Using an original magnetocapacitance method, based on the simultaneous measurement of capacitances between a quasi-two-dimensional electron system in a single quantum well of GaAs and two gates located on opposite sides of it, we investigate the magnetic field-induced quantum phase transitions between the double-layer and single-layer-like states of the system. The measurements are performed for samples with quantum-well widths of 50 and 60 nm. The double-layer state is formed by layers of two-dimensional electrons located near opposite walls of the quantum well. It is characterized by quantum magnetic oscillations of the compressibility of each layer, with the oscillation frequency determined by the electron density in the corresponding layer. In the single-layer-like state, compressibility minima are observed only when all electrons fill one or two spin sublevels of the lowest Landau level (i.e., when the total filling factor νtot = 1 or 2). In this state, a relationship between the measured capacitances is observed, which is characteristic of the presence of only a single electron layer between the gates. One transition from the double-layer- to the single-layer-like state occurs upon reaching the quantum limit, i.e., when νtot ≈ 2, regardless of the electron density in the system and the quantum-well width. In the range of 1 < νtot < 2, different behaviors of the electron systems in wells of different widths are observed. In the 50-nm-wide well, the single-layer-like state exists for all investigated values of the filling factor νtot ≤ 2. In the 60-nm-wide well, for 1 < νtot < 2, a double-layer state is observed with an incompressible state of electrons in the layer with higher density at a filling factor of one in that layer. As a result, three magnetic-field-induced quantum phase transitions are observed for samples with a quantum-well width of 60 nm, while for the sample with a 50-nm-wide quantum well, only one transition is observed. This dependence of the patterns of quantum phase transition on the quantum-well width is presumably due to the different tunnel coupling between the layers. For the first time, the existence of a magnetic-field-induced compressible single-layer-like state in a nominally double-layer electron system is established.

In samples of field-effect transistors based on GaAs/AlGaAs heterostructures with an electron system in a single 50-nm-wide GaAs quantum well, a transition stimulated by a quantizing magnetic field has been detected from a bilayer state of the system in zero magnetic field to a single-layer state when only the lowest Landau level is filled. In contrast to the results for the 60-nm-wide quantum well obtained in [S. I. Dorozhkin, A. A. Kapustin, I. V. Fedorov, V. Umansky, and J. H. Smet, Phys. Rev. V 102, 235307 (2020)], the single-layer state is observed not only in incompressible quantum Hall effect states of the electron system at filling factors of 1 and 2, but also in compressible states between these filling factors. The spatial location of the single-layer system in the quantum well has been established; it appears to be independent of the electron distribution over the layers in a low magnetic field. A possible qualitative explanation for this observation has been proposed. The detected transition is supposedly due to the negative compressibility of two-dimensional electron systems caused by exchange-correlation contributions to the electron−electron interaction.

A bilayer electron system that is formed in a 60-nm-wide GaAs quantum well and has a large difference of the electron densities in the layers has been studied. It has been found that, when a magnetic field is tilted from the normal to the plane of the system, integer quantum Hall effect states at the filling factors of Landau levels of 1 and 2 disappear; instead, fractional quantum Hall effect states in the interval between these filling factors appear at the filling factors νF = 4/3, 10/7, and 6/5 with odd denominators and at the filling factor νF = 5/4. Several different states can be observed under the variation of the magnetic field. The detected fractional quantum Hall effect states are interpreted as combined states with the same filling factor 1 in the layer with the higher density and with the filling factors νF – 1 in the layer with the lower density. These states are formed because of the redistribution of electrons between the layers, which occurs under the variation of the magnetic field. The appearance of the state with the filling factor νF = 5/4 with the even denominator is presumably attributed to the dominance of the interlayer electron–electron interaction over the intralayer one for electrons in the layer with the lower density.

