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Quantum Electronics and Laser Science Conference

Collective oscillations, excitonic molecules and dephasing of excitons at low density

Th. Östreich

Published May 12, 2000• 0 citations
OpenAlex

Abstract

Summary form only given. Large-radius excitons in semiconductors suffer strong Coulomb interaction on close approach. This is a distinctive difference in comparison with two-level systems in quantum optics. A mean field theory of interacting excitons in semiconductors leads to purely repulsive interaction, and does not account for spin-dependent polarization mixing and the formation of excitonic molecules (biexcitons). We have developed a theory for the nonlinear optical response, which can account for both. The coherent polarization is driven by exciton-exciton correlation, which can be expressed in terms of spin-dependent retarded memory functions. The effective equation is a generalized Gross-Pitaevskii equation.

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Summary form only given. Large-radius excitons in semiconductors suffer strong Coulomb interaction on close approach. This is a distinctive difference in comparison with two-level systems in quantum optics. A mean field theory of interacting excitons in semiconductors leads to purely repulsive interaction, and does not account for spin-dependent polarization mixing and the formation of excitonic molecules (biexcitons). We have developed a theory for the nonlinear optical response, which can account for both. The coherent polarization is driven by exciton-exciton correlation, which can be expressed in terms of spin-dependent retarded memory functions. The effective equation is a generalized Gross-Pitaevskii equation.
In semiconductors the attractive Coulomb interaction between electrons and holes causes one- and two-photon resonances, known as excitons and exciton molecules, respectively. Large nonlinearities are observed in the spectral vicinity of these resonances. These nonlinearties are well-suited for the realization of optical bistability1),2),3) as has been demonstrated by Gibbs et al. 1)for GaAs and by Miller et al.2) for InSb. The electron-hole correlations, the screening and the energy renormalization are most conveniently calculated by the Green's function formalism. The optical dielectric function can be expressed in terms of the retarded photon self-energy which is also called the polarization function. This connection is not restricted to the linear response regime.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
An excitonic approach to the ultrafast optical response of confined semiconductors at elevated densities below the Mott transition is presented. The theory is valid from the coherent regime, where coherent excitonic transitions and biexcitons dominate, to the incoherent regime, where excitonic occupations dominate. Numerical simulations of the 1s1s1s exciton dynamics during intense circularly polarized pump pulses in two different Coulomb-interaction regimes are performed for two-dimensional semiconductors: Moderate Coulomb interaction is compared with dominating Coulomb interaction with respect to the light-matter interaction strength. The different many-body contributions are disentangled and it is found, that excitonic Rabi oscillations in the Coulomb-dominated regime are considerably less strong. By also comparing circular and linear excitation in a MoSe2_22​ monolayer, it is found, that linear excitation creates a regime, where excitonic Rabi oscillations are almost completely suppressed.
Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.
Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.