Shinya Nishino

Flat Bands of a Tight-Binding Electronic System with Hexagonal Structure

A constructive method to find flat bands is demonstrated for a model describing tight-binding electrons on the hexagonal lattice in which each atomic site has three orbitals. The system may represent σ-electrons of an s p 2 -hybridized material but we assume transfer integrals between orbitals to be free parameters for general discussion. Finding highly degenerate eigenfunctions of each flat band is identified as finding a localized eigenfunction, which is determined as a basis function of an irreducible representation of, for example, a point group C 6 v . This approach yields not only flat bands on all over the k -space but also some partial flat bands only on a partial k -space. In the former case, if the flat band locates at the bottom (or the top) of a band structure, it is shown that Mielkes condition holds, allowing occurrence of the flat band ferromagnetism.

Flat-Band Localization in Weakly Disordered System

We present a detailed analysis of the insulator–metal–insulator transition of a disordered system, starting from a characteristic three-dimensional system possessing highly degenerated localized ei...

Three-dimensional Flat-Band Models

Typical three-dimensional flat-band models of tight-binding electronic systems on cubic and diamond lattices are presented to demonstrate the wide applicability of the method proposed by Nishino et...

Localization of Long-Wavelength Acoustic Phonons in a Disordered Anomalous Soft Solid with Parabolic Dispersion Relation

An anomalously soft bulk solid with a parabolic acoustic-phonon dispersion relation of ω= a k 2 type is extensively investigated qualitatively and quantitatively from a microscopic point of view. The peculiar dispersion relation leads us to a characteristic spectral dimension, a mechanical instability and a thermal instability, and the sound wave obeys a special wave equation in the long-wavelength limit. When the instabilities are suppressed by a cutoff frequency or a suitable unharmonicity, acoustic phonons exhibit many peculiar features. A significant localization character is numerically observed in the low-frequency region of acoustic phonons when we introduce disorder into the solid. It is clarified that the localization is qualitatively stronger in force-constant-disordered systems than in mass-disordered systems.

Peculiar behaviors of excited modes in harmonic chains with correlated disorder

The localization behaviors of harmonic chains with correlated random masses are theoretically investigated. We show that the specific long-range correlation in a mass sequence gives rise to the occurrence of peculiar localized eigenmodes at high frequencies as well as an anomalous behavior in level statistics in vibrational spectrum.