Symmetry of linear dielectric response tensors: Dispersion models fulfilling three fundamental conditions

Abstract

Physically correct dispersion models must fulfill three fundamental conditions (time-reversal symmetry, Kramers–Kronig consistency, and conformity with sum rules). The application of these conditions on systems exhibiting low crystal symmetry, spatial dispersion, and/or magneto-optic effects is a non-trivial task. The aim of this contribution is to present an approach using decomposition of dielectric tensors into a set of independent spectral functions. For the derivation, the most general case of anisotropic dielectric response with optical activity is considered. The contribution discusses both the natural optical activity exhibiting spatial dispersion and the local magneto-optic effect of rotation of the plane of polarization induced by the external magnetic field. If the response tensor is expressed up to the term linear in the direction of the wave vector, then its symmetry can be classified into 16 types. Formulas expressing each type of the dielectric tensor using independent spectral functions are presented (the most complex case with the lowest symmetry requires 15 spectral functions). The symmetry for different internal and external conditions is demonstrated with the help of several simple models based on solving the classical equations of motion. It is shown that interpreting free particles in the magnetic field as bound particles is not correct. Instead, the Landau levels in a non-dissipative system must be interpreted as splitting of diamagnetic part of the dielectric response, rather than energy of bound states.