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Physical review. B, Solid state

Singlet and triplet biexciton spectra of molecular crystals

Constantine Mavroyannis

Published Sep 15, 1977• 3 citations
Publisher

Abstract

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 ${10}^{18}$-${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ 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 ${\mathrm{cm}}^{\ensuremath{-}1}$.

DOI
10.1103/physrevb.16.2871

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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.
I report on the effect of a moderate excess electron population on nonlinearities in modulation-doped CdTe quantum wells. I show that the electron population does not qualitatively affect the nature of correlations between excitons. In this respect, I bring strong evidence of the existence of unbound and bound (stable) two-exciton states in the presence of electrons and charged excitons (trions). In time-resolved pump and probe experiment, they lead to the observation of electromagnetically induced transparency and optical Stark shift of the exciton resonance. Rabi flopping of excitons within a sea of electrons is also clearly evidenced through ac Stark splitting and gain without inversion. The quantum coherence is more robust to electron induced dephasing than what would have been expected. I demonstrate third and higher-order exciton correlations in the presence of electrons, which manifest, for increasing exciton densities, through the blue-shift of counter-polarized exciton resonance, the red-shift of the biexciton resonance and the exciton to biexciton crossover. I also evidence correlated behavior of excitons and trions under excitation which manifests itself by crossed trion-exciton effects. I observe a wealth of phenomena encompassing bleaching, crossed bleaching, induced-absorption and energy shifts of the resonances. Significant differences are found between the nonlinear optical effects induced by an exciton and a trion population. Electron scattering with electron and exciton is shown to strongly broaden the high energy tail of exciton and trion resonance lineshapes. Variations of electron density result in a clear modification of both resonance lineshapes. The dynamics of the formation of trions is also studied. I propose a two-channel mechanism for their formation; they are formed through bi- and tri-molecular processes. This implies that both negatively and positively charged excitons coexist in a quantum well, even in the absence of excess carriers. The model is applied to a time-resolved photoluminescence experiment performed on a very high quality InGaAs quantum well sample, in which the photoluminescence contributions at the energy of the trion, exciton and at the band edge can be clearly separated and traced over a broad range of times and densities. The unresolved discrepancy between the theoretical and experimental radiative decay time of the exciton in a doped semiconductor is explained.
We study the elementary excitations of a model Hamiltonian for the $\ensuremath{\pi}$ electrons in polydiacetylene chains. In these materials, the bare band gap is only half the size of the observed single-particle gap and the binding energy of the exciton of 0.5 eV amounts to 20% of the single-particle gap. Therefore, exchange and correlations due to the long-range Coulomb interaction require a numerically exact treatment which we carry out using the density-matrix renormalization group method. Employing both the Hubbard-Ohno potential and the screened potential in one dimension, we reproduce the experimental results for the binding energy of the singlet exciton and its polarizability. Our results indicate that there are optically dark states below the singlet exciton, in agreement with experiment. In addition, we find a weakly bound second exciton with a binding energy of 0.1 eV. The energies in the triplet sector do not match the experimental data quantitatively, probably because we do not include polaronic relaxation effects.
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A formal, regorous theory of Frenkel excitons interacting with an external electromagnetic field is doveloped within the framework of a two-level-atom model in which the dipole approximation is employed in describing the atom-field (taken as a c-number) interaction. The model exciton Hamiltonian is shown to be identical in form with the Heisenberg model Hamiltonian for S=1/2 spins with anisotropic long-range exchange interactions. Instead of treating excitons as a non-ideal Bose gas, atomic polarization operators and level population defference are taken up as two fundamental quantities to describe Frenkel excitons. A pair of equations satisfied by these two quantities are derived. It is shown that Frenkel excitons are generally expressed as quantum-mechanical nonlinear polarization waves, the nonlinearity being characterized by the level population. A discussion is given on the interrelationship between such polarization waves and those derivable from the classical Drude-Lorentz model. With the aid of several approximation procedures similar to those employed in nonlinear optics, a set of equations describing nonlinear exciton-photon coupled modes are derived. Brief discussion is given on the eigenfrequencies of nonlinear Frenkel excitons and nonlinear polaritons. The existence of nonlinear exciton-photon coupled modes whose properties are different from those of polariton modes is suggested.