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

为了阐明某些重费米子材料中的超导机制，我们研究了推广的周期安德森模型中的电荷涨落及其与超导的可能联系.利用对三维强关联电子系统适用的动力学平均场理论，我们已经表明电荷波动确实被传导电子和f电子之间的排斥相互作用增强，并且电荷波动发散以引起（一级的）F电子价态跃迁。它们真正分歧的点是量子临界点。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，发现的价不稳定性的参数是相当大的，其现实性可能会受到质疑。我们已经指出，在我们的研究中为了简单起见完全忽略了传导电子和f电子之间的混合对波矢的依赖性，这对于考虑实际材料中现有机制的真实性可能是重要的。用动力学平均场理论研究超导不稳定性是困难的，因为动力学平均场理论只能处理s波超导态。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。使用FLEX，我们已经表明，增强的电荷波动引起的非单调依赖的转变温度（压力）。虽然在这项研究中发现的增强的波动不同于上面讨论的价波动，这一发现是重要的，因为它表明，超导转变温度的非单调依赖性可以发生两种不同类型的波动，在这种情况下，在一个单一的模型，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.