Metal-insulator transition in vanadium dioxide and titanium oxide using the three-dimensional periodic shell model and DV-X(alpha) cluster method (Japanese text)

The purpose of this study is to calculate electronic structures of the metallic and insulating phases of vanadium dioxide and titanium sesquioxide by using a combination of the three-dimensional periodic shell model and the discrete-variational (DV)-X alpha cluster method. When temperature decreases, vanadium dioxide undergoes a crystallographic phase transition and a metal-insulator (MI) transition at 340K. Unlike the clear cut MI transition in vanadium dioxide, titanium sesquioxide exhibits a broad crossover between a metallic and an insulating state around 450K, which is also an MI transition. Since the DV-X alpha cluster method can calculate the energies of electron states, the combination of the periodic shell model and the cluster method must contain the possibility to clarify the origin of the MI transition in vanadium dioxide and titanium sesquioxide from the energetic point of view. Therefore, the calculation using this combination is of great significance in order to understand the very important phenomena of vanadium dioxide and titanium sesquioxide, particularly the MI transition.; Besides the effects of intersite repulsive nearest neighbor electron-electron (d-d) Coulombic interaction and the spin-spin interaction by means of a generalized Hubbard Hamiltonian, the Hamiltonian in the insulating phase includes Anderson's attractive potential due to the electron-phonon interaction which stabilize the three-dimensional periodic distribution of cation pairs. The shell model estimates the electron-phonon coupling constants and provides direct theoretical evidence that the three-dimensional periodic distribution of cation pairs are stabilized in the insulating phase. In addition, the DV-X alpha cluster method calculates the electron energy in clusters, the values for the intersite repulsive nearest-neighbor d-d interaction, and the spin-spin interaction.; In vanadium dioxide, the electron-phonon interaction effect and the correlation effect for 3d electrons are found to split d band into the empty upper and the occupied lower Hubbard bands and also to result in an obvious energy gap between these bands in the insulating phase. By contrast, the electron correlation effect and the spin correlation effect are found to be mainly responsible for the broad crossover between a metallic and an insulating state in titanium sesquioxide, although there is some contribution from the electron-phonon interaction. The present calculations describe the characteristic phenomenon in these materials.