It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

The authors review the physics of ultrafast dynamics in semiconductors and their heterostructures, including both the observed experimental phenomena and the theoretical description of the processes. These are probed by ultrafast optical excitation, generating nonequilibrium states that can be monitored by time-resolved spectroscopy. Light pulses create coherent superpositions of states, and the dynamics of the associated phase relationships can be directly investigated by means of many-pulse experiments. The commonly used experimental techniques are briefly reviewed. A variety of different phenomena can be described within a common theoretical framework based on the density-matrix formalism. The important interactions of the carriers included in the theoretical description are the phonon interactions, the interactions with classical and quantum light fields, and the Coulomb interaction among the carriers themselves. These interactions give rise to a strong interplay between phase coherence and relaxation, which strongly affects the non equilibrium dynamics. Based on the general theory, the authors review the physical phenomena in various semiconductor structures including superlattices, quantum wells, quantum wires, and bulk media. Particular results which have played a central role in understanding the microscopic origins of the relaxation processes are discussed in detail.

Theory of ultrafast phenomena in photoexcited semiconductors

Atomically thin transition metal dichalcogenides are direct-gap semiconductors with strong light-matter and Coulomb interactions. The latter accounts for tightly bound excitons, which dominate their optical properties. Besides the optically accessible bright excitons, these systems exhibit a variety of dark excitonic states. They are not visible in the optical spectra, but can strongly influence the coherence lifetime and the linewidth of the emission from bright exciton states. Here, we investigate the microscopic origin of the excitonic coherence lifetime in two representative materials (WS2 and MoSe2) through a study combining microscopic theory with spectroscopic measurements. We show that the excitonic coherence lifetime is determined by phonon-induced intravalley scattering and intervalley scattering into dark excitonic states. In particular, in WS2, we identify exciton relaxation processes involving phonon emission into lower-lying dark states that are operative at all temperatures.

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Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides.

Many-body correlations and excitonic effects in semiconductor spectroscopy

Excitons are quasi-particles that form when Coulomb-interacting electrons and holes in semiconductors are bound into pair states. They have many features analogous to those of atomic hydrogen. Because of this, researchers are interested in exploring excitonic phenomena, from optical, quantum-optical and thermodynamic transitions to the possible condensation of excitons into a quantum-degenerate state. Excitonic signatures commonly appear in the optical absorption and emission of direct-gap semiconductor systems. However, the precise properties of incoherent exciton populations in such systems are difficult to determine and are the subject of intense debate. We review recent contributions to this discussion, and argue that to obtain detailed information about exciton populations, conventional experimental techniques should be supplemented by direct quasi-particle spectroscopy using the relatively newly available terahertz light sources. Finally, we propose a scheme of quantum-optical excitation to generate quantum-degenerate exciton states directly.

Semiconductor excitons in new light

The phonon scattering assisted luminescence of semiconductor quantum well excitons after short pulse excitation is investigated. The presented analysis is based on the low-density limit of a set of equations for quantum correlation functions for electrons, phonons, and photons. The dynamics of the correlation functions describes the optical excitation and the decay of the coherent exciton polarization as well as the generation of an incoherent exciton occupation and its luminescence decay. Numerical solutions of the equations of motion demonstrate strong competition effects of the exciton-phonon and the exciton-photon interaction on a picosecond time scale and lead to a nonmonotonous temperature dependence of the time-resolved spontaneous emission. The angle resolved emission resembles the generation and decay dynamics of the exciton density for different in-plane momenta.

Quantum theory of phonon-assisted exciton formation and luminescence in semiconductor quantum wells

Theory of Ultrafast Spatio‐Temporal Dynamics in Semiconductor Quantum Wells: Electronic Wavepackets and Near‐Field Optics

A microscopic theory for secondary emission of a semiconductor quantum well is presented where disorder and phonon scattering are treated consistently. Coherent and incoherent contributions to the secondary emission are computed for model systems with different degrees of disorder. The results show that the simultaneous influence of both scattering mechanisms is generally nonadditive, such that a full calculation is required to obtain reliable results. Only in strongly disorder dominated structures it is a reasonable approximation to model phonon scattering by a phenomenological decay time.

Interplay between coherent and incoherent scattering in quantum well secondary emission

Nonlinear propagation of optical pulses through an extended bulk semiconductor is investigated using the coupled semiconductor Maxwell‐Bloch equations including excitation induced correlations. For short pulse excitation around the exciton resonance, the theory describes the development of polariton beats and their suppression at increasing input pulse intensities due to the coupling of single exciton states to the Coulomb‐correlated continuum of two‐exciton states. A comparison of the theoretical results with experimental observations for CdSe bulk material is presented.

Nonlinear Polariton Pulse Propagation in Bulk Semiconductors

A fully microscopic quantum theory for the photoluminescence of a semiconductor quantum well is summarized. The dynamic equations for the interacting electron–hole pairs (excitons), phonons and photons are presented and specialized for the situations of interacting electron–hole populations and low density excitonic populations. Signatures of phonon assisted exciton formation are discussed in the low density limit, where the early dynamics is found to be strongly dependent on the emission angle. For long times the decay can be described by an angle-independent decay rate.

S. Kuckenburg

Papers

Quantum theory of phonon-assisted exciton formation and luminescence in semiconductor quantum wells

Theory of Ultrafast Spatio‐Temporal Dynamics in Semiconductor Quantum Wells: Electronic Wavepackets and Near‐Field Optics

Interplay between coherent and incoherent scattering in quantum well secondary emission

Nonlinear Polariton Pulse Propagation in Bulk Semiconductors

Many-Body Quantum Theory of Spontaneous Emission of Semiconductor Quantum Wells