| Since high Tc superconductors were discovered, scientists have done much research onthem, and many theory models have been proposed to explain the superconductivity, but so far,the mechanism of high Tc superconductivity is still an open problem. In 2001, the scientistsfrom Tokyo and Stanford University published a paper in the journal of Nature and declared thatthey had found the evidence for the connection between the phonon and the high Tcsuperconductivity; measurements of angle-resolved photoemission spectroscopy and tunnelinghave provided further evidence that the phonon is relevant to high Tc superconductivity; asignificant contribution of the electron-phonon interaction to the superconductivity has beenalso observed in mercury-based compounds by x-ray-absorption spectroscopic measurements.It is reasonable to study the superconductivity of HgBa2Can-1CunO2n+2+δ(n =1,2,3) systemswithin the framework of BCS theory. Our research suggests that high Tc superconductivitycan't be explained perfectly if the van Hove singularity or the non-phonon interaction wereconsidered separately; only when the van Hove singularity and the non-electron-phononinteraction are considered simultaneously can the properties ofthe HgBa2Can-1CunO2n+2+δ(n =1,2,3) system be well explained. Within the framework of BCStheory, using the self-consistent approximation method we have studied the critical temperatureTc and isotope effect a of HgBa2Can-1CunO2n+2+δ(n = 1,2,3) system, the obtained results are inaccordance with experiments.The dissertation contains three chapters:In chapter 1, we review briefly the discovery of superconductivity, the basic characteristicsof superconductivity, the development of superconductivity theory, BCS theory, the differentstages of superconductivity study, the type of superconductors and the applications ofsuperconductors.In chapter 2, we illustrate in detail the research results about HTSC including high Tc-thebreakthrough in superconductivity research, the common features of the HTSC'S crystalstructure, the abnormal characteristics of normal and superconducting states, the research on themechanism for HTSC.In chapter 3, the effects that Van Hove singularity and the non-electron-phonon interactionhave on Tc andαare discussed. When the non-electron-phonon interaction is not considered,Tc andαincrease with increasing Fermi Temperature TF, but they both have a saturation value;when the non-electron-phonon interaction is not considered, Tc increases with increasingnon-electron-phononλnp, Tc increases considerably fast whenλnp is relatively small, with increasingλnp, Tc increases slower and slower; while a decreases monotonously withincreasingλnp to the limit zero. For HgBa2Can-1CunO2n+2+δ(n=1,2,3) system, only when VanHove singularity and the non-electron-phonon interaction are considered simultaneously can theexperiment results of Tc andαbe well explained.
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