Ferromagnetism and Superconductivity in Two-band Hubbard Models

s of Doctor′s Theses (Received The Degree of Doctorof Engineering in 2006) ..................................................................................................................................................................... 24 Abstracts of Papers (Published in 2006) .....................................................................................................................A1s of Papers (Published in 2006) .....................................................................................................................A1 Abstracts of Books and Reviews (Published in 2006) ....................................................................................A-64s of Books and Reviews (Published in 2006) ....................................................................................A-64 Research Reports of the Faculty of Engineering, Mie University Publication Committee(*Chairman) Naoki ISU* Professor,Department of Information Engineering Yasuo TAKEDA Dean,Faculty of Engineering Yasuyuki SUZUKI Professor,Department of Mechanical Engineering Hiroshi KAWAKAMI Associate Professor,Department of Mechanical Engineering Hideki SATOU Associate Professor,Department of Electrical and Electronic Engineering Yusuke AOKI Assistant Professor,Department of Electrical and Electronic Engineering Toshikazu KITAGAWA Professor,Department of Chemistry for Materials Atsushi HIRANO Assistant Professor,Department of Chemistry for Materials Satoshi ASANO Associate Professor,Department of Architecture Hiroyuki TAKAI Associate Professor,Department of Architecture Kazuhiko ONO Associate Professor,Department of Information Engineering Ichiro TAKEUCHI Assistant Professor,Department of Information Engineering Takashi TAKEO Professor,Department of Physics Engineering Yuuji HUJIWARA Assistant Professor,Department of Physics Engineering Faculty of Engineering,Mie University 1577 Kurimamachiya-cho,Tsu,Mie 514-8507 JAPAN Ferromagnetism and Superconductivity in Two-band Hubbard Models Kazuhiro Sano and Yoshiaki Ōno∗ (Department of Physics Engineering) (Received July 18, 2007) Abstract We investigate ferromagnetism and superconductivity in two types of two-band Hubbard models: the multi-orbital Hubbard model and the d-p model, with particularly paying attention to effect of the interplay between the electron correlation and the band splitting. As strong correlation plays a crucial role for these phenomena, we employ two complementary approaches: the numerical diagonalization method for one-dimensional models and the dynamical mean-field theory for the infinite-dimensional model. These approaches give us reliable results beyond the perturbative approximation or the usual mean-field like approximation. For the one-dimensional models, we calculate the critical exponent Kρ based on the Tomonaga-Luttinger liquid theory and determine phase diagram of superconducting(SC) region by the condition Kρ > 1. The SC region appears near partially polarized ferromagnetic region in the multi-orbital Hubbard model with finite band splitting. Analysis of paring correlation functions for the ground state indicates that the triplet paring is relevant to the superconductivity. In the one-dimensional d-p model, we find enhancements of the singlet and triplet paring correlations at the SC region. Although only the singlet paring is relevant to superconductivity near half-filling, the triplet paring increases with electron filling and is relevant to the superconductivity as well as the singlet paring near full-filling. In the infinite-dimensional d-p model, we calculate the local green’s function on the basis of the dynamical mean-field theory, where the effective impurity Anderson model is solved using the numerical diagonalization method. It shows the phase diagrams of the metal-insulator transition on the ground state at half-filling and quarter-filling as functions of the Coulomb interaction and the band splitting. We obtain the transition temperatures for the ferromagnetism and the superconductivity as functions of the Coulomb interaction, the band splitting and the electron filling. It indicates that the transition temperature of the triplet superconductivity is higher than that of the singlet superconductivity near the ferromagnetic state. These results suggest a close relationship between the ferromagnetism and the superconductivity as a common feature of the two-band Hubbard models.We investigate ferromagnetism and superconductivity in two types of two-band Hubbard models: the multi-orbital Hubbard model and the d-p model, with particularly paying attention to effect of the interplay between the electron correlation and the band splitting. As strong correlation plays a crucial role for these phenomena, we employ two complementary approaches: the numerical diagonalization method for one-dimensional models and the dynamical mean-field theory for the infinite-dimensional model. These approaches give us reliable results beyond the perturbative approximation or the usual mean-field like approximation. For the one-dimensional models, we calculate the critical exponent Kρ based on the Tomonaga-Luttinger liquid theory and determine phase diagram of superconducting(SC) region by the condition Kρ > 1. The SC region appears near partially polarized ferromagnetic region in the multi-orbital Hubbard model with finite band splitting. Analysis of paring correlation functions for the ground state indicates that the triplet paring is relevant to the superconductivity. In the one-dimensional d-p model, we find enhancements of the singlet and triplet paring correlations at the SC region. Although only the singlet paring is relevant to superconductivity near half-filling, the triplet paring increases with electron filling and is relevant to the superconductivity as well as the singlet paring near full-filling. In the infinite-dimensional d-p model, we calculate the local green’s function on the basis of the dynamical mean-field theory, where the effective impurity Anderson model is solved using the numerical diagonalization method. It shows the phase diagrams of the metal-insulator transition on the ground state at half-filling and quarter-filling as functions of the Coulomb interaction and the band splitting. We obtain the transition temperatures for the ferromagnetism and the superconductivity as functions of the Coulomb interaction, the band splitting and the electron filling. It indicates that the transition temperature of the triplet superconductivity is higher than that of the singlet superconductivity near the ferromagnetic state. These results suggest a close relationship between the ferromagnetism and the superconductivity as a common feature of the two-band Hubbard models.