Translation-Invariant Excitons in a Phonon Field

Victor D Lakhno

doi:10.3390/condmat6020020

Abstract

Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of excitons interacting with a phonon field leads to a nonzero contribution of phonons into the exciton ground state energy only in the case of weak or intermediate electron-phonon coupling. A conclusion is made that self-trapped excitons cannot exist in the limit of strong coupling. Peculiarities of the absorption and emission spectra of translation invariant excitons in a phonon field are discussed. Conditions when the hydrogen-like exciton model remains valid in the case of electron-phonon interaction are found.

Highlights

We answered the fundamental question of the role of polaron effects in exciton physics
Though the important role of electron-phonon interaction (EPI) for excitons in polar media was revealed in a lot of experiments, the question of why the hydrogen-like model appears to be valid under these conditions has remained open far [27]
We have shown that, in the case of exciton-phonon interaction described by Fröhlich Hamiltonian, the hydrogen-like model turns out to be applicable if the energy of a transition to the excited state does not exceed the energy of an optical phonon

Summary

Introduction

As in the case of polarons, a description of free excitons in a homogeneous polar medium should be translation invariant (TI) Extensive literature on excitons highlights in detail numerous phenomena concerned with them For this reason, we will only dwell upon some qualitative differences between the theories of self-trapped excitons in polar media and translation—invariant theory of excitons with electron-phonon interaction (EPI). Numerous theoretical investigations of the problem gave rise to the idea of a considerable contribution of EPI into the exciton coupling energy as a result of which a simple hydrogen-like model was replaced by a modified one where the polarization cloud surrounding an electron and a hole, that is, the polaron effect is taken into account by the replacement of the Coulomb interaction by the screened one.

Hamiltonian of an Exciton in a Polar Crystal

Exciton Ground State in a Polar Crystal in the Case of Weak and Intermediate

Exciton Ground State in a Polar Crystal in the Case of Strong

Spectrum of a TI Exciton

Peculiarities of Light Absorption and Emission by TI Excitons

Conclusions