The trion as an exciton interacting with a carrier

The X⁻ trion is essentially an electron bound to an exciton. However, due to the composite nature of the exciton, there is no way to write an exciton-electron interaction potential. We can overcome this difficulty by using a commutation technique similar to the one we introduced for excitons interacting with excitons, which allows to take exactly into account the close-to-boson character of the excitons. From it, we can obtain the X⁻ trion creation operator in terms of excitons and electrons. We can also derive the X⁻ trion ladder diagram between an exciton and an electron. These are the basic tools for future works on many-body effects involving trions.     

Commutation technique for interacting close-to-boson excitons

The correct treatment of the close-to-boson character of excitons is known to be a major problem. In a previous work, we have proposed a “commutation technique” to include this close-to-boson character in their interactions. We here extend this technique to excitons with spin degrees of freedom as they are of crucial importance for many physical effects. Although the exciton total angular momentum may appear rather appealing at first, we show that the electron and hole angular momenta are much more appropriate when dealing with scattering processes. As an application of this commutation technique to a specific problem, we reconsider a previous calculation of the exciton-exciton scattering rate and show that the proposed quantity is intrinsically incorrect for fundamental reasons linked to the fermionic nature of the excitons. Received 25 October 2001 Published online 25 June 2002     

Kinetic properties of a system of spatially separated excitons and electrons in the presence of a Bose condensate of excitons

A system of interacting, spatially separated excitons and electrons is examined in the presence of a Bose condensate of excitons. The kinetic properties of the system that are governed by the interaction of excitations in the exciton subsystem with electrons are investigated. It is shown that a nonequilibrium distribution of excitations in the exciton subsystem gives rise to an induced electron current. Experimental observation of the kinetic phenomena described can provide new information on the exciton phase state. Zh. éksp. Teor. Fiz. 116, 1440–1449 (October 1999)     

Charged excitons in quantum dots: novel magnetic behavior and Auger processes

We describe theoretically multiply-charged excitons interacting with a continuum of delocalized states. Such excitons exist in relatively shallow quantum dots and have been observed in recent optical experiments on InAs self-assembled dots. The interaction of an exciton and delocalized states occurs via Auger-like processes. To describe the optical spectra, we employ the Anderson-like Hamiltonian by including the interaction between the localized exciton and delocalized states of the wetting layer. In the absence of a magnetic field, the photoluminescence line shapes exhibit interference effects. When a magnetic field is applied, the photoluminescence spectrum demonstrates anticrossings with the Landau levels of the extended states. We show that the magnetic-field behavior of charged excitons is very different to that of diamagnetic excitons in three and two-dimensional systems.     

Polaronic exciton in quantum wells wires and nanotubes

We investigate the effect of the longitudinal-optical phonon field on the binding energies of excitons in quantum wells, well-wires and nanotubes based on ionic semiconductors. We take into account the exciton-phonon interaction by using the Aldrich-Bajaj effective potential for Wannier excitons in a polarizable medium. We extend the fractional-dimensional method developed previously for neutral and negatively charged donors to calculate the exciton binding energies in these heterostructures. In this method, the exciton wave function is taken as a product of the ground state functions of the electron polaron and hole polaron with a correlation function that depends only on the electron-hole separation. Starting from the variational principle we derive a one-dimensional differential equation, which is solved numerically by using the trigonometric sweep method. We find that the potential that takes into account polaronic effects always give rise to larger exciton binding energies than those obtained using a Coulomb potential screened by a static dielectric constant. This enhancement of the binding energy is more considerable in quantum wires and nanotubes than in quantum wells. Our results for quantum wells are in a good agreement with previous variational calculations. Also, we present novel curves of the exciton binding energies as a function of the wire and nanotubes radii for different models of the confinement potential.     

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.     

The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

Exciton interaction potential in polar crystals

The problem whether polaron effects can lead to a repulsive barrier in the exciton interaction potential is reinvestigated, because this effect is crucial for the possibility of a Bose-Einstein condensation of excitons (rather than of excitonic molecules). The energy for two excitons is calculated accurately as a function of their mean distance in the case of a heavy hole mass by using an integral expansion method of molecular physics. The resulting interaction potential shows for certain polaron radii a very weak repulsive barrier. Taking into account corrections to the Haken potential which have been introduced by Pollmann and Büttner, it is shown that the interaction potential between two excitons in the relative singlet state is always attractive, so that the exciton system is also in polar materials unstable against exciton molecule formation.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Shiva diagrams for composite-boson many-body effects: how they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way.     

