Polarons in ionic crystals

The behavior of an electron in polarizable medium has a long history of study with versatile developments in condensed matter physics. In 1933 Landau conceived of the self-trapping of an electron in a potential field of polarization induced by itself (digging its own hole, so to speak) as a possible origin of the color center in alkali halides (see Sections 4.7 and 4.8), recognized by their strong absorption bands in the visible region. Although the color center itself turned out later to be an electron at a lattice defect, his idea was further developed by Pekar, Fröhlich, Lee and Pines, Feynman and others, partly stimulated by the field-theoretical approaches to an electron in a self-induced electromagnetic field in a vacuum, and was applied to similar or related problems in condensed matter physics. We shall describe some of these developments and applications in this chapter, with the use of the dielectric theory developed in Chapters 5 and 6.

Let us consider the fluctuating electric field in an isotropic insulator caused by lattice vibrations. The fluctuation–dissipation theorem allows us to express it in terms of the dielectric dispersion as follows. In the absence of an external charge, eq. (1.1.3) with D = ∈eE + P gives ∈ek · Ek = –k · Pk. The polarization density P due to lattice vibrations causes electrostatic potential ø(r) through E = – ∇ø(r).