Teturo Inui

Coexistence of Local and Band Characters in the Absorption Spectra of Solids I. Formulation

The problem of coexistence of the local and band aspects in the fundamental absorption spectra (or the impurity-induced infrared absorption of lattice vibrations) is formulated with the use of the Greens function method. By a suitable decomposition of the hamiltonian of the electron-hole relative motion (or the dynamical matrix for the lattice vibrations), one can derive a line shape expression in which coexist the both aspects, namely, the metastable excitons (or the quasi-local modes) on the one hand and the Van Hove singularities on the other hand. Their interference results in the antiresonance of the quasi-local states and the metamorphism of Van Hove singularities.

Relativistic Electronic Structure of KI Crystal

Energy bands in KI are calculated by means of the relativistic Greens function method. In setting up the potential, one parameter is used so that the gap energy agrees with the observed value. It is found that the highest filled band is completely split off into a couple of bands on account of the strong spin-orbit interaction. Both the top of the valence band and the bottom of the conduction band are located at the point k =0. The d bands which originate from the atomic 3 d states in the K + ions lie just above the lowest s -like conduction band. The results are discussed with reference to recent experimental information. It is suggested that the d bands centered on the alkali ions are responsible for the extra excitons observed in potassium and rubidium halides.

Coexistence of Local and Band Characters in the Absorption Spectra of Solids. II. Calculations for the Simple Cubic Lattice

Line shapes of the fundamental absorption and the impurity-induced infrared absorption of lattice vibrations are calculated in order to clarify the complementary interplay of the local and band characters. The shift-broadening matrix method is applied to a monatomic simple cubic lattice with nearest neighbor interaction. As one varies the short range electron-hole attractive potential in the electronic case or the mass and the force constant of the impurity in the vibrational case, Van Hove singularities undergo a metamorphism. A variety of shapes appear in the spectra as the result of the interplay of the both characters. A few remarks are made concerning the available experimental data.

Cyclotron resonance of hot electrons in pure germanium

The frequency dependent non-ohmic behavior of conduction electrons in the static magnetic field, under the influence of applied microwave field, is investigated. As the electrons become hotter, the electron acoustical-phonon interaction becomes larger and the relaxation time shorter, so that the half-width of the cyclotron resonance line (ωτ) -1 grows up. The result of the calculation shows that the relation (ωτ) -1 ∝( P / m x ) 1/ n holds, where P denotes the microwave power. In the case where practically only spontaneous emission of phonons takes place, n takes the one extreme value 2.5, while it does the other extreme value 4 in the case where both emission and absorption of phonons occur in sufficient magnitudes. Evidently, the average electron energy e e is a function of ω c -ω for a given power. Since the relaxation time depends on e e , it is a function of ω c -ω. Hence the absorption line deviates from the ordinary Lorentzian curve in which the relaxation time is taken constant throughout the rang...

Anharmonic Effects on the Vibration Spectrum of the U-Centers in Alkali-Halide Crystals

Broadening of infrared absorption lines due to localized modes of lattice vibrations of U-centers in alkali-halide crystals is investigated by taking into account vibration anharmonic terms. A model is assumed such that a vibration spectrum of an ionic crystal is modified by the presence of a U-center, thus giving rise to a few localized modes whose frequencies lie outside the continuous spectrum (about three times as large as the frequency of the optical mode), and general anharmonic parts are expanded in terms of these vibration normal coordinates. It is shown that third-order terms are ineffective because of an energy conservation relation, and that fourth-order terms each involving three optical modes and one localized mode are responsible for the broadening. The absorption line is of a Lorentzian shape. A simple expression for the damping constant is derived which yields a relation between the line-widths and the ratio, \(\hbar\omega_{\text{op}}^{*}/kT\), where ω op * is the optical-mode frequency fo...