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Combined Exciton-Electron Optical Processes in Optical Spectra of Modulation Doped QWs
Abstract
In modulation-doped quantum well structures with electron concentration of about 10(11) cm(-2), a new resonant optical transition involving four particles (one hole and three electrons) was found in external magnetic fields in photoluminescence excitation and reflectivity spectra. This transition reveals as a narrow line between exciton and trion lines. It is identified with a combined process in which a photocreated exciton binds with an electron forming a trion and promotes for the second electron a transition to higher Landau levels.
... To this end we will study below the band shape of the combined optical quantum transitions involving the creation of one magnetoexciton and the simultaneous excitation of an electron from the lower to upper Landau levels. The experimental results in this direction were published in the papers [3,4,5] . Both aspects of the magnetoexciton physics are strongly correlated with the knowledge concerning the influence of the excited Landau levels accumulated in the frame of two earlier published papers [1,2] . ...
The Bose-Einstein Condensation (BEC) of the two-dimensional magnetoexcitons on the superposition state is studied. The superposition of two excitonic states formed by electron and hole on the lowest Landau levels (0, 0) and on the first excited Landau levels (1, 1) was considered. The generalized Bogoliubov u-v transformation was deduced. The criterion on the exciton concentration was established. The influence of the BEC on the absorption band shape is discussed.
Reflectivity and photoluminescence spectra from CdTe/CdMgTe modulation-doped quantum well structures were studied. We have found that in reflectivity spectra the value and the sign of the Zeeman splitting of the trion lines depend on the electron concentration in the quantum well, whereas, the value and sign of the exciton line splitting are constant for all studied electron concentrations. On the other hand, in the photoluminescence spectra the sign and value of the Zeeman splitting are the same for trion and exciton. Such "renormalization" of the trion g-factor is explained in the model of combined exciton-electron processes.
In the case of a two-leg Hubbard ladder we present a procedure which
allows the exact deduction of the ground state for the four-particle
problem in an arbitrary large lattice system, in a tractable manner,
which involves only a reduced Hilbert space region containing the ground
state. In the presented case, the method leads to nine analytic, linear
and coupled equations providing the ground state. The procedure which is
also applicable to few particle problems and other systems is based on
an r-space representation of the wavefunctions and construction of
symmetry adapted orthogonal basis wave vectors describing the Hilbert
space region containing the ground state. Once the ground state is
deduced, a complete quantum-mechanical characterization of the studied
state can be given. Since the analytic structure of the ground state
becomes visible during the use of the method, it is important not only
to the understanding of theoretical aspects connected to exact
descriptions or potential numerical approximation scheme developments,
but is also relevant for a large number of potential technological
application possibilities placed between nano-devices and quantum
calculations, where the few particle behaviour and deep understanding
are important key aspects.
The Hamiltonian describing the interaction of the two-dimensional (2-D)
magnetoexcitons with photons propagating with arbitrary-oriented wave
vectors in the three-dimensional (3-D) space is deduced. The
magnetoexcitons are characterized by the numbers n and n of the electron
and hole Landau quantizations, by circular polarization σ of the
holes in the p-type valence bands and by in-plane wave vectors k. The
photons are characterized by the wave vectors k→ with in-plane
component k and perpendicular component k, which is quantized in the
case of microresonator. The interaction is governed by the conservation
law of the in-plane components k of the magnetoexcitons and photons and
by the rotational symmetry around the axis perpendicular to the layer,
which leads to the alignment of the magnetoexcitons under the influence
of the photons with circular polarization σ→k→±
and with probability proportional to |.
The reflection and photoluminescence spectra of modulation-doped CdTe/CdMgTe quantum-well structures have been studied. It was found that the magnitude and sign of the Zeeman splitting of the trion reflection line depend on the electron concentration in the quantum well, whereas the magnitude and sign of the splitting of the exciton line are absolutely the same for all the electron concentrations under study. In the photoluminescence spectra, the magnitude and sign of the Zeeman splittings for the exciton and trion were the same. This “renormalization” of the trion g factor is explained in terms of the model of combined exciton-electron processes.
Reflectivity and photoluminescence spectra from CdTe/CdMgTe modulation doped quantum well structures were studied. We have found that the value and the sign of the trion reflectivity line's Zeeman splitting depends on the electron concentration in the quantum well, whereas the value and sign of the exciton line splitting are absolutely equal for all studied electron concentrations. In the photoluminescence spectra the sign and value of the exciton and trion Zeeman splittings are found to be equal. Such "renormalization" of the trion g-factor is explained in the model of combined exciton electron processes. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints
The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.
