Electron-phonon superconductivity

Physics of Superconductors, Vol. 1, ed. K.H. Bennemann and J.B. Ketter-son, Springer-Verlag, Berlin, Germany, 2003 R 275 J.P. Carbotte and F. Marsiglio, Electron-Phonon Superconductivity , p.233... 

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]. 

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. 

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 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. 

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. 

The successful prediction of superconductivity in the high pressure Si phases added much credibility to the total energy approach generally. It can be argued that Si is the best understood superconductor since the existence of the phases, their structure and lattice parameters, electronic structure, phonon spectrum, electron-phonon couplings, and superconducting transition temperatures were all predicted from first principles with the atomic number and atomic mass as the main input parameters. 

It has now become apparent that f-band superconductors can be understood in a normal way, like d-band ones" we have just to think about density of states, bandwidth lattice unstabilities and electron correlations to interpret it. This was clearly summarized by Smith after the discovery of superconductivity of Pa and Am. Superconductivity of Am is made by the J = 0 ground state of its six 5 f electrons as was stressed by Johansson , this could also be the case for stabilized trivalent europium metal. The importance of lattice instabilities (like in A-15 high Tc superconductors) was put forward by Fournier who showed that the very large 6T/8p slope for U was mainly due to a very targe change in the electron-phonon coupling associated with the low temperature phase transition. 

Raman spectra indicate that phonons are coupled to electronic states in BaPb BijPj (53) and in Ba1.xKxBiOs (58). These studies do show a strong electron - phonon interaction is present in the superconducting phases, but do not prove that these modes are responsible for high Tc driven by a phonon - only mechanism. 

Tunneling Spectroscopy has revealed electron - phonon coupling strengths for optical phonons in Ba K BiOg which suggest that phonon mediated coupling is responsible for superconductivity in this system (59). 

Shirai, M., Suzuki, N. and Motizuki, K., Microscopic Theory of Electron - Phonon Interaction and Superconductivity of BaPbj.jjB Og. Solid State Comm. 60(6) 489 (1986). 

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