Isotopic Renormalization of the Electronic Excitation Energy Spectrum

Abstract

It has been more than six decades since the introduction of the quasi-particle exciton by Frenkel [161], and the extreme fertility of this idea has been demonstrated most powerfully. According to Frenkel, the exciton is an electron excitation of one of the atoms (ions) of a crystal lattice because of the translation at symmetry that moves through the crystal in an electrically neutral formation. Since Frenkel, the concept of an exciton has been developed in the papers of Peierls [162]] and Slater and Schokley [163]. Problems concerning light absorption by the solid state have been considered somewhat differently (Wannier [164] and Mott [165]). According to the Wannier-Mott results, the exciton is the state of an electron and hole bonded by the Coulomb force. The electron and hole the in exciton state are spatially separated, and their charges are screened. In the Frenkel papers, the excitations localized on the lattice site were described thus; after the Wannier-Mott papers, the excitons became divided into Frenkel (small radius) excitons (for details, see Davydov [166]) and Wannier-Mott (large radius) excitons [167]. However, a description of the basic difference between these two models is absent (Davydov [166], Knox [167], and Agranovich and Ginsburg [168]). The experimental discovery (see, e.g., Gross [169] of the Wannier-Mott exciton in the hydrogenlike absorption spectrum of semiconducting crystals was the basis for a new subject — exciton physics (see also [109]). The influence of external perturbation (electrical and magnetic fields, one-axial and hydrostatic deformation) on the optical spectra ofWannier-Mott excitons (see, e.g., Gross [169]) and their energetic characteristics has been demonstrated repeatedly. These investigations permitted high-accuracy measurements of exciton binding energy and also of their translational mass, values of effective masses of the electron and hole, their g-factors, etc. Moreover, the detailed account of photon-exciton interaction has led to the concept of polaritons (Pekar [170]). From the time of the experimental discovery of the Wannier-Mott exciton, the problem of the interaction of excitons and the crystal lattice has persisted for more than four decades (Haken [171]).