Superconductivity interactions

Alone among all known physical phenomena, the transition in low-temperature (T < 25 K) superconducting materials (mainly metals and alloys) retains its classical behaviour right up to the critical point thus the exponents are the analytic ones. Unlike the situation in other systems, such superconducting interactions are tndy long range and thus... 

Fig. 35. The superconducting interaction parameter A as a function of the bare density of states for various NaCl and Cr3Si structure compounds (after Hulm et a/. ).

Of course, condensed phases also exliibit interesting physical properties such as electronic, magnetic, and mechanical phenomena that are not observed in the gas or liquid phase. Conductivity issues are generally not studied in isolated molecular species, but are actively examined in solids. Recent work in solids has focused on dramatic conductivity changes in superconducting solids. Superconducting solids have resistivities that are identically zero below some transition temperature [1, 9, 10]. These systems caimot be characterized by interactions over a few atomic species. Rather, the phenomenon involves a collective mode characterized by a phase representative of the entire solid. 

Hamiltonians equivalent to (1) have been used by many authors for the consideration of a wide variety of problems which relate to the interaction of electrons or excitons with the locaJ environment in solids [22-25]. The model with a Hamiltonian containing the terms describing the interaction between excitons or electrons also allows for the use of NDCPA. For example, the Hamiltonian (1) in which the electron-electron interaction terms axe taken into account becomes equivalent to the Hamiltonians (for instance, of Holstein type) of some theories of superconductivity [26-28]. 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

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 gap in superconductivity between the fifth and sixth groups of the periodic table, discovered by Matthias,24 is seen to correspond to the transition from crest to trough superconductivity. It does not require for its explanation the assumption20- 25 that there are mechanisms of superconductivity other than the electron-phonon interaction. 

The foregoing discussion leads to the conclusion that static deformations as well as phonons should be stabilized for superconducting metals by the change in effective radius associated with unsynchronized resonance of electron-pair bonds. Deformation from cubic to tetragonal symmetry, presumably the result of this interaction, has been reported for VsSi at temperatures below 21 K26- 27 and for Nb2Sn at temperatures below 43°K.28... 

The theory of superconductivity based on the interaction of electrons and phonons was developed about thirty years ago. I 4 In this theory the electron-phonon interaction causes a clustering of electrons in momentum space such that the electrons move in phase with a phonon when the energy of this interaction is greater than the phonon energy hm. The theory is satisfactory in most respects. 

Nevertheless deviations from eq. (9.19) have been observed for the intermetallic compound Auln2 [108,109] and for T1 [110,111], Requirements for the validity of eq. (9.19) are the absence of changing internal fields due to nuclear magnetic or electronic magnetic ordering in the relevant temperature range, the absence of nuclear electronic quadrupole interactions and no superconductive transition. 

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