Nonlinear dependence of the magnetophotoluminescence energies of asymmetric GaAs/Ga 0.67 Al 0.33 As quantum wells on an external magnetic field W. Zawadzki Institute of Physics, Polish Academy of Sciences, 02668 Warsaw, Poland S. Bonifacie, S. Juillaguet, C. Chaubet, and A. Raymond Groupe d’Etude des Semiconducteurs, UMR CNRS 5650, Université Montpellier II, 34095 Montpellier cedex, France Y. M. Meziani RIEC, Ultra-broadband Signal Processing, Tohoku University, 2-1-1 Katahira, Aoba-Ku, 980-8577 Sendai, Japan M. Kubisa and K. Ryczko Institute of Physics, Wroclaw University of Technology, 50-370 Wroclaw, Poland Received 15 November 2006; revised manuscript received 4 April 2007; published 15 June 2007 Nonlinear dependence of the magnetophotoluminescence MPL energies in modulation-doped asymmetric GaAs/Ga 0.67 Al 0.33 As quantum wells of different widths are investigated experimentally and theoretically as functions of an external magnetic field. The investigated structures have only one electric subband populated with electrons. Contrary to the theoretical descriptions existing in the literature and based on the oscillations of screening, the observed maxima of MPL energies do not occur at integer filling factors and do not change into minima for higher well widths. We interpret our observations assuming that the oscillations of MPL energies are due to an oscillatory electron transfer between a GaAs well and a reservoir outside the well. We obtain a very good description of the experimental data concerning both the maxima positions and the oscillation amplitudes for different well widths and electron densities. Our interpretation is corroborated by the quantum Hall data obtained on the same samples. DOI: 10.1103/PhysRevB.75.245319 PACS numbers: 73.21.Fg, 78.67.De, 71.70.Ch I. INTRODUCTION From the early days of optical experiments with semicon- ductor heterostructures, it was observed that the energies of interband magnetophotoluminescent MPL transitions ex- hibit striking nonlinear behavior as functions of an external magnetic field. 1 Such nonlinearities are characteristic of two- dimensional 2D systems and are not seen on bulk materi- als. Since the first observations, the nonlinear behavior be- came the subject of numerous experimental and theoretical investigations, persisting until today. The investigated systems can be divided into two catego- ries. The first consists of structures in which, for reasons of material composition, electron density, or the shape of the quantum well QW, more than one conduction subband is populated with electrons. 2–9 The nonlinear MPL energies ob- served on such structures were consistently explained by an electron transfer between the subbands in question. As an external magnetic field is increased, the oscillating Landau density of states at the Fermi energy is shifted which may cause the electron transfer between electric subbands. Since higher subbands have a larger spatial extension than lower subbands, the electron transfer changes the charge distribu- tion in the well. This process affects the corresponding elec- tric potential the band bending and, in turn, the subband energies. Thus, the whole system “breathes” periodically as the field is swept, which is reflected in the MPL energies. The situation is different if one deals with a system in which only one subband is occupied. An important example of such a situation is a rather narrow and not strongly doped GaAs/Ga 0.67 Al 0.33 As quantum well. In this case one cannot explain the nonlinearities by the above mechanism. Two the- oretical calculations for this situation were proposed and both reached similar conclusions. 10,11 As the consecutive Landau levels LL cross the Fermi energy in an increasing magnetic field, the oscillatory density of states gives rise to oscillations of screening. These oscillations result in the os- cillations of the gap renormalization which is repeated by the interband energies. For symmetric QWs, the MPL energies should show positive spikes at even filling factors. Tsuchiya et al. 12 extended this work to asymmetric QWs. Such wells allow one to separate in the real space electrons and holes which influences the screening of photogenerated holes by the 2D gas. The calculation predicted that, for a 10 nm wide QW, when the electrons and holes are spatially not well sepa- rated, one should observe positive spikes in the interband energies. On the other hand, for a 30 nm wide QW, in which electrons and holes are much better separated, the screening effects for holes are much smaller. As a result, the theory predicted for this situation negative spikes of interband en- ergies at even filling factors. For the intermediate width of d = 20 nm the theory predicted almost no spikes. In a more recent work, Asano and Ando 13,14 investigated theoretically MPL energies in both symmetric and asymmet- ric QWs using a numerical diagonalization method. The re- sults were obtained in the form of numerous  functions which had to be phenomenologically broadened in order to represent MPL peaks. In Refs. 13 and 14, the authors could not confirm the phase reversal of peaks as a function of the well width predicted in Ref. 12. It should be noted that in the theoretical work based on the oscillations of screening 10,11 the comparison of the theory PHYSICAL REVIEW B 75, 245319 2007 1098-0121/2007/7524/2453197 ©2007 The American Physical Society 245319-1