BCS - theory

The bound Cooper pairs can neither transport energy, nor can they participate in phonon scattering. As a result, the electronic component of thermal conductivity is diminished in the superconducting state while the phonon contribution is enhanced because of the longer 

As stated previously, the basic concept behind the BCS theory is that two electrons with opposite spins and opposite momenta (in the center of mass system) can, through phonon interactions with the lattice atoms, experience an attractive force sufficient to overcome their Coulomb repulsion and form a loosely boimd pair with zero net spin. Because they have zero net spin, they behave as Bosons and any number may occupy the groimd state. The details of the BCS theory are too complicated to be presented here (the reader is referred to the original paper (Bardeen, Cooper, and Schrieffer, 1957) cited in the references). Instead, we shall just present some of the predictions of the theory that can be tested. 

The essential result from the BCS theory is that the energy gap 2Aq between the superconducting state and the normal state at 0 K is given by 

U is the attractive potential between the two electrons that make up the Cooper pair N E) is the density of states at the Fermi level 

The condensation energy between the superconducting and normal states at T = 0 is 

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It will be intriguing to theoretically examine the possibility of superconductivity in CNT prior to the actual experimental assessment. A preliminary estimation of superconducting transition temperature (T ) for metallic CNT has been performed considering the electron-phonon coupling within the framework of the BCS theory [31]. It is important to note that there can generally exist the competition between Peierls- and superconductivity (BCS-type) transitions in lowdimensional materials. However, as has been described in Sec. 2.3, the Peierls transition can probably be suppressed in the metallic tube (a, a) due to small Fermi integrals as a whole [20]. 

J. Bardeen (Urbana), L. N, Cooper (Providence) and J, R. SchriefFer (Philadelphia) theory of superconductivity, usually called the BCS theory. 

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... 

The BCS theory leads to the following equation for the critical temperature, Tc, for superconductivity ... 

Afterwards, measurements of the specific heat have been carried out in a wider pressure range [29,37-39]. It was thus evident that there is a discontinuity at the transition temperature which, at the melting pressure, gave a AC/C 2, (well above the 1.43 value expected from BCS theory) which decreased as the pressure diminished. 

The jump in ce is due to the fact that the superconducting metal has a new degree of freedom, i.e. the possibility of entering the superconducting state. For simple superconductors, such as A1 and Sn, the Bardeen-Cooper-Schrieffer (BCS) theory [18-22] gives ... 

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

While, in the BCS theory, such attractive force for electron Cooper pair is provided by phonons, for dense quark matter, where phonons are absent, the gluon exchange interaction provides the attraction, as one-gluon exchange interaction is attractive in the color anti-triplet channel1 One therefore expects that color anti-triplet Cooper pairs will form and quark matter is color superconducting, which is indeed shown more than 20 years ago [13, 14],... 

The properties of the asymmetric superconductors have been an exciting subject since the advent of the BCS theory of superconductivity more than four decades ago. While the early studies were motivated by the effects of the para-... 

In a superconducting system, when one increases the temperature at a given chemical potential, thermal motion will eventually break up the quark Cooper pairs. In the weakly interacting Bardeen-Copper-Schrieffer (BCS) theory, the transition between the superconducting and normal phases is usually of second order. The ratio of the critical temperature TcBCS to the zero temperature value of the gap AbGS is a universal value [18]... 

The structure of the gap function (33) is then inspired by a physical consideration of a quark pair as in the usual BCS theory we consider here the quark pair on each Fermi surface with opposite momenta, p and —p so that they result in a linear combination of Jn = 0, 1 (see Fig. 3). 4... 

From BCS theory it is known, that in order to form Cooper pairs at T = 0 in a dense Fermi system, the difference in the chemical potentials of the Fermions to be paired should not exceed the size of the gap. As previous calculations within this type of models have shown [24], there is a critical chemical potential for the occurrence of quark matter pf > 300 MeV and values of the gap in the region A < 150 MeV have been found. Therefore it is natural to consider the problem of the color superconducting (2SC) phase with the assumption, that quark matter is symmetric or very close to being symmetric (pu pd). 

Bardeen, Leon Cooper and John Robert Schrieffer, which, from their initials, was called BCS theory. 

At this time, the fastest growing area in the field of nanophysics is in the studies of buckyballs and nanotubes. After the discovery [33] of the Qo molecule, many properties of the molecule and solids formed from the molecule were explored. The doped C6o crystals showed interesting behavior, including superconductivity. [34] The standard model, including the GW quasiparticle theory, was used [35] successfully to explore the energy band structure, and the superconducting properties appear to be consistent with the BCS theory. [36]... 

The classical tunneling experiment of Giaever (1960) provided unambiguous proof of the BCS theory of superconductivity. The STM as a local tunneling probe is certainly suitable to probe the local properties of superconductors, such as the local structure of the Abrikosov flux lattice. The work of Hess and co-workers (1989, 1990, 1990a, 1991) is a prominent example. 

Superconductivity has not only been beneficial to science and technology but also has been highly rewarding to its scientists. Thus far, Nobel Prizes in Physics have been awarded on four occasions to scientists working in this area. The first of these was for the discovery of superconductivity by Kamerlingh Onnes, awarded in 1913. In 1972 the prize went to John Bardeen, Leon Cooper, and Robert Schrieffer for the BCS theory. The following year (1973), the Prize was awarded to Brian Josephson, L. Esaki and I. Giaever for the... 

Gloom for Oxide Superconductors Dismayed at the progress through the years, even with the most promising room-temperature metallic, binary oxides, many scientists abandoned the search for new high temperature oxide superconductors. Also, it should be mentioned that a deep-rooted prejudice had developed which claimed that the BCS theory had imposed a maximum transition temperature limit of 25 K for all superconducting materials, and that this temperature had already been achieved in certain alloys of niobium. Some scientists, however, were steadfast in their determination to break this barrier, optimistic in their outlook, and they continued their search for this unusual phenomenon in other metallic oxide systems. 

Measurement of the specific heat at Tc should yield quite informative data. Information can be gained about the binding energy of the electrons in the Cooper pairs as mediated by electron-phonon coupling (in the BCS theory). 

Classical BCS theory dictated that superconductors with the highest Tc s would not be thermodynamically stable phases. Softening the phonons would raise Tc but would ultimately lead to structural instabilities. Increasing the density of states at the Fermi level would raise Tc but would eventually lead to an electronic instability. 

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... 

It is beyond the scope of this text to describe the mechanism for charge transfer in the high-temperature superconductors. While there is still a great deal of discussion on the applicability of BCS theory (cf. Section 6.1.1.3) to HTSC materials, it is safe to say that many of the principles still apply—for example, density of states at the Fermi level. The interested reader should refer to existing literature [3,4] for more information on the strucmre and theory of copper oxide superconductors. 

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