BCS Superconductivity

Earlier, I criticized the Cooper pair being philosophically unacceptable because the proposed pair is not seen elsewhere outside of the BCS superconductivity theory. The same measurement must be placed against the Covalon-Conduction theory proposed here. We shall show therefore, that a number of physical property changes observed in [TCNQ-TTF] (tetracyano-p-quinodimethane-tetrathiofulvalene), an organic compound, as a function of temperature can be interpreted and understood in terms of Covalon-conduction . 

The BCS superconducting state is characterized by an attractive potential between electrons arising from an electron-phonon interaction. We will now review how this interaction is derived (9). The direct electron-phonon interaction is a result of the potential between the electrons and the nuclear charges when the nuclei vibrate about their equilibrium positions. The electron-ion (e-i) interaction is expanded in terms of displacements Qj of the nuclear coordinates from their equilibrium positions Rn... 

The symmetric limit corresponds very probably to the BCS superconductivity in the conducting polymer24 (SN)X. It seems that there the ratio of the longitudinal and transverse correlation lengths is temperature independent, as in Equ. (45). 

Fieri, P. and Strinati, G.C., Strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation, Phys. Rev. B, 61,15370, 2000. 

A purely electronic transition to a non-BCS superconducting state under pressure with Tc = 39 K has been described recently by Takabayashi et al. (2009) for the disorder-free CS3Q0 cesium fulleride with A15 crystal structure. At ambient pressure, this compound behaves as an antiferromagnetic insulator. 

Another interesting study is that of Yang et al. [28]. They used a NMR quantum computer to simulate the BCS superconductivity Hamiltonian. In the experiment, performed in the two-qubit chloroform dissolved in acetone- /6, they observed the energy gap between the superconductor and normal states, directly from the NMR spectrum. 

Starting with the expressions for the energy and the entropy of the BCS superconducting state at finite temperature, Eqs. (8.23), (8.24), and the definition the temperature-dependent gap, Eq. (8.25), use a variational argument on the free energy to prove the finite-temperature gap equation, Eq. (8.26). Then use the BCS model defined in the previous problem, with the gap being a temperature-dependent quantity A(T), to show that ... 

Superconductivity The physical state in which all resistance to the flow of direct-current electricity disappears is defined as superconductivity. The Bardeen-Cooper-Schriefer (BCS) theoiy has been reasonably successful in accounting for most of the basic features observed of the superconducting state for low-temperature superconductors (LTS) operating below 23 K. The advent of the ceramic high-temperature superconductors (HTS) by Bednorz and Miller (Z. Phys. B64, 189, 1989) has called for modifications to existing theories which have not been finahzed to date. The massive interest in the new superconductors that can be cooled with liquid nitrogen is just now beginning to make its way into new applications. 

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 ... 

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 ... 

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]... 

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). 

The inset of Fig. 2 shows that the generalization of the BCS relation Tc 0.57 A(T = 0. fiq) g(pq), between the critical temperature Tc of the superconducting phase transition and the pairing gap A at T = 0 is satisfactorily fulfilled in the domain of the phase diagram relevant for compact stars. 

Figure 3. Phase diagrams for different form-factor models Gaussian (solid lines), Lorentzian a = 2 (dashed lines) and NJL (dash-dotted). In /3-equilibrium, the colorsuperconducting phase does not exist for Co Gi. In the inset we show for the Gaussian model the comparison of the numerical result with the modified BCS formula Tf = 0.57 A(T = 0, fiq) g(Hq) for the critical temperature of the superconducting phase transition.

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]... 

Symmetry of superconducting state. No Hebel-Slichter coherence peak was observed in either k -(ET)2Cu(NCS)2 or c-(ET)2Cu[N(CN)2]Br in NMR measurements, ruling out a BCS s-wave state. The symmetry of the superconducting state of c-(ET)2Cu(NCS)2 had been controversially described as normal BCS-type or non-BCS type however, scanning tunneling spectroscopy showed f-wave symmetry with line nodes along the direction near ti/4 from k - and Kc-axes [228, 229], and thermal conductivity measurements were consistent with this result [230]. c-(ET)2Cu [N(CN)2]Br showed the same symmetry [231]. 

K-(MDT-TTF)2Aul2 (X = 3.5 K) exhibited a Hebel-Slichter coherent peak just below Tc, indicating a BCS-type gap with s-symmetry [269], while t/-wave like superconductivity has been suggested for /l-(BDA-TTP)2SbF6 [254, 255]. 

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