Bardeen, Cooper, and Schrieffer

The electronic theory of metallic superconduction was established by Bardeen, Cooper and Schrieffer in 1957, but the basis of superconduction in the oxides remains a battleground for rival interpretations. The technology of the oxide ( high-temperature ) superconductors is currently receiving a great deal of attention the central problem is to make windable wires or tapes from an intensely brittle material. It is in no way a negative judgment on the importance and interest of these materials that they do not receive a detailed discussion here it is simply that they do not lend themselves to a superficial account, and there is no space here for a discussion in the detail that they intrinsically deserve. 

Bardeen, Cooper, and Schrieffer (BCS) theory, 23 804, 836 Bareboat charters, 25 327 Barex, composition of, 3 386t... 

Another interesting application of the total energy approach involves superconductivity. For conventional superconductors, the 1957 theory of Bardeen, Cooper and Schrieffer [26] has been subject to extensive tests and has emerged as one of the most successful theories in physics. However, because the superconducting transition temperature Tc depends exponentially on the electron-phonon coupling parameter X and the electron-electron Coulomb parameter p, it has been difficult to predict new superconductors. The sensitivity is further enhanced because the net attractive electron-electron pairing interaction is proportional to X-p, so when these parameters are comparable, they need to be determined with precision. 

We may now consider the most basic form of the relationship between lattice properties and one of the most important physical properties of the bismuthates, the superconducting Tc, as derived from the theories of Bardeen, Cooper and Schrieffer ... 

In 1957 the research team of Bardeen, Cooper, and Schrieffer produced a theory, now known as the BCS theory, that managed to explain all the major properties of... 

In 1957, Bardeen, Cooper, and Schrieffer published their theory of superconductivity, known as the BCS theory. It predicts that under certain conditions, the attraction between two conduction electrons due to a succession of phonon interactions can slightly exceed the repulsion that they exert directly on one another due to the Coulomb interaction of their like charges. The two electrons are thus weakly bound together forming a so-called Cooper pair. It is these Cooper pairs that are responsible for superconductivity. In conventional superconductors, these electrons are paired so that their spin and orbital angular momenta cancel. They are described by a wave function, known as an order parameter. In this case the order parameter has symmetry similar to that of the wave function of s electrons and represents a singlet state. 

In 1957, Bardeen, Cooper and Schrieffer proposed [3] a quantum theory of superconductivity, known as the BCS theory, for which they received a Nobel Prize. Their theory in non-mathematical terms can be summarized as follows ... 

ID 2D 3C10 3D AcrH+ AF BCS bddt2- One dimensional Two dimensional Tridecylmethylammonium, [(CioH2i)3NCH3]+ Three dimensional Acridinium, [Ci3H10N]+ Antiferromagnetic Bardeen, Cooper, and Schrieffer 4 ,5,6,7,8,8 -Hexahydro-1,4-benzodithiin-2,3-dithiolato, [C8H10S4]2 ... 

Fig. 12.26. A plot of the maximum superconducting critical temperature with time showing, in addition, the important discoveries of the Meissner effect, the microscopic Bardeen, Cooper and Schrieffer (BCS) theory and the temperature barrier, set by the boiling point of liquid nitrogen. (Reproduced by courtesy of Dr. J.M. Bell,...

Superconductors are a special sort of material which conducts with no resistance below a temperature called the critical temperature (Figure 5.14). As we have seen, the conductivity of conductors falls with increasing temperature, as the lattice vibrations increase and hinder the flow of current. In a superconductor the electrons are thought to move in pairs with the lattice vibrations in a concerted process, so there is no resistance. Bardeen, Cooper and Schrieffer proposed a theory (called BCS theory) to explain superconductivity involving the movement of electrons with opposite spin in pairs. When an electron moves past a lattice point. 

Hence to produce a gap, one has to devise a physically meaningful wave function that has phase coherence and equal amplitudes for the and a potential U which is attractive (i.e., leads to matrix elements U = -V). In the next section, we review how Bardeen, Cooper and Schrieffer (7) (BCS) met this challenge. 

As the mechanism of superconductivity in these doped fullerites was not clear, the greatest attention was directed to the standard mechanism of superconductivity. The conventional theory is based on the electron-phonon interaction and generalized in the Eliashberg equations which include the Bardeen, Cooper and Schrieffer (BCS) equation as a weak-coupling limit [78]. For real superconductors the ratio for the weak-coupling limit is close to the value of 3.52, and for stronger coupling materials it increases up to about 5.1... 

After the initial discovery by Onnes of superconductivity in mercury, tin, and lead, research focused on the discovery of new superconducting phases with even higher values. It was found that 25 % of the elements of the periodic table are superconductors and that a plethora of alloys exhibit superconductivity [16]. A theory to describe the phenomenon of superconductivity was introduced by Bardeen, Cooper, and Schrieffer (BCS) which, as originally formulated, placed an upper limit on Tc of about 35 to 40 K [19]. For a synopsis of the historical development of superconductor theory, see [20]. We shall use the term low temperature superconductor (LTS) as a reference to those materials which possess values less than the theoretical limit of 35 to 40 K imposed by the original BCS theory. 

Superconductivity was first discovered in mercury by H. Kamerlingh Onnes in 1911 (329) and eluded attempts at explanation until, in 1957, Bardeen, Cooper, and Schrieffer formulated the BCS theory (29) based on an electron-lattice-electron interaction. This theory and two others [by W. A. Little (268) and H. Frohlich (152)] are briefly described a full review is beyond the scope of this article. Interest in this area has been heightened by the report of superconducting fluctuations in the one-dimensional organic material, tetrathio-fulvalenium tetracyanoquinodimethanide, (TTF)(TCNQ) (97). 

The choice of the point is critical and determined by the condition that the ground state should contain a certain number of electrons. It is not apparent that this number always should be an integer, and we may have to accept states of the type used by Bardeen, Cooper, and Schrieffer in their theory of superconductivity, he., a superposition of states with varying number of particles. This difficulty has not occurred in actual applications carried out so far. 

The first detailed quantum-mechanical explanation of superconductivity was given by Bardeen, Cooper, and Schrieffer in 1957 [7] (commonly called the BCS theory). Since then various advances in the mathematics of the theory have been made, but the basic physical interpretation has not changed. In this theory conduction electrons of equal but opposite angular momentum fall as pairs into a lowest energy state which is separated from the first excited state by a temperature dependent gap in the spectrum of allowed energies. The existence of... 

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 ... 

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