Ground state energy of N Frenkel excitons

By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing in the N exciton normalization factor – the cancellation being exact within terms in 1/N_s where N_s is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely appears at various stages in the precise calculation of the Hamiltonian mean value.     

On the N-exciton normalization factor

The N-ground-state-exciton normalization factor, namely 〈v| B ₀ ^N B ₀ ^dagN| v〉 = N!F _N, with B ₀ ^d ag the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity F_N turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution exists in their many-body effects, which relies directly on F_N. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and in the BCS theory of superconductivity, we rederive important relations verified by the F_N's. We also give new explicit expressions of F_N valid for η = Na _x ³/ small but N ² a _x ³/ large, as F_N does not read in terms of η but Nη, the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, F_N does not appear alone in physical quantities, but through ratios like F _{N + p}/F _N. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects. Received 30 May 2002 / Received in final form 12 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Application of the Multi-Doorway Continuum Shell Model to the Magnetic Dipole Strength Distribution in 58Ni

The usual continuum shell model is extended so as to include a statistical treatment of multi-doorway processes. The total configuration space of the nuclear reaction problem is subdivided into the primary doorway states which are coupled by the initial excitation to the nuclear ground state and the secondary doorway states which represent the complicated nature of multi-step reactions. The latter are evaluated within the exciton model which gives the coupling widths between the various finestructure subspaces. This coupling is determined by a statistical factor related to the exciton model and a dynamical factor given by the interaction matrix elements of the interacting excitons. The whole structure defines the multi-doorway continuum shell model. In this work it is applied to the highly fragmented magnetic dipole strength in ⁵⁸Ni observed in high resolution electron scattering.     

Assembly of sol–gel-grown Li<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CoO<Subscript>2</Subscript> nanocrystals through electromagnetic irradiation

We report the fabrication of assembled nanostructures from the pre-synthesized nanocrystals building blocks through optical means of exciton formation and dissociation. We demonstrate that Li _x CoO₂ nanocrystals assemble to an acicular architecture, upon prolonged exposure to ultraviolet–visible radiation emitted from a 125 W mercury vapor lamp, through intermediate excitation of excitons. The results obtained in the present study clearly show how nanocrystals of various materials with band gaps appropriate for excitations of excitons at given optical wavelengths can be assembled to unusual nanoarchitectures through illumination with incoherent light sources. The disappearance of exciton bands due to Li _x CoO₂ phase in the optical spectrum of the irradiated film comprising acicular structure is consistent with the proposed mechanism of exciton dissociation in the observed light-induced assembly process. The assembly process occurs through attractive Coulomb interactions between charged dots created upon exciton dissociation. Our work presents a new type of nanocrystal assembly process that is driven by light and exciton directed.     

Direct and spatially indirect excitons in GaAs/AlGaAs superlattices in strong magnetic fields

Luminescence and luminescence excitation spectra are used to study the energy spectrum and binding energies of direct and spatially indirect excitons in GaAs/AlaAs superlattices, with different widths of the electron and hole minibands, located in a high magnetic field perpendicular to the heterolayers. It is found that the ground state of the indirect excitons formed by electrons and holes and spatially separated between neighboring quantum wells lies between the ls ground state of the direct excitons and the continuum threshold for dissociated exciton states in the minibands. Indirect excitons in superlattices have a significant oscillator strength when the binding energy of the exciton exceeds the order of the width of the resulting miniband. The behavior of the binding energy of direct and indirect heavy hole excitons during changes in the tunneling coupling between the quantum wells is established. It is shown that a strong magnetic field, which intensifies the Coulomb interaction between the electron and hole in an exciton, weakens the bond in a system of symmetrically bound quantum wells. The spatially indirect excitons studied here are analogous to first order Wannier-Stark localized excitons in superlattices with inclined bands (when an electrical bias is applied), but in the present case the localization is of purely Coulomb origin. Zh. éksp. Teor. Fiz. 112, 1106–1118 (September 1997)     

