Cooper electron pairs

The fundamental concept of the theory appears at first sight paradoxical electrons in the superconductor are mutually attracted forming so-called Cooper electron pairs . 

These last few years superconductivity in metals and alloys has mainly been explained with the help of the so-called Cooper electron pairs. At the low temperatures at which super-conductivity occurs, the metal ions do not vibrate any more. In that case the movement of an electron through the lattice is enough to deform that lattice. The metal ions in the vicinity of the electron move towards that electron and thus provide a net positive charge, causing a second electron to be attracted, (fig. 11.4.13b). In the figure b and c, the metal ions have been reduced in size because the figure is more clear then. 

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... 

Now — L is the Landau-Ginzburg free energy, where m2 = a(T — Tc) near the critical temperature, is a macroscopic many-particle wave function, introduced by Bardeen-Cooper-Schrieffer, according to which an attractive force between electrons is mediated by bosonic electron pairs. At low temperature these fall into the same quantum state (Bose-Einstein condensation), and because of this, a many-particle wave function (f> may be used to describe the macroscopic system. At T > Tc, m2 > 0 and the minimum free energy is at = 0. However, when T [Pg.173]

Figure 1. Illustration of lone electron pair preferences in alcohol dimers, cooperative and anticooperative binding sites for a third monomer, ring strain and steric repulsion in alcohol trimers, alternation of residues in alcohol tetramers, and chain, branch, and cyclic hydrogen bond topologies in larger clusters.

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. 

By comparing the resonance frequency Eq.(ll) and the phonon vibration frequency Eq.(12), we see that they are almost the same, 0.3 0.4 x 1014 s 1. This affirms the possibility of a spin-paired covalent-bonded electronic charge transfer. For vibrations in a linear crystal there are certainly low frequency acoustic vibrations in addition to the high frequency anti-symmetric vibrations which correspond to optical modes. Thus, there are other possibilities for refinement. In spite of the crudeness of the model, this sample calculation also gives a reasonable transition temperature, TR-B of 145 °K, as well as a reasonable cooperative electronic resonance and phonon vibration effect, to v. Consequently, it is shown that the possible existence of a COVALON conduction as suggested here is reasonable and lays a foundation for completing the story of superconductivity as described in the following. 

We focus here on HCN as an element in a chain of H-bonded units. The presence in this molecule of only one proton and one lone electron pair provides a simple testing ground for ideas about cooperativity. 

The first section in this chapter focuses on HCN as an element in a chain of H-bonded units. The presence in this molecule of only one proton and one lone electron pair provides a simple testing ground for ideas about cooperativity. The linearity of the complex also simplifies analysis of electron density redistributions caused by multiple bonding. HCCH is similar in some ways, but its absence of a lone electron pair causes significant distinctions. 

Attempts have been made to estimate quantitatively the various effects possible from the theoretical viewpoint on an electrochemical interface for superconductors have been made. For example, it was established [154, 156, 158] that the probability of the electron-pair tunneling is, in principle, always substantially lower than that for usual electrons (all other factors being equal), a result that implies the prediction of inhibition near 7. Kuznetsov [158] considered in detail the mechanisms of the processes with the participation of Cooper pairs. For instance, the energy barriers were estimated for a variety of mechanisms, including the transfer to one and the same particle (capable of multielectron transformation) to two spatially separated particles, and also the transfer of the pair to one particle with the simultaneous transition of one of the pair s electrons to the normal state. It was found that the properties of the system can vary substantially, depending on the relationship between the band gap, the medium reorganization energy, and the overpotential. 

Blatt [36], Coleman [37, 38], then Bratoz and Durand [39] investigated a special N-electron wave function in which all geminals were constrained to have the same form, and established the relationship between this function and that used by Bardeen, Cooper and Shieffer (BCS) [40] to describe superconducting systems with electron pairs. The underlying wave function was termed as the antisymmetrized geminal power (AGP) function. 

Berthelot and colleagues have estimated the pATes values of the phenohc OH group in the intramolecular hydrogen-bonded systems 1, 2 and 3. The higher basicity pATes of 1 and 2 compared to phenol (—0.07) can be explained by cooperative effects involved in hydrogen-bond formation the oxygen electron pairs are more basic in OH- B than in the free OH group . The push-puU effect shown by the curved arrows in 3 opposes the cooperativity effect and pATes falls. 

The superconductivity in the A3(C6o) compounds is of the conventional Bardeen-Cooper-Schrieffer (BCS) type. The relatively high superconducting transition temperature (18 K for A = potassium) is ascribed to electron pair formation mediated by the high energy internal modes [38]. 

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