Bardeen Cooper Schrieffer model

Haag, R. (1962). The mathematical structure of the Bardeen-Cooper-Schrieffer model. 11 Nuovo Cimento 25(2), 287-299. 

Rosseinsky et al. also suggested a simple reason for the large increase in transition temperature when Rb is substituted for K. The most elementary, widely understood theory of superconductivity, the weak-coupling Bardeen-Cooper-Schrieffer (BCS) model,[Bat57] predicts a simple connection between transition temperature Tc, phonon energy w, electron-phonon coupling strength V, and the density of electron states at the Fermi surface N EfI... 

The nature and origin of superconductivity was described in 1957 by John Bardeen, Leon Neil Cooper, and John Robert Schrieffer. Together they created the Bardeen Cooper Schrieffer (BCS) model. It occurs for many metals, alloys, intermetallic compounds, and doped semiconductors. The transition temperatures range from 92.5 K for Ybc CUjOg j, down to 0.001 K for the element Rh. And there are some materials that become superconducting only under high-pressure conditions. These materials all have to be extremely pure, even just one impurity in 10,000 atoms can severely affect the superconducting property. 

If there are many valence protons and neutrons present in the nucleus, traditional shell model calculations lead to insurmountable difficulties. Fortunately, the Bardeen-Cooper-Schrieffer (BCS) theory provides a good approximation method to the seniority-zero shell model, and allows to describe very complex nuclei, too. In the BCS quasiparticle calculations long chains of nuclei can be treated in a relatively simple way. The method was first applied in the theory of superconductivity by Bardeen et al. (1957), then used for nuclear physics by Bohr et al. (1958), Soloviev (1958), and Belyaev (1959). The quasiparticle concept was introduced into nuclear physics by Valatin (1958) and Bogoliubov (1958). The theory is explained in detail in several textbooks (Lawson 1980 Ring and Schuck 1980 Soloviev 1981 Heyde 1990 Nilsson and Ragnarsson 1995 Fenyes 2002). 

In 1957, Bardeen, Cooper, and Schrieffer (BCS) finally formulated a rough theoretical model for superconductivity. In this BCS model, the problem of electron pairing among free electrons was solved in a surprising way. The coupling between the electrons of the pair lies in the formation of the Cooper pair, which is held together by electron-phonon interactions. The BCS model explains the energy gap, since such a gap is a typical feature of the Cooper pair. 

The BCS theory, however, developed in 1957 by three physicists, John Bardeen, Leon Cooper, and Robert Schrieffer, does estabhsh a model for the mechanism behind superconductivity. Bardeen, Cooper, and Schrieffer received the Nobel Prize in physics in 1972 for their theory. It was known that the flux quantum was inversely proportional to twice the charge of an electron, and it had also been observed that different isotopes of the same superconducting element had different critical temperatures. Actually, the heavier the isotope, the lower the critical temperature is. The critical temperature, in K, of an isotope with an atomic mass, M, expressed in kg.moT can be predicted by the following equation ... 

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. 

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