Electric Field Effects on the Dielectric Constant of Solids

TLDR

The changes in the dielectric constant can be described using only two functions. The real part of the dielectric constant is derived from the imaginary part via Kramers‑Kronig relations in anisotropic solids near critical points. The study provides closed‑form expressions for the real and imaginary dielectric constant changes at all four critical point types, shows that infinite‑band approximations hold near critical points, and gives Lorentzian broadening formulas using complex Airy functions.

Abstract

Calculations of the imaginary part of the dielectric constant of an anisotropic solid in the region of a critical point are used to obtain the real part of the dielectric constant through Kramers-Kronig relations. Changes in the real and imaginary parts of the dielectric constant are expressed in closed form for all four types of critical points. Description of these changes can be made with only two functions. The effect of the finite extent of a band is investigated, and it is shown that previous calculations of the change in the imaginary part of the dielectric constant, based on bands of infinite extent, are valid as long as transitions are restricted to regions near the critical point. Closed-form expressions for the Lorentzian broadening of the changes in the dielectric constants are given in terms of Airy functions of complex argument.