We have used Optically Detected Resonance (ODR) spectroscopy to probe the electronic properties of undoped and barrier-doped GaAs/Al 0.3 Ga 0.7 As multiple-quantum-well (MQW) samples with well widths between 12.5 and 20 nm in magnetic fields up to 15 T at low temperatures. The simultaneous observation of electron and hole CR along with several internal transitions of neutral excitons (IETs) verifies the symmetry-related energy differences of the internal transitions to differences between electron and hole CR. The observed degeneracy of the 1s 3 2p + IET from the two radiative magneto-excitons is due to the very small electron g-factor. ODR measurements on 20 nm wide MQWs (not-intentionally-and barrier-doped) exhibit transitions of the negatively charged excitonic complex.
Internal spin-singlet and spin-triplet transitions of charged excitons X − in magnetic fields in quantum wells have been studied experimentally and theoretically. The allowed X − transitions are photoionizing and exhibit a characteristic double-peak structure, which reflects the rich structure of the magnetoexciton continua in higher Landau levels (LL's). We discuss a novel exact selection rule, a hidden manifestation of translational invariance, that governs transitions of charged mobile complexes in a magnetic field. 73.20.Dx, 71.70.Di, 76.40.+b, 78.90.+t Recently there has been considerable interest in charged excitonic complexes, X − and X + , commonly referred to as trions. The X − complex, which can be observed in photoluminescence-and reflectance spectra of low-density, quasi-2D electron gases (2DEGs), has been the subject of extensive experimental and theoretical work since its observation in 1993 [1]. The bulk of this work to date has been concerned with inter-band transitions only. Intraband, or internal, transitions of X − , which lie in the far-infrared (FIR), can provide additional important insight into the properties of the ground and excited states of this complex.The X − -complex, consisting of an exciton binding an additional electron, is superficially similar to its close relative, the negatively charged donor ion,. Both complexes are often considered to be the semiconductor analogs of the hydrogen ion, H − . When the H − ion is treated in the infinite proton mass approximation, such analogy is exact for the D − complex -a localized positive charge binding two electrons. This analogy fails, however, in certain very important aspects for the mobile X − complex. In particular, we show here that the magnetic translations for the X − imply the existence of an exact selection rule that prohibits certain bound-tobound internal X − transitions, the analogs of which are very strong for the D − . In an arbitrary uniform B this selection rule is applicable to charged electron-hole, as well as to one-component electron systems. In the latter case Kohn's theorem [3] based on translational invariance also works. Due to the center-of-mass separation for electron systems in B, both theorems -though based on different operator algebras -give in this case equivalent predictions. To understand the main qualitative features, we first consider the strictly-2D electron-hole (e-h) system in high magnetic fields. In this limit, hω ce ,hω ch ≫ E 0 = π/2 e 2 /ǫl B , where E 0 is the binding energy of the 2D magnetoexciton (MX) in zero LL's [4] and l B = (hc/eB) 1/2 . The mixing between different LL's can then be neglected, and the X − states can be classified by total electron and hole LL numbers, (N e N h ). The corresponding basis for(r h ), and includes different three-particle 2e-h states such that the total angular momentum projection M z = N e − N h − m 1 − m 2 + M h (and N e = n 1 + n 2 , N h ) are fixed. Here φ (e,h) nm are the e-and h-single-particle factored wave functions in B; n is the LL quantum num...
Internal transitions of quasi-two-dimensional, negatively charged magnetoexcitons ( X-) and their evolution with excess electron density have been studied in GaAs/AlGaAs quantum wells. In the dilute electron limit, due to magnetic translational invariance, the optically detected resonance spectra are dominated by bound-to-continuum bands in contrast to the negatively charged donor system D-, which exhibits strictly bound-to-bound transitions. With increasing excess electron density Landau-level filling factors nu<2 the X--like transitions are blueshifted; they are absent for nu>2. The blueshifted transitions are explained in terms of a new type of collective excitation---magnetoplasmons bound to a mobile valence band hole.
Optically detected resonance spectroscopy has been used to study resonant absorption of electrons, holes, and their complexes in GaAs/Al x Ga 1Ϫx As quantum wells ͑QW's͒ in magnetic fields up to 15 T. In undoped multiple-QW samples with well widths of 12.5, 15, and 20 nm, in addition to an electron and two hole cyclotron resonances, 1s→np ϩ,Ϫ ͑in the hydrogenic notation͒ internal exciton transitions ͑IET's͒ arising from two distinct neutral heavy-hole magneto-excitons were observed. The unique capability of observing electron and hole cyclotron resonance as well as several IET's in a single sample permitted verification of a predicted relationship resulting from the symmetry of the magnetoexciton Hamiltonian, namely, ប( e Ϫ h )ϭE 1s-np ϩ ϪE 1s-np Ϫ , where e ( h ) is the electron ͑hole͒ cyclotron frequency, and E 1s-np ϩ (E 1s-np Ϫ ) is the energy of the 1s→np ϩ (1s→np Ϫ ) transition.
The Shubnikov–de Haas (S–dH) measurements at 1.5 K clearly demonstrated the existence of a two-dimensional electron gas (2DEG) in the modulation-doped Al0.25Ga0.75As/InyGa1−yAs/GaAs single and step quantum wells, and the fast Fourier transformation results for the S–dH data clearly indicated the electron occupation of one subband in the asymmetric single and step quantum wells. While the electron carrier density of the 2DEG in the step quantum well was larger than that in the single quantum well due to the larger conduction-band discontinuities, the mobility of the 2DEG in the step quantum well was smaller than that in the single quantum well because of the interface scattering resulting from the embedded step well. The electron effective mass in the step quantum well was smaller than that in the single quantum well, which was consistent with a smaller mass of the embedded deep step layer. The electronic subband energy, the energy wave function, and the Fermi energy in the InyGa1−yAs step quantum wells were calculated by using a self-consistent method taking into account exchange-correlation effects together with strain and nonparabolicity effects.
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