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

我们研究了扩展的周期Anderson模型中的电荷涨落及其与超导的可能关联，以阐明一些重费米子材料中的超导机制.利用适用于三维强关联电子系统的动力学平均场理论，我们证明了传导电子与f电子之间的排斥作用确实增强了电荷涨落，并且电荷涨落发散导致f电子价态跃迁(一阶).它们真正发散的点是一个量子临界点。这一结果支持了超导电性是由增强的电荷(价)涨落引起的观点。然而，发现价不稳定的参数相当大，其真实性值得怀疑。我们已经指出，在我们的研究中完全忽略了传导电子和f电子之间混合的波矢相关性，这对于考虑实际材料中当前机制的现实可能是重要的。用动力学平均场理论研究超导不稳定性是困难的，因为只有S波超导态可以用动力学平均场理论来处理。作为另一种方法，我们采用涨落交换近似(FLEX)来研究超导转变温度。利用FLEX，我们证明了增强的电荷涨落导致了转变温度(与压力)的非单调依赖关系。尽管本研究中发现的增强涨落不同于上面讨论的价涨落，但这一发现是重要的，因为它表明在单一模型中，超导转变温度的非单调依赖可以通过两种不同的涨落发生，在这种情况下，电荷和自旋。

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.