Budget Amount *help 
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥2,600,000 (Direct Cost: ¥2,600,000)

Research Abstract 
In discussing the polaron effect and superconductivity in an electronphonon coupled system, either the Froelich or the Holstein model is usually adopted as a theoretical basis. However, the electronphonon complex system in a JahnTeller crystal exhibits a new feature similar to the confinement problem in the quarkgluon system due to the existence of degenerate states and the concomitant internal structure. Generally the internal structure can be described in terms of a concept of pseudoangular momentum and its conservation law imposes a restriction on the way how the electronphonon interaction works. Taking explicitly such a restriction into account, I have written down the Hamiltonian of the system, based on which I have shown using the MigdalEliashberg theory that only some class of vertex corrections is allowed in this system. This restriction on the possible vertex corrections leads me to the finding that the effective mass of the JahnTeller polaron decreases drastically in c
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omparison with that of the Holstein model. In particular, when the electronphonon coupling constant α is large, I have derived analytically that the effectivemass enhancement factor is not the usual Holstein factor e^<2α> but (2/πα)^<1/2>e^α. I have extended the above study on the oneelectron problem to the manyelectron one and investigated the effect of the vertex corrections on the superconducting transition temperature T_c from a viewpoint of the Eliashberg's theory on strongcoupling superconductivity. As a result, I have found that T_c does not become high in the scenario of bipolaron superconductivity due to the very heavy effective mass even in the JahnTeller system, when α becomes so high that the vertex corrections cannot be neglected. For the case of α smaller than that, the vertex corrections do not contribute at all and thus the conventional McMillan formula (or the AllenDynes one) suffices in estimating T_c. Incidentally, the firstorder vertex correction vanishes rigorously in the JahnTeller system, which makes the applicable range of the Eliashberg theory very wide. On this ground, I can deny the frequentlymentioned argument that superconductivity in the JahnTeller system differs very much from that in other electronphonon systems. In summarizing those results, I come to the conclusion that we should start with treating the HubbardHolstein (HH) model in the pursuit of solving the profound problem in superconductivity, namely, constructing a strongcoupling theory of superconductivity in a stronglycorrelated electronphonon system where the vertex corrections cannot be neglected. From this perspective, I have established a new general method of treating the vertex corrections and successfully applied it to the homogeneous electron liquid with fully incorporating correlation effects. I have also succeeded in extending the twosite solution to the HH model to the infinitesite system in one dimension by using a variabledisplacement LangFirsov transformation as well as the LiebWu exact solution to the Hubbard model. Less