The article consists of two parts describing two associated properties of two-dimensional magnetoexcitons. In the first part, the theory of combined exciton-cyclotron resonance in the quantum well structures is developed for a strong magnetic field. In the first part, we calculate the absorption band structure for optical quantum transitions with circularly polarized radiation creating a two-dimensional exciton and simultaneously exciting one of the resident electrons from the lowest to the first excited Landau level. In the second part, we discuss the collective elementary excitations of the system of two-dimensional magnetoexcitons in the ground state of Bose–Einstein condensation on the arbitrary wave vector ≠ 0 in the Hartree–Fock approximation. The breaking of the gauge symmetry of the initial Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
In this paper we review results of studies of two types of spatially graded quantum well structures containing various layers of diluted magnetic semiconductors Cd1-xMnx Te or Cd1-x-yMnxMgy Te. The design of the structures has been recently proposed by us and suitable samples have been grown by a modified molecular beam epitaxy method. In the structures of the first type a digital profiling of the composition of the constituent material in the growth direction allowed to produce quantum wells with a specifically required shape of the confining potential (including parabolic, half-parabolic, triangular, and trapezoidal). Such samples were used for (i) determination of the conduction and valence band offsets in MnTe/CdTe and MgTe/CdTe systems, (ii) for the demonstration of an enhanced exciton binding in a parabolic confining potential as well as for (iii) demonstration of the possibility of "spin-splitting engineering" in diluted magnetic semiconductors quantum structures. In the second type of the structures, a precise in-plane profiling of either quantum well width or the barrier width or n-type doping intensity was realized. These structures were subsequently used for studies of the evolution of optical spectra with an increase in the concentration of confined two-dimensional gas of conduction electrons.
A combined exciton-cyclotron resonance is found in photoluminescence excitation and reflectivity spectra of semiconductor quantum wells containing an electron gas of low density. In external magnetic fields, an incident photon creates an exciton in the ground state and simultaneously excites one of the resident electrons from the lowest to one of the upper Landau levels. A theoretical model is developed, which gives a good quantitative description of the energy position and the intensity of the combined exciton-cyclotron resonance.
The line shape of the optical and magneto-optical absorption of negatively charged excitons in three- and two-dimensional (2D) semiconductors has been studied. The absorption coefficients have been determined using envelope wave functions obtained by variational means. At zero field, the charged exciton lines are disposed at the low-energy side of the threshold frequency with a rapidly decreasing long tail. In the two-dimensional case, the maximum corresponds to the threshold frequency, while in the 3D case, this maximum is shifted to lower transition energies. The magnetic field gives rise to a Landau quantization of the spectra, which reduces to a series of sharp lines in the two dimensional case.
We study the dynamics of the charged and neutral excitons in a modulation-doped GaAs quantum well by time-resolved photoluminescence under a resonant excitation. The radiative lifetime of the charged exciton is found to be surprisingly short, 60 ps. This time is temperature independent between 2 and 10 K, and increases by a factor of 2 at 6 T. We discuss our findings in view of present theories of exciton radiative decay. [S0163-1829(98)03143-9].
An optical method is suggested to determine the concentration of two-dimensional electrons in modulation-doped quantum wells at low and moderate electron densities between 10^{9} and 2x10^{11} cm^{-2}. The method is based on an analysis of magneto-reflectivity spectra of charged excitons (trions). The circular polarization degree and the oscillator strength of the charged excitons contain information about the density and spin polarization of two-dimensional electron gas. The method is applied to CdTe/(Cd,Mg)Te and ZnSe/Zn,Mg)(S,Se) heterostructures.
The magnetoluminescence spectra of symmetric quantum wells containing an electron gas show an abrupt changeover from Landau-level behavior (i.e., linear shift of energy with magnetic field) to quadratic (excitonlike) behavior as the field is increased. This so-called "Mott transition" occurs when the electron filling factor v(e) is 2, i.e., when the lowest Landau level is just filled. We show that the changeover is a natural consequence of the hidden symmetry that has been shown to hold in two-dimensional systems at high fields. This symmetry is broken when the integer parts of v(e)/2 and V-h//2 differ (v(h), the hole filling factor, is very small in these experiments), This symmetry breaking can also account for the new emission bands that are observed in such spectra when v(e) becomes larger than 2, and these bands can be described, at least qualitatively, in the framework of the magnetoexciton theory. These bands include the red-shifted magnetoplasmon and shake-up satellites and the blue-shifted cyclotron satellites. We also discuss the possible existence of a new type of trion (chargcd exciton), associated with the electron n(e) = 1 Landau level, and conclude that these trions should be observable.
The positively and negatively charged excitons,X+andX−, respectively, are identified by their magnetic circular dichroism in the absorption spectra of modulation-doped CdTe/Cd0.69Mg0.23Zn0.08Te multiple quantum wells at small carrier densities (≈1010cm−2). In these quantum wells with a width of 8 nm the binding energies of the second electron of theX−exciton and of the second hole of theX+exciton are very similar, 2.9 meV and 2.6 meV, respectively. At larger hole densities a transition to the conducting state is observed. In a sample with intermediate hole density (low 1011cm−2) the insulating phase is restored by application of a magnetic field.
Optical and magneto-optical properties are studied for II-VI semiconductor multiple quantum wells (MQWs) doped with donors in the barriers to give electron concentrations of 2 1010 to 6 1011 cm-2 in the well layers. Following on from the recent identification of negatively charged excitons X- (two electrons bound to one hole) in CdTe/Cd1-xZnxTe MQWs, this paper presents more specifically the circular polarisation of the luminescence associated with X- and with the normal exciton X (one electron and one hole) in this type of structure. Very similar magneto-optical properties are observed for modulation doped Zn0.9Cd0.1Se/ZnSe MQWs, and X- is identified in these wells with a binding energy as large as 7 meV for the second electron at 50Å, well-width.
