Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na _x ³/)ⁿ with n ≥ 2. An exact procedure to get these density dependent terms is given. Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Electron-hole diagrams versus exciton diagrams: the simplest problem on interacting excitons

We study the interaction of an exciton with a distant metal, which is the simplest problem on interacting excitons: The semiconductor and metal electrons being “different” species, we do not have to worry about the tricky consequences of Pauli exclusion between identical carriers, which appear in any other problem on interacting excitons. We show how the exciton absorption, in the presence of semiconductor-metal interaction, can be derived in a very simple and transparent way from an exciton diagram procedure, provided that we use the appropriate exciton-metal interaction vertex, which contains the scattering from an exciton state to another exciton state under a Coulomb excitation. We also show that the resolution of this problem using standard electron-hole diagrams is dreadfully complicated at the lowest order in the semiconductor-metal interaction already, preventing a full calculation of the exciton-metal coupling from this usual technique. Received 26 February 2001     

Ab initio study of the Fe intra- and inter-layer magnetic order in Fe/Ir(001) superlattices

We reconsider the semiconductor trions from scratch. We first determine the very many “reasonable” ways to write the trions in first quantization. We then select the forms which are easy to relate to physical pictures. In a second part, we derive the corresponding creation operators in second quantization. We pay particular attention to the expression of the X^- trion in terms of exciton and free-electron, as it is the one adapted to future works on many-body effects with trions. Received 27 May 2002 / Received in final form 18 December 2002 Published online 20 June 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Polaron effects on excitons in parabolic quantum wells: fractional-dimension variational approach

Polaron effects on excitons in parabolic quantum wells are studied theoretically by using a variational approach with the so-called fractional dimension model. The numerical results for the exciton binding energies and longitudinal-optical phonon contributions in GaAs/Al_0.3Ga_0.7As parabolic quantum well structures are obtained as functions of the well width. It is shown that the exciton binding energies are obviously reduced by the electron (hole)-phonon interaction and the polaron effects are un-negligible. The results demonstrate that the fractional-dimension variational theory is effectual in the investigations of excitonic polaron problems in parabolic quantum wells.     

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.     

Comparison study of energy bands and Wannier-Mott excitons in mixed Zn(P As ) and Zn Cd P crystals

Excitonic absorption, reflection and photoluminescence spectra of mixed Zn(P_1-xAs_x)₂ crystals over the full range of x ( 0 ? x ? 1) and Zn_1-xCd_xP₂ crystals at 0 ? x ? 0.05 have been studied at low temperatures (1.8 K). The decrease of the energy gap in Zn(P_1-xAs_x)₂ at the increase of x occurs slightly sublinearly. The rydbergs of excitonic series in this crystals decrease as well, and the dependences Ry ( x ) for all series are strongly superlinear at small x. In Zn_1-xCd_xP₂ crystals the energy gap and rydbergs decrease at the increase of x (at 0 ? x ? 0.05) as well. The dependences of E_g and Ry on x are considerably stronger in Zn(P_1-xAs_x)₂ than in Zn_1-xCd_xP₂. At the increase of x the half-width of excitonic absorption lines increases monotonically in both type crystals that is evidence of the increasing role of fluctuations of crystal potential. Received 13 March 2002 Published online 9 July 2002     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Variational calculations of ionized-donor-bound excitons in GaAs-Al x Ga 1 - x As quantum wells

Using a two-parameter wave function, we calculate variationally the binding energy of an exciton bound to an ionized donor impurity (D^+,X) in GaAs-Al_xGa_1-xAs quantum wells for the values of the well width from 10 to 300 ?, when the dopant is located in the center of the well and at the edge of the well. The theoretical results confirm that the previous experimental speculation proposed by Reynolds et al. [Phys. Rev. B 40, 6210 (1989)] is the binding energy of D^+,X for the dopant at the edge of the well. In addition, we also calculate the center-of-mass wave function of the exciton and the average interparticle distances. The results are discussed in detail. Received 17 July 2000 and Received in final form 13 November 2000     

Electro-optical properties of excitons in polydiacetylene chains

We show how to compute the optical functions (reflectivity, transmission, and absorption) of polydiacetylene chains diluted in their monomer matrix exposed to a uniform electric field in the chain direction, in the excitonic energy region. Adopting a model electron-hole potential, we derived an analytical expression for the effective chain susceptibility, which gives the optical functions. The resulting absorption shows excitonic peaks below the gap and Franz-Keldysh oscillations above the gap. The method has been applied for a 3BCMU polydiacetylene chain, showing a good agreement with experimental spectra. Received 5 November 1998 and Received in final form 23 February 1999     

Third order response to a multifrequency photon field in semiconductors

This paper contains a detailed calculation of the photoinduced current density at third order in the coupling between a semiconductor and a multifrequency photon field, starting from its standard textbook expression which reads in terms of a triple commutator. Due to a major intrinsic problem linked to this triple commutator, such a derivation has been made possible quite recently only, thanks to the tools developed in the composite-boson many-body theory we have recently constructed. The photoinduced current density is shown to ultimately read in a compact form, in terms of the “Pauli scatterings” and “Coulomb scatterings” for exciton-exciton interactions introduced in this theory. Representation of this third order response in Shiva diagrams, which visualize interactions between excitons, is also given to better grasp the physics of the various contributions.     

