Jahn-Teller Polaron and its Superconductivity

Jahn-Teller Polaron 及其超导性

• 批准号: 13640354
• 负责人: TAKADA Yasutami
• 金额: $ 2.11万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640354/
• 关键词: Superconductivity; Polaron; Jahn-Teller system; Electron-phonon interaction; Hubbard-Holstein model; Electron correlation; Eliashberg theory; Vertex correction; フラーレン; クーロン斥力

In discussing the polaron effect and superconductivity in an electron-phonon coupled system, either the Froelich or the Holstein model is usually adopted as a theoretical basis. However, the electron-phonon complex system in a Jahn-Teller crystal exhibits a new feature similar to the confinement problem in the quark-gluon 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 pseudo-angular momentum and its conservation law imposes a restriction on the way how the electron-phonon 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 Migdal-Eliashberg 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 Jahn-Teller polaron decreases drastically in c … More omparison with that of the Holstein model. In particular, when the electron-phonon coupling constant α is large, I have derived analytically that the effective-mass 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 one-electron problem to the many-electron 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 strong-coupling 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 Jahn-Teller 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 Allen-Dynes one) suffices in estimating T_c. Incidentally, the first-order vertex correction vanishes rigorously in the Jahn-Teller system, which makes the applicable range of the Eliashberg theory very wide. On this ground, I can deny the frequently-mentioned argument that superconductivity in the Jahn-Teller system differs very much from that in other electron-phonon systems.In summarizing those results, I come to the conclusion that we should start with treating the Hubbard-Holstein (HH) model in the pursuit of solving the profound problem in superconductivity, namely, constructing a strong-coupling theory of superconductivity in a strongly-correlated electron-phonon 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 two-site solution to the HH model to the infinite-site system in one dimension by using a variable-displacement Lang-Firsov transformation as well as the Lieb-Wu exact solution to the Hubbard model. Less

在讨论电子-声子耦合系统中的极化子效应和超导电性时，通常采用Froelich模型或Holstein模型作为理论基础。然而，由于简并态的存在和伴随的内部结构，Jahn-Teller晶体中的电子-声子复合系统表现出了类似于夸克-胶子系统中禁闭问题的新特征，通常可以用赝角动量的概念来描述，其守恒定律限制了电子-声子相互作用的方式。考虑到明确这样的限制，我已经写下了系统的哈密顿量，在此基础上，我使用Migdal-Eliashberg理论证明了在这个系统中只允许某些类别的顶点校正。这种对可能的顶点修正的限制使我发现Jahn-Teller极化子的有效质量在c ...更多信息 与Holstein模型相似。特别地，当电子-声子耦合常数α较大时，本文用解析方法导出了有效质量增强因子不是通常的Holstein因子e^<2α>，而是（2/πα）^<1/2>e^α，并将上述单电子问题的研究推广到多电子问题，研究了顶点修正对超导转变温度T_（？）从Eliashberg的强耦合超导理论的观点出发，结果发现，即使在Jahn-Teller系统中，当α很大，顶点修正不能忽略时，由于有效质量很大，在双极化子超导的情况下，T_c也不会变高。当α小于该值时，顶点修正对T_c的估计没有任何影响，因此用传统的McMillan公式（或Allen-Dynes公式）就可以估计T_c。顺便提一下，一阶顶点修正在Jahn-Teller系统中严格地消失，这使得Eliashberg理论的适用范围非常广泛。在此基础上，我可以否定经常提到的Jahn-Teller系统中的超导性与其他电子-声子系统中的超导性有很大不同的论点。在总结这些结果时，我得出的结论是，我们应该从Hubbard-Holstein（HH）模型开始，以寻求解决超导性中的深刻问题，即，在强关联的电子-声子系统中建立了一个超导电性的强耦合理论，其中顶点修正不能忽略。从这个角度出发，我建立了一种新的处理顶点修正的通用方法，并成功地将其应用于充分考虑关联效应的均匀电子液体。我还成功地扩展了两个网站的解决方案，HH模型的无限网站系统在一维通过使用可变位移Lang-Firsov变换以及Lieb-Wu精确解的Hubbard模型。少

项目成果

H.Koizumi, Y.Takada: "Geometric Phase Current in Solids : Derivation in a Path-Integral Approach"Physical Review B. 65・15. 153104:1-153104:4 (2002)

H.Koizumi、Y.Takada：“固体中的几何相电流：路径积分方法的推导”物理评论 B. 153104:1-153104:4 (2002)

Y.Takada, H.Yasuhara: "Dynamical Structure Factor of the Homogeneous Electron Liquid : Its Accurate Shape and the Interpretation of Experiments on Aluminum"Physical Review Letters. 89・21. 216402:1-216402:4 (2002)

Y.Takada、H.Yasuhara：“均质电子液体的动态结构因子：其精确形状和铝实验的解释”物理评论快报 89・21 216402：1-216402：4（2002）。

高田康民: "多電子系の動的応答理論(その1)"固体物理. 37・7. 455-463 (2002)

高田康民：“多电子系统的动态响应理论（第1部分）”固体物理学37・7（2002）。

Y.Takada, A.Chatterjee: "Possibility of a Metallic Phase in the Charge-Density-Wave -Spin-Density-Wave Crossover Region in the One-Dimensional Hubbard-Holstein Model at Half Filling"Physical Review B (Rapid Communication). 67・8. 081102:1-081102:4 (2003)

Y.Takada、A.Chatterjee：“半填充时一维哈伯德-荷尔斯泰因模型中电荷密度波-自旋密度波交叉区域中金属相的可能性”物理评论 B（快速通讯）。 67・8.081102:1-081102:4 (2003)

Y. Takada: "Inclusion of Vertex Corrections in the Self-Consistent Calculation of Quasiparticles in Metals"Physical Review Letters. 87. 226402 : 1-4 (2001)

Y. Takada：“在金属中准粒子的自洽计算中包含顶点校正”物理评论快报。