced great clarification in the field of superconductivity.2... 

One conceptual element of the BCS theory is the formation of - Cooper pairs, namely pairing of -> electrons close to the Fermi level due to a slight attraction resulting from phonon interaction with the crystal lattice. These pairs of electrons act like bosons which can condense into the same energy level. An energy band gap is to be left above these electrons on the order of 10-3 eV, thus inhibiting collision interactions responsible for the ordinary - resistance. As a result, zero electrical resistivity is observed at low temperatures when the thermal energy is lower than the band gap. The founders of the BCS theory, J. Bardeen, L. Cooper, and R. Schrieffer, were awarded by the Nobel Prize in 1972. 

The prefix co- is used to indicate that two or more entities are joined or have equal standing (as in, for example, coexist, cooperate, and coordinate). It is therefore appropriate that the term covalent bond is used to describe molecular bonds that result from the sharing of one or more pairs of electrons. 

Type-I superconductors are well explained by the Bardeen-Cooper-Schrieffer (BCS) theory. In this, the superconducting state is characterised by having the mobile electrons coupled in pairs. Each pair consists of two electrons with opposite spins, called Cooper pairs. At normal temperatures, electrons strongly repel one another. As the temperature falls and the lattice vibrations diminish, a weak attractive force between pairs of electrons becomes significant. In Type-I superconductors the glue between the Cooper pairs are phonons (lattice vibrations). 

The mechanism of superconductivity is still under investigation, but BCS theory is the currently accepted model. In short, what the model says is that the crystals line up very well in the pure material, with little to no defects present. The oxidation of copper is somewhere between +2 and +3, and that free electrons join up in the crystal and form what is known as Cooper pairs. As a pair of electrons they are less likely to scatter when they come across a defect in the crystal, and so they can travel very far and very fast. This allows the current from an outside potential to be transported with high efficiency. 

The situation is different in a superconductor. In a conventional superconductor, the electric current cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs. The Cooper pairs are named for physicist Leon N. Cooper who, with John Bardeen and John Robert Schrieffer, formulated the first successful model explaining superconductivity in conventional superconductors. A key conceptual element in this theory is the pairing of electrons close to the Fermi level into pairs through interaction with the crystal lattice. 

A bonus question means that it is not a simple one. So do not feel alarmed if you could not solve it without looking at the answer. In BHg, boron misses a pair of electrons compared with how many it needs to reach Nirvana. What happens is that two molecules cooperate and use one of their B—H bond pairs to be shared with the boron atom in the other molecule. These shared B—H bonds form bridged B—H—B moieties, which have electron pairs belonging to the three centers, as shown below ... 

Why do electrons in some cases behave as single electrons and sometimes as a pair of electrons when the temperature is lowered The mechanism for the Cooper pair explains some of the characteristics of superconductivity. If there is a gap, the pairing properties become visible because pairs of electrons obey the Bose-Einstein statistics and all condense into the lowest state. It costs energy to excite across the gap, therefore there is no resistance at low temperature. 

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