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Journal of Physics C Solid State Physics

On the theory of coherent pairing of excitons in molecular crystals

Constantine Mavroyannis

Published Apr 28, 1977• 2 citations
Publisher

Abstract

The theory of the coherent pairing of excitons in the presence of a resonant electromagnetic field is generalized to describe the biexciton spectra of molecular crystals, which contain several molecules (atoms) in the unit cell. The excitation spectrum for crystals like anthracene having two molecules per unit cell is discussed in detail. It is found that, at high exciton densities and under resonance of near-resonance conditions and at temperatures below some value T c , the formation of four biexciton states is feasible provided that the dielectric gaps induced by the electromagnetic field are less than those of the corresponding biexciton states. Expressions for the absorption coefficient describing optical transitions to the biexciton states are derived.

DOI
10.1088/0022-3719/10/8/024

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Journal of Physics Condensed Matter•Apr 6, 1992•1 citation
The theory of the coherent pairing of excitons in the presence of a resonant electromagnetic field is generalized to describe the biexciton spectra of molecular crystals, which contain several molecules (atoms) in the unit cell. The excitation spectrum for crystals like anthracene having two molecules per unit cell is discussed in detail. It is found that, at high exciton densities and under resonance of near-resonance conditions and at temperatures below some value T c , the formation of four biexciton states is feasible provided that the dielectric gaps induced by the electromagnetic field are less than those of the corresponding biexciton states. Expressions for the absorption coefficient describing optical transitions to the biexciton states are derived.
The theory of the coherent pairing of Frenkel excitons in the presence of a resonant electromagnetic field is generalized to include the effect of the electron spin. It is shown that at high exciton densities and when the electromagnetic field is at resonance or near resonance, the removal of the spin degeneracy of the exciton pairs results in generating two fields, the singlet and the triplet biexciton fields, respectively. The gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ due to the singlet and triplet biexciton fields, respectively, are calculated and they are found to be independent of one another only in the limit when the exchange interactions between the charges disappear. In this limit, the energy modes for singlet and triplet biexciton fields have well-defined meaning and propagate through the crystal independently. A dielectric gap is induced by the electromagnetic field, which produces the energy splitting in the singlet biexciton spectrum, and it must be less than that of ${\ensuremath{\Delta}}_{+}$ for the singlet biexciton state. For finite values of the exchange interaction, the gap functions ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ depend strongly on each other and consequently the singlet and triplet biexciton fields are strongly mixed together. Optical transitions to the singlet and triplet biexciton states are considered and the corresponding expressions for the absorption coefficient are derived. The ground-state energy describing the binding energy arising from the singlet and triplet biexciton fields is calculated and discussed. Numerical estimates indicate that at high exciton densities, namely, for exciton concentrations 1018{10}^{18}1018-1019{10}^{19}1019 ${\mathrm{cm}}^{\ensuremath{-}3}$ and when the ratio of the average exciton-exciton interaction over the average kinetic energy is between 0.7 and 2 (strong-coupling limit), the energy gap due to the singlet biexciton state is in the range 40-650 ${\mathrm{cm}}^{\ensuremath{-}1}$, the corresponding transition temperature is 33-534 \ifmmode^\circ\else\textdegree\fi{}K, while the binding energy is 22-684 ${\mathrm{cm}}^{\ensuremath{-}1}$.
Great progress has been made in recent years in experimental studies of excitonic molecules, both in direct-band and indirect-band semiconductors. The exciton systems in these semiconductors differ substantially. In direct-band semiconductors with dipole-allowed optical transitions, the direct-recombination times are extremely small. Consequently the processes of binding of excitons into excitonic molecules and their decay occur under strongly nonequilibrium conditions. Hence one can obtain the fundamental information on biexcitons in these semiconductors by nonlinear optical methods. This review discusses the processes on which the various methods are based: two-photon resonance excitation of biexcitons, induced one-photon conversion of an exciton into a biexciton, two-photon resonance Raman scattering involving biexciton states, etc., and their application to studying biexcitons with the example of CdS. Problems of bistability involving biexcitons are also briefly discussed. In indirect semiconductors, where recombination occurs with the emission of a phonon, the lifetimes of excitons are large, and quasiequilibrium can be established in the exciton system. Under these conditions the information on the properties of the molecules is obtained by analyzing their radiative-decay spectra. The problem of detecting biexcitons in indirect semiconductors, radiative decay of molecules, and the effect on their stability of external electric, strain, and magnetic fields are discussed in detail with the examples of Si and Ge. Also the results of investigating the quantum statistical behavior of a dense gas of spin-oriented excitons (in a magnetic field under conditions in which the biexcitons are destabilized) are briefly presented (using the example of uniaxially compressed germanium), and the question of the possibility of their Bose condensation is discussed.
A general theoretical description is derived for the resonance fluorescence of dilute gases and molecular single crystals with special emphasis on optical rotation spectra. The validity of previous theoretical work on dilute gases is confirmed by proving that the damping constants connecting excited states on different molecules are zero. It is shown that the intensities of optical rotation spectra of molecular crystals are much larger than the corresponding quantities for gases. An important theoretical prediction is that the natural line breadth of a resonance fluorescence emission band belonging to an exciton state in a molecular crystal should be larger than the width of the corresponding optical absorption line. The dependence of the intensity of the optical rotation spectrum on the relative orientation of the crystal with respect to the incident beam of light is discussed.
Abstract A model which allows to treat self‐consistently many‐body exciton effects, including biexciton formation, is proposed for the theoretical description of an excitonic polarization induced by an intense electromagnetic field. In the presence of a pump field the normal spectrum of electromagnetic waves in the vicinity of the nonlinear biexciton resonance is shown to be composed of four polariton branches, where each is the superposition of two photons and two excitons. In the self‐consistent field approximation, the structure of the interconnected, strongly nonlinear exciton and biexciton resonances is studied, including optical Stark shift, multistable behaviour, etc. For a certain range of the exciton interaction parameters at sufficiently strong pump wave the system of excitons and excitonic molecules transforms abruptly to a dense coherent electron–hole “liquid”. Appearance and temporary evolution of an exciton–biexciton system after switching on a pump is also considered.