We report on magneto-optical experiments on n-modulation doped, diluted magnetic semiconductor (DMS) quantum wells (QW's). A realignment of electronic spins induced by exchange interaction with magnetic ions is clearly observed. Sets of “regular free-particle like” transitions have been identified. The appearance of the subsequent satellite emission lines and the striking behaviour of the ground state emission are speculatively assigned to many body effects and/or to field induced localisation in a quantum Hall system with clearly resolved spin states.
Magnetic semiconductors offer a unique possibility for strongly tuning the intrinsic alloy disorder potential with applied magnetic field. We report the direct observation of a series of steplike reductions in the magnetic alloy disorder potential in single ZnSe/Zn(Cd, Mn)Se quantum wells between 0 and 60 T. This disorder, measured through the linewidth of low-temperature photoluminescence spectra, drops abruptly at ~19, 36, and 53 T, in concert with observed magnetization steps. Conventional models of alloy disorder (developed for nonmagnetic semiconductors) reproduce the general shape of the data, but markedly underestimate the size of the linewidth reduction.
The oscillator strength of negatively charged excitons (trions) in ZnSe/(Zn,Mg)(S,Se) quantum-well structures with n-type modulation doping is studied by means of reflectivity as a function of electron concentration, temperature, and external magnetic fields. The trion oscillator strength is found to increase linearly with increasing electron concentration up to 6×1010cm-2. The trion nonradiative damping shows no dependence on the electron concentration or external magnetic field. An optical method, based on the analysis of the polarization of the trion line, is proposed to investigate two-dimensional electron gases of low density from 109 up to 1011cm-2.
The study of exciton and trion excitations in CdTe-based modulation-doped quantum well (QW) structures was presented. The investigations were based on studying the photoluminescence excitation (PLE) and reflectivity spectra of the doped QWs under the applied magnetic fields. The study revealed that the resonant lines corresponding to optical transitions, for both excitons and trions, were accompanied by the excitation of additional electrons from the below to the above states of the Fermi level.
We study quenching of neutral excitonic optical transitions in GaAs quantum wells with increasing excess electron density. This occurs abruptly at ∼1010 cm-2 with the emergence of the negatively charged exciton at lower transition energy. With further increasing density X- evolves smoothly into the Fermi-edge singularity. Polarized magneto-optical spectra confirm our assignment.
We report the observation of the positively charged exciton and of the triplet state of the negatively charged exciton in modulation doped GaAs quantum wells. Applying a gate voltage at high magnetic fields we find that the photoluminescence line of the two-dimensional electron gas smoothly transforms into a negatively charged exciton and not into a neutral exciton. The Zeeman splitting of this line exhibits an abrupt change at the metal-insulator transition.
We report on a spectroscopic study of the lowest-energy electron-hole transitions of the two-dimensional electron gas (2DEG), with a density varied by photoexcitation in GaAs/Al0.1Ga0.9As quantum wells and under a perpendicularly applied magnetic field B. The transition into the phase consisting of a charged exciton singlet (X-s) ground state and neutral exciton (X) excited state occurs at a filling factor nu=1. The relative intensities of the X-s and X transitions measured by photoluminescence excitation at T=2 K, as a function of nu
We consider the ground and excited states of D- centers, i.e., neutral donors D0 trapping an extra electron, in the spin-singlet and spin-triplet states in GaAs/Ga1-xAlxAs quantum wells (QW’s) in quantizing magnetic fields B>6 T. Taking into account the effects of band nonparabolicity and magnetopolaron corrections, we derive the energies of the dipole-allowed transitions and their line strengths. Very good agreement (e.g., within 1–3 cm-1 below the region of the resonant magnetopolaron splittings) with the experimental data of Huant et al. for the singlet transitions is found.
The negatively charged exciton X- is identified by its circular polarization properties in 1.7 K magentoabsorption spectra of CdTe/Cd1-xZnxTe multiple quantum wells modulation doped with electron concentrations Ns~=2×1010 to 1.5×1011 cm-2. The binding energy of the second electron of X- is 0.20 3D Rydbergs at 100 Å well width. The species X- and the neutral exciton X exist in zero field for low Ns. At Ns=1.45×1011 cm-2 a Fermi edge singularity is seen at B=0 but X- appears with field, at filling factor nu=2, while X appears at nu=1.
We report on optical measurements of a two-dimensional electron gas near the metal-insulator transition. We observe the appearance of excitons and negatively charged excitons, X-, at the onset of the transition. The fact that these excitons appear at a relatively large average electron density shows that transition is induced by localization of single electrons in the electrostatic potential fluctuations of the remote ionized donors.
Acta Physica Polonica A 94
- T Wojtowicz
- M Kutrowski
- G Karchewski
- J Kossut