Electron Interaction in Very Long Linear Conjugated Molecules. II : Elementary Excitations in a System with Small Energy Gap

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概要

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• Lowlying excited states in a one-dimensional system which has a small energy gap (ε_g) in the spectra of H_0, the one-electron Hamiltonian, are investigated. Plasmons and excitons are our main interests. These states are investigated in the framework of the tight-binding approximation. In usual one-dimensional systems, such as very long linear conjugated molecules, the plasmon levels sink into the level continuum given by excitation energies of one-pair states. However, it is shown that the plasma oscillations are stable when their energies are sufficiently larger than the energy gap. On the other hand, the plasma oscillations with sufficiently small momentum whose energies in case of εg=0 were smaller than the present energy gap seem to be dissolved away into the level continuum. A formulation to derive exciton solutions is given. The screening effect for the attractive force between the electron and the hole is investigated by means of the Gell-Mann and Brueckner technique and is found to grow larger as the energy gap becomes smaller. By this screening effect the possibility of getting the exciton-like bound state diminishes as εg→0. As a collorary we have found that the potential energy of two electric charges z_1e and z_2e separated by a distance r in a three dimensional system with small energy gap becomes z_1z_2e^2exp(-αr/r if r≪|B/ΔB|, where |B| is a measure of the Fermi energy and ΔB is a measure of the gap, while it becomes z_1z_2e^2/εr if r≫|B/ΔB|, where ε∝r_3^<-1>(|B|/(ΔB)^2) ×(e^2/a_B).

• 理論物理学刊行会の論文
• 1959-11-25

著者

• Izuyama Takeo

  Research Institute For Fundamental Physics Kyoto University

• IZUYAMA Takeo

  Research Institute for Fundamental Physics, Kyoto University

関連論文

• Electron Interaction in Very Long Linear Conjugated Molecules. II : Elementary Excitations in a System with Small Energy Gap
• Collective Excitations of Electrons in Degenerate Bands. I : Spin Waves in Stoner's Model of Ferromagnetism
• Collective Excitation of Electrons in Degenerate Bands. II : Collective Excitations in a Metallic p-Band

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