New Developments in the Green'sFunction Method and Construction of the StrongCoupling Theory for Superconductivity with Vertex Corrections
Project/Area Number  10640363 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  The University of Tokyo 
Principal Investigator 
TAKADA Yasutami The Univ. of Tokyo, ISSP, Associate Professor, 物性研究所, 助教授 (00126103)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)

Keywords  Strong Electron Correlation / Superconductivity / Green's Function / Vertex Correction / ElectronGas Model / Excitonic Scattering between Electron and Hole / GaugeInvariant SelfConsistent Method / SelfEnergy Revision Operator Theory / 強電子相関 / 超伝導 / グリーン関数 / バーテックス補正 / 電子ガス模型 / 電子正孔間の励起子散乱 / ゲージ不変自己無撞着法 / 自己エネルギー改訂演算子理論 / 強結合理論 / ハバート模型 / 自己エネルギー改訂演算子法 
Research Abstract 
In order to illuminate fundamental physics in dynamical processes in a stronglycorrelated system, I propose a theory of twofold hierarchy The first stage is to set up a firm framework to provide exact results without attention to feasibility of computation and the second one is to introduce a relevant approximation to the key quantity in the framework with taking full account of available resources of computation. Since I have already established the theory of the selfenergy revision operator F for the first stage, the main objective of this study is the second stage, namely, to obtain a good approximation to F. The simplest approximation is the gaugeinvariant selfconsistent (GISC) method in which I neglect the vector vertex function ΓィイD2νィエD2 in relating the scalar vertex function Γ with the selfenergy Σ through the Ward identity. I have improved on this GISC systematically by introducing the ratio function R, defined as the ratio between Γ and the longitudinal part of ΓィイD2νィエD2. I exploit its asymptotic properties in various limits to construct a good approximate form for R. For its illustration, I apply this algorithm to the electron gas and find the following : (i) Near the Fermi surface, RPA is found to provide rather accurate results because of the strong cancellation between Γ and Σ due to the Panli principle; (ii) it is not the case for the processes far from the Fermi surface; and (iii) a strong lowerenergy shift is observed in the dynamic structure factor owing to the attractive electronhole excitonic multiple scatterings. I shall apply the same method to real crystals. As for superconductivity, I develop a theory on the GISC level and investigated the validity of the conventional Eliashberg theory in various aspects. I shall extend the theory so as to provide more accurate results with full attention to the role of NambuGoldstone modes in Γ.

Report
(4results)
Research Output
(23results)