We collect and review works which treat two-dimensional electron gases (2DEGs) in quantum wells (QWs, mostly GaAs/ GaAlAs heterostructures) in the presence of quantizing magnetic fields as open systems in contact with outside reservoirs. If a reservoir is sufficiently large, it pins the Fermi level to a certain energy. As a result, in a varying external magnetic field, the thermodynamic equilibrium will force oscillations of the electron density in and out of the QW. This leads to a number of physical phenomena in magneto-transport, interband and intraband magneto-optics, magnetization, magneto-plasma dispersion, etc. In particular, as first proposed by Baraff and Tsui, the density oscillations in and out of QW lead to plateaus in the integer quantum Hall effect (IQHE) at values observed in experiments. The gathered evidence, especially from magneto-optical investigations, allows us to conclude that, indeed, in most GaAs/GaAlAs hetrostructures one deals with open systems in which the electron density in Qws oscillates as the magnetic field varies. Relation of the density oscillations to other factors, such as electron localization, and their combined influence on the quantum transport in 2DEGs, is discussed. In particular, a validity of the classical formula for the Hall resistivity rxy.B/Nec is considered. It is concluded that the density oscillations are not sufficient to be regarded as the only source of plateaus in IQHE, although such claims have been sometimes made in the past and present. Still, our general conclusion is that the reservoir approach should be included in various descriptions of 2DEGs in the presence of a magnetic field. An attempt has been made to quote all the relevant literature on the subject.

The Quantum Hall Effect (QHE) and Shubnikov-de Haas effect are investigated experimentally using n type modulation-doped GaAs/GaAlAs quantum wells (QWs) additionally doped in the well with beryllium acceptor atoms. It is presently shown that the localized magneto-acceptor (MA) states which possess discrete energies above the corresponding Landau levels (LLs) lead to two observable effects in magneto-transport: magnetic thaw-down and magnetic boil-off of 2D electrons. Both effects are related to the fact that electrons occupying the localized MA states cannot conduct. Thus in the thaw-down effect the electrons fall down from the MA states to the free Landau states. This leads to a shift of the Hall plateau towards higher magnetic fields as a consequence of an increase of the 2D electron density NS. In the boil-off effect the electrons are pushed from the free Landau states to the empty MA states under high enough Hall electric field. This process has an avalanche character leading to a dramatic increase of magneto-resistance, consequence of a decrease of NS.

The quantum Hall effect (QHE) and the Shubnikov-de Haas effect in the QHE regime are investigated experimentally using modulation doped n-type GaAs/GaAlAs quantum wells additionally doped in the well with beryllium. It is known that acceptor states introduced by Be atoms have a localized character in the conduction band due to a combined effect of the well and a magnetic field parallel to the growth direction and that they possess discrete energies above the corresponding conduction Landau levels. It is presently shown that the localized magnetoacceptor (MA) states lead to two observable effects in magnetotransport in the ultraquantum limit: magnetic thaw down and magnetic boil-off of two-dimensional (2D) electrons. Both effects are related to the fact that electrons occupying localized MA states cannot conduct. Thus in the thaw down effect the electrons fall down from the MA states to the free Landau states, which leads to a shift of the Hall plateau toward higher magnetic fields as a consequence of an increase of the 2D electron density Ns. In the boil-off effect the electrons are pushed from the free Landau states to the MA states which leads to a dramatic increase of resistance, as a consequence of the decrease of Ns. Differences between the above effects and those induced by magnetodonors in 2D systems are emphasized. We analyze the magnetic boil-off effect theoretically assuming that it is caused by the quantum Hall electric field present in our experiments. It is demonstrated that a sufficiently strong electric field in the crossed-field configuration can indeed populate localized MA states above the Landau levels.

We performed a local spectroscopy of the Landau levels density of states using gated mesoscopic Hall bars placed at very low temperature in the integer quantum Hall regime. The transverse and longitudinal conductances were measured while scanning both the two-dimensional electron density and the applied magnetic field. We observe a succession of sharp peaks due to backscattering across the samples caused by tunneling effects. Using temperature as a parameter in the range of 0.1-1 K, we characterize those tunnel processes: a resonant double-barrier tunneling and a single-barrier tunneling which corresponds to the variable range hopping regime. We show that for vanishing temperature and noninteger filling factor nu the conductance sigma(T=0, nu) does not vanish unlike the case of wide samples: instead, it converges to a limit function sigma(S)(nu) that is a noisy image of the Landau levels density of states.

We have investigated experimentally and theoretically the effect of repulsive and attractive ionized impurities on the resistivity components (ρxx and ρxy) in the quantum Hall effect regime. GaAs/GaAlAs asymmetric modulation-doped quantum wells with additional delta doping (by Si donor atoms or Be acceptor atoms) in the GaAs channel or at the AlGaAs/GaAs interface has been grown using molecular beam epitaxy technique. Magnetotransport experiments, performed on samples doped with Si-attractive atoms, showed a plateau width increasing toward lower magnetic field at even filling factor. However, when samples were delta doped with Be repulsive atoms, the increase was observed in the opposite side. Part of the results was explained using a model based on the fifth Klauder’s approximations where we demonstrate that the asymmetrical increase of the Hall plateaus with even filling factor (Landau gaps) is related to the asymmetry induced in the density of states by the additional impurities: the resulting disorder short range potential broadens and shifts the Landau levels but also creates impurity bands on the lower energy side of the Landau levels in the case of donors and on the upper energy side of the Landau levels in the case of acceptors. We notice that this asymmetrical behavior was not experimentally observed for odd filling factor plateaus (exchange gaps). We have also experimentally underscored the screening effect by free two-dimensional electrons of this disorder short range potential. Moreover, for delta-doped Be samples, the whole ν=1 Hall plateau was shifted toward higher magnetic field with respect to the classical Hall effect. This shift, observed for all samples, cannot be explained by the asymmetry of the density of states but rather by a magnetic delocalization of electrons from the upper energy impurity band associated with the last Landau level (n=0) into the free n=0 Landau states when this impurity band overtakes the Fermi level at the end of the ν=2 plateau. This magnetic delocalization effect is the opposite effect of the magnetic freeze out. © 2009 The American Physical Society

Nonlinear dependence of the magnetophotoluminescence (MPL) energies in modulation-doped asymmetric GaAs/Ga0.67Al0.33As 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.

We calculate the density of states of a two-dimensional electron gas located at the interface of a strongly disordered GaAlAs/GaAs heterojunction. The disorder potential is created by two delta doped layers. The first layer includes the parent donors which provides the well with electrons and creates a smooth disorder potential. The second layer is doped with either acceptor or donor impurities, and is located inside the well, thus creating a strongly disordered potential. We calculate the density of states in the presence of a magnetic field of arbitrary strength by taking into account all perturbative terms in the fifth Klauder's approximation. We find an anharmonic spectrum, strongly asymmetric, for the Landau level density of states. At low field, the attractive potential creates the well-known band tails or impurity bands. At higher field, we show that impurity bands are also created by repulsive potentials. We discuss the consequences of the anharmonicity and asymmetry on physical properties in the quantum Hall effect regime.