Theoretical study of a new critical point and superconductivity caused by valence fluctuations in strongly correlated electron systems

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We have studied the charge fluctuations in an extended periodic Anderson model and its possible relevance to superconductivity to clarify the superconducting mechanism in some of the heavy fermion materials.By using the dynamical mean filed theory, which works well for strongly correlated electron systems in 3 dimensions, we have shown that the charge fluctuations are indeed enhanced by the repulsive interaction between a conduction electron and an f-electron, and that the charge fluctuations diverges to cause f-electron valence transition (of the first order) . The point where they indeed diverge is a quantum critical point. This result supports the idea that the superconductivity is caused by the enhanced charge (valence) fluctuations. However, the parameters for which the valence instability is found are rather large and its reality could be questioned. We have pointed out that the wave vector dependence of the mixing between a conduction electron and an f-electron, which is completely neglected for simplicity in our study, might be important to consider the reality of the present mechanism in actual materials.It is difficult to study superconducting instability using the dynamical mean field theory, because only s-wave superconducting state can be treated with the dynamical mean field theory. As an alternative method, we resort to a fluctuation exchange approximation (FLEX) to study the superconducting transition temperature. Using the FLEX, we have shown that the enhanced charge fluctuations cause nonmonotonic dependence of the transition temperature (on pressure) . Although the enhanced fluctuations found in this study differs from the valence fluctuations discussed above, this finding is important in that it shows that nonmonotonic dependence of the superconducting transition temperature can occur by two different kinds of fluctuations, charge and spin in this case, in a single model.