Strong-coupling theory of superconductivity with vertex corrections

Abstract

The studies on the development of theories for superconductivity of the alkali fullerides and for the vertex function were discussed in order to confirm the mechanism of superconductivity of the materials. The alkali fullerides were believed to have superconductivity at T(sub c) in the range from 20 to 30K by the intramolecular high frequency phonon modes, because of the crude estimation of T(sub c) in the conventional Migdal Eliashberg theory for superconductivity. An analysis in the atomic limit of the Hubbard Holstein (HH) model has revealed that the self-energy on the real frequency axis diverged at nonzero frequencies, leading to the complete vanishment of the one-electron Green's function at the corresponding frequencies. The self-energy in a case of nonzero bandwidth has been investigated in the HH model in the limit of infinite spatial dimensionality. The concept of the dynamical localization-delocalization transition was obtained from the fact that the divergence in the self-energy disappeared at certain critical value of the bare bandwidth.

物質の超伝導性機構を確認するためのアルカリフラーレンの超伝導性およびバーテックス関数の理論開発研究を論じた。従来の超伝導性に関するMigdal-Eliashberg理論によるTc概算値により、アルカリフラーレンは分子内高振動数フォノンモードにより20Kから30Kの範囲のTcにおいてほぼ超伝導性を示すと考えた。Hubbard-Holstein(HH)模型の原子極限解析は、実振動数軸の自己エネルギーが非ゼロ振動数において発散し、相当する振動数において1電子Green関数の完全な消滅につながることを明らかにした。無限空間次元の極限におけるHH模型で非ゼロバンド幅の場合の自己エネルギーを検討した。自己エネルギーの発散は裸のバンド幅の一定臨界値で消滅するという事実から動的局在化・非局在化転移の概念を得た。