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.     

Kinetics of dark excitons and excitonic trions in InGaAs single quantum well

Magnetooptical studies performed on a wide InGaAs/GaAs single quantum well indicate that optically non-active (dark) excitons with total angular momentum play the role of a reservoir for the creation of free multiparticle excitonic complexes. After analyzing the magnetic field evolution of the circularly polarized components of the low energy structure appearing in the main excitonic luminescence line we assign this feature to the excitonic trion formation. The binding energy of the excitonic trions was estimated to be of the order of 1 meV. Received: 29 October 1997 / Received in final form: 20 February 1998 / Accepted: 21 February 1998     

Secondary peak in the optical absorption spectra: A possible criterion for Bose condensation of excitons

By solving the BCS and Bethe-Salpeter equations, we confirm the result by Chu and Chang that a secondary peak appears in the optical absorption spectrum immediately after the 1S-exciton peak in the presence of a condensed phase. The observation of the secondary peak indicates the presence of exciton condensate.     

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.     

Polaronic effects on two-dimensional excitons

Summary We calculate the binding energy of a two-dimensional exciton for a set of states labelled by the quantum numberm associated to the angular momentum in the direction perpendicular to the surface. The Fr?hlich electron-phonon and hole-phonon interactions are taken into account. The statem=0 is more bound with respect to that obtained by the Wannier exciton theory with the screening given by the static dielectric constant and the reduced mass calculated by the electron and hole polaronic masses. The opposite effect is found for the statem=1,2,... Whenm becomes large, the hydrogenic series is recovered with the screening and reduced mass defined above. Our results are compared with the experimental data concerning exciton luminescence GaAs/Al _x Ga_1−x As, CuCl/CaF₂ and CdTe/Cd_1−x Zn _x Te quantum wells. The authors of this paper have agreed to not receive the proofs for correction.     

Optical investigations of GaAs/Ga1−x Al x As Quantum wells grown by molecular-beam epitaxy

Summary Measurements of photoluminescence, excitation photoluminescence and reflectance are performed at various temperatures on a series of GaAs/Ga_1−x Al _x As quantum well structures grown by molecularbeam epitaxy. The selective photoluminescence data of the GaAs buffer layers are analysed in order to correlate the optical properties with the growth conditions. The Stokes shift of the excitation emission line from quantum wells is investigated under various excitation conditions. A considerable decrease of the Stokes shift is observed in the case of nonresonant and intense excitations. Also the extrinsic photoluminescence, as well as its temperature dependence, are interpreted. In addition, the temperature effects on both the bulk and quantum well spectra are shown to clarify the excitation features and the contribution of the interband transitions. To speed up publication, the authors of this paper has agreed to not receive the proofs for correction.     

Magnetoexciton ground state for heavy- and light-hole excitons in anisotropic semiconductors

Summary We show how to compute the eigenvalues of an anisotropic Schr?dinger equation for light- and heavy-hole excitons in the presence of a magnetic field using a perturbational approach and a simplified deltalike interaction potential. Performing the calculation with a potential approapriate to bulk GaAs crystal we obtain a simple relation between the binding energy at zero field and the diamagnetic shift at low fields.     

Heavy- and light-hole excitons in anisotropic semiconductors

Summary We show how to compute the eigenvalues of an anisotropic Schroedinger equation for light-and heavy-hole excitons using a simplified deltalike interaction potential. Performing the calculation with a potential appropriate to bulk GaAs crystal, we obtain the excitonic binding energies for the heavy- and light-hole excitons, with the heavy-hole binding energy greater than that for the light hole. Inversion of this order for the case of a quantum well is discussed and expalined     

Core excitons in the electronic polaron model

Summary The electronic polaron model of the exciton is used to study the dielectric response of a medium to the excitation of a ?core? level, by adopting the method of direct solution of the Eulerian functional variational equations. The dynamical response of the electronic polarization affects the electron-hole attraction and the exciton binding energy, in a way which depends on the basic parameters of the crystal (dielectric constant, effective masses, lattice parameter) through the core exciton radius and the polaron radius. When the former is much larger than the latter, static dielectric screening results. When the exciton radius is comparable to the polaron radius, the screening is reduced and the binding energy is increased. Core exciton binding energies are computed in a number of substances using the effective-mass approximation. Space dispersion of the dielectric function coupled to intervalley interaction may, however, contribute in some cases to reducing the excitonic radius and bringing about an instability to a deep state that would invalidate the effective-mass approximation. Based on work supported by the Italian Research Council (C.N.R.) through a contract G.N.S.M.