Collective Excited States and Dielectric Constant in Insulators

Abstract

The electron interaction in insulators is studied with special attentions focused on the dielectric properties and the exciton states. Use is made of Hubbard’s formalism and of the propagator formalism for an electron-hole pair. The following results are obtained: (a) the relations between the internal dielectric constant and the external one are elucidated, (b) an expression of the internal dielectric constant is given in a convenient form to see local field corrections due to lattice periodicity, (c) conditions for applicability of the effective mass equation (EME) to shallow excitons are made clear, (d) the screening constant appearing in EME is the same as the uniform static dielectric constant, (e) exchange correction for EME is not so small even for shallow excitons in silicon and germanium as is usually expected.