Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

Abstract

Crystal optical properties of insulating materials possessing incommensurately modulated phases are studied in the framework of a microscopic model. Quantum-mechanical expressions for the microscopic dielectric permittivity tensor are derived. It is shown that the contributions from the long-wavelength reciprocal lattice vectors with the lowest microscopic indices should be taken into account in the optical response of the incommensurate crystals. This justifies, from the standpoint of microscopic theory, a mesoscopic approach to the problem of light propagation in incommensurate crystals adopted in a number of earlier studies. The mesoscopic tensors associated with the first-order spatial dispersion are obtained and analyzed in detail. The optical gyration is revealed to be described by the dielectric tensor components linear in both the light wave vector and the mesoscopic incommensurate modulation wave vector. The latter contributions correspond to the gyration mechanism related to the mesoscopic inhomogeneity of the optical medium under study.