%0 Journal Article
%T An Analysis of Strong Coupling in the High Tc Superconductors
%A J. H. Turner
%J International Journal of Superconductivity
%D 2014
%R 10.1155/2014/587287
%X A new McMillan formula is assembled for the High Temperature Superconductors that evidences strong coupling in these materials. The McMillan-Hopfield parameter is calculated in each case, in addition to the Bergmann and Rainer enhancement frequency. The cubic symmetry of the CuO layers and the lattice cohesion and oxygen presence are suggested reasons for the effect. 1. Introduction Since the elaboration of the microscopic theory of superconductivity by Bardeen et al. (BCS) [1], further theoretical developments have provided an explanation of how a higher Tc is possible in terms of strong coupling between lattice vibrations and charge carriers. BCS theory took no account of the strong retarded time-dependant electron-phonon interaction indicated in some materials by neutron scattering, Raman, infrared, and electron spectroscopies. An approximation to the strong coupling theory formulated by McMillan [2] has so far provided an accurate correlation with data gained from high Tc materials up to a possible 40¡ãC. Beyond 40¡ãC, however, it proved to be inaccurate and inappropriate, so it was inapplicable to the new HTSC Perovskites, discovered by Bednorz and Muller [3]. In this paper, McMillan¡¯s approximation is reformulated by using solutions of Eliashberg field equations and reassembling his formula, providing new constants in the approximate formula. Results of band calculations to estimate the total phonon densities of states (TPDOS) and electron-phonon interaction parameters have been inappropriate for the HTSCs [4]. Estimates have been successful for non-HTSCs via (a) tunneling data [5] and (b) inelastic neutron scattering (INS) experiments that can provide accurate estimates of the TPDOS. INS data has been collected for the HTSCs [6¨C8] and it forms a basis for the approximation here. Since only alloys or compounds have their Tc above 10£¿K, finding common properties between these and the HTSCs has helped this enquiry. The A15 compounds contain transitional elements, so do the HTSC Perovskites. Again, the Al5 compounds have cubic symmetry in composition, as do the layered CuO structures in the Perovskites. A normal feature of all previously higher Tc superconductors included a larger value for their electron-phonon interaction parameter . For Nb3Sn this is 1.67 and in the past a maximum has been considered to exist for this parameter above which lattice instability would occur. In this paper, it is considered that stronger rigidity is that aspect of the Perovskites structure which promotes strong coupling. Instability is therefore unlikely, and values for
%U http://www.hindawi.com/journals/ijsu/2014/587287/