Electron-phonon and exciton-phonon bound states

Abstract

A review is given of the theoretical and experimental work which has shown the possibility of forming bound states of an electron or an exciton with an optical phonon. The specific feature of these bound states is that an unconserved particle (a phonon) contributes to their formation; such states are stable only because their decay is forbidden by the conservation laws for energy and momentum. As distinct from the virtual phonons of a polaron 'cloud', the phonon which takes part in the formation of a bound state is almost real. Most attention is devoted to wide-band systems, in which the width of the electron (or exciton) band is larger than the phonon frequency; this is the normal situation for semiconductors and ionic crystals. I n these systems bound states are formed near the threshold for phonon emission. T h e formation of bound states is favoured by strong electron-phonon coupling, small phonon dispersion, and a large mass for the particle which interacts with the phonons. Hybrid states occupy an intermediate position between bound states and the usual polaron states; these arise when the energy of an optical phonon is equal to one of the electronic frequencies, and under these conditions the distinction between 'virtual' and 'real' phonons practically disappears. A discussion is also given of excitons in molecular crystals, which are treated as narrow-band systems; here the existence of bound states is not related to the presence of a threshold in the exciton spectrum. T h e existence of bound and hybrid states must have a marked effect on a number of physical phenomena, in particular the optical properties, as has already been demonstrated in a series of experiments.

Fröhlich polaron and bipolaron: recent developments

“…The coherent part of the spectrum, ǫ k , possesses an interesting property of flattening at large lattice momenta in the adiabatic limit, t ≫ ω 0 (Fehske and Trugman , 2007;Romero et al , 1998Romero et al , , 1999Stephan , 1996;Wellein et al , 1996;Wellein and Fehske , 1997). In the weakcoupling limit, the flattening can be readily understood as hybridization between the bare electron spectrum and a phonon mode (Levinson and Rashba , 1973). The resulting polaron dispersion is cosine-like at small k and flat at large k. As a result the polaron DOS should be peaked close to the top of the polaron band.…”

Band Structure of the Jahn-Teller Polaron from Quantum Monte Carlo

“…3). The polaron spectrum is flat in the outer part of the Brillouin zone due to hybridization with dispersionless phonon modes [15], which results in a massive peak in DOS at the top of the band. The Van Hove singularities are invisible because they are absorbed by the peak.…”

Real Time Quantum Dynamics of Spontaneous Translational Symmetry Breakage in the Early Stage of Photo-Induced Structural Phase Transitions

“…Hence, even if it tries to move only to a neighboring lattice site from its original one, it has to annihilate all these phonons (larger distortion) and has to make them again at the neighboring site, newly. This phonon dressing picture was also developed by Rashba and his co-workers [14].…”