Exciton condensation in coupled quantum wells

Bound electron-hole pairs—excitons—are Bose particles with small mass. Exciton Bose-Einstein condensation is expected to occur at a few degrees Kelvin—a temperature many orders of magnitude higher than for atoms. Experimentally, an exciton temperature well below 1 K is achieved in coupled quantum well (CQW) semiconductor nanostructures. In this contribution, we review briefly experiments that signal exciton condensation in CQWs: a strong enhancement of the indirect exciton mobility consistent with the onset of exciton superfluidity, a strong enhancement of the radiative decay rate of the indirect excitons consistent with exciton condensate superradiance, strong fluctuations of the indirect exciton emission consistent with critical fluctuations near the phase transition, and a strong enhancement of the exciton scattering rate with increasing concentration of the indirect excitons revealing bosonic stimulation of exciton scattering. Novel experiments with exciton condensation in potential traps, pattern formation in exciton system and macroscopically ordered exciton state will also be reviewed briefly.     

Nonlinear time-independent and time-dependent propagation of light in direct-gap semiconductors with paired excitons bound into biexcitons

We study a new class of nonlinear cooperative phenomena that occur when light propagates in direct-gap semiconductors. The nonlinearity here is due to a process, first discussed by A. L. Ivanov, L. V. Keldysh, and V. V. Panashchenko, in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. For the geometry of a ring cavity, we derive a system of nonlinear differential equations describing the dynamical evolution of coherent excitons, photons, and biexcitons. For the time-independent case we arrive at the equation of state of optical bistability theory, and this equation is found to differ considerably from the equations of state in the two-level atom model and in the exciton region of the spectrum. We examine the stability of the steady states and determine the switchover times between the optical bistability branches. We also show that in the unstable sections of the equation of state, nonlinear periodic and chaotic self-pulsations may arise, with limit cycles and strange attractors being created in the phase space of the system. The scenario for the transition to the dynamical chaos mode is found. A computer experiment is used to study the dynamic optical bistability. Finally, we discuss the possibility of detecting these phenomena in experiments. Zh. éksp. Teor. Fiz. 112, 1778–1790 (November 1997)     

Probing Bose-Einstein condensation of excitons with electromagnetic radiation

We examine the absorption spectrum of electromagnetic radiation from excitons, where an exciton in the 1s state absorbs a photon and makes a transition to the 2p state. We demonstrate that the absorption spectrum depends strongly on the quantum degeneracy of the exciton gas, and that it will generally manifest many-body effects. Based on our results we propose that absorption of infrared radiation could resolve recent contradictory experimental results on excitons in Cu(2)O.     

强耦合表面激子内部激发态的性质

采用线性组合算符和幺正变换方法,研究极性晶体中强耦合表面激子内部激发态的性质.计算了表面激子的激发态能量、激发能量和平均声子数.     

Remote dipolar interactions for objective density calibration and flow control of excitonic fluids

In this Letter we suggest a method to observe remote interactions of spatially separated dipolar quantum fluids, and in particular, of dipolar excitons in GaAs bilayer based devices. The method utilizes the static electric dipole moment of trapped dipolar fluids to induce a local potential change on spatially separated test dipoles. We show that such an interaction can be used for model-independent, objective fluid density measurements, an outstanding problem in this field of research, as well as for interfluid exciton flow control and trapping. For a demonstration of the effects on realistic devices, we use a full two-dimensional hydrodynamical model.     

High-resolution nonlinear laser spectroscopy of exciton relaxation in GaAs quantum wells

This paper describes measurements of exciton relaxation in GaAs/AlGaAs quantum well structures based on high resolution nonlinear laser spectroscopy. The nonlinear optical measurements show that low energy excitons can be localized by monolayer disorder of the quantum well interface. We show that these excitons migrate between localization sites by phonon assisted migration, leading to spectral diffusion of the excitons. The frequency domain measurements give a direct measure of the quasi-equilibrium exciton spectral redistribution due to exciton energy relaxation, and the temperature dependence of the measured migration rates confirms recent theoretical predictions. The observed line shapes are interpreted based on solutions we obtain to modified Bloch equations which include the effects of spectral diffusion.