A bilayer electron system that is formed in a 60-nm-wide GaAs quantum well and has a large difference of the electron densities in the layers has been studied. It has been found that, when a magnetic field is tilted from the normal to the plane of the system, integer quantum Hall effect states at the filling factors of Landau levels of 1 and 2 disappear; instead, fractional quantum Hall effect states in the interval between these filling factors appear at the filling factors νF = 4/3, 10/7, and 6/5 with odd denominators and at the filling factor νF = 5/4. Several different states can be observed under the variation of the magnetic field. The detected fractional quantum Hall effect states are interpreted as combined states with the same filling factor 1 in the layer with the higher density and with the filling factors νF – 1 in the layer with the lower density. These states are formed because of the redistribution of electrons between the layers, which occurs under the variation of the magnetic field. The appearance of the state with the filling factor νF = 5/4 with the even denominator is presumably attributed to the dominance of the interlayer electron–electron interaction over the intralayer one for electrons in the layer with the lower density.

In samples of field-effect transistors based on GaAs/AlGaAs heterostructures with an electron system in a single 50-nm-wide GaAs quantum well, a transition stimulated by a quantizing magnetic field has been detected from a bilayer state of the system in zero magnetic field to a single-layer state when only the lowest Landau level is filled. In contrast to the results for the 60-nm-wide quantum well obtained in [S. I. Dorozhkin, A. A. Kapustin, I. V. Fedorov, V. Umansky, and J. H. Smet, Phys. Rev. V 102, 235307 (2020)], the single-layer state is observed not only in incompressible quantum Hall effect states of the electron system at filling factors of 1 and 2, but also in compressible states between these filling factors. The spatial location of the single-layer system in the quantum well has been established; it appears to be independent of the electron distribution over the layers in a low magnetic field. A possible qualitative explanation for this observation has been proposed. The detected transition is supposedly due to the negative compressibility of two-dimensional electron systems caused by exchange-correlation contributions to the electron−electron interaction.

A study is performed of microwave absorption in inhomogeneous two-dimensional electron systems characterized by a finite size or by a modulation of parameters. Experiments and calculations are compared to show that resonance maxima in absorption are observed at the frequencies of Bernstein modes corresponding to the characteristic wave vector of inhomogeneity k. At low k, the absorption maxima at the second harmonic of the cyclotron resonance are observed in addition to the main resonance at the frequency of cyclotron magnetoplasmon with wave vector k. At high k corresponding to condition $$k{{R}_{{\text{c}}}} > 1,$$ the position of the resonant absorption are parameterized in coordinates ( $$k{{R}_{{\text{c}}}},~\,\,{{{\omega }} \mathord{\left/ {\vphantom {{{\omega }} {{{{{\omega }}}_{{\text{c}}}}}}} \right. \kern-0em} {{{{{\omega }}}_{{\text{c}}}}}}$$ ), where $${{{{\omega }}}_{{\text{c}}}}$$ is the cyclotron frequency, $${{R}_{{\text{c}}}}$$ is the cyclotron radius of an electron, and ω is the circular frequency of radiation.

Equilibrium edge currents emerging due to the variation of occupation of individual Landau spin sublevels near the sample edge are calculated for 2D electron systems placed into a transverse quantizing magnetic field. The calculation is applicable directly to the model of edge strips of compressible and incompressible electron phases, which takes into account the self-consistent screening of the electric potential forming the sample boundary. In such a model, the currents under investigation are transferred by states at the Fermi level and flow in spatially separated strips of the compressible electron phase, in which the electric field is fully screened. The values of currents in each strip of the compressible phase are universal and are determined by the electron cyclotron frequency, the value of the g factor, the Landau level number, and the spin projection onto the magnetic field direction. It is shown that except for special cases, the edge current considered here produce the diamagnetic moment of the sample.

Methods used to process data for Shubnikov–de Haas oscillation beats in two-dimensional electron systems with lifted of spin degeneracy have been considered. A criterion for beat node development in systems with a nonlinear dependence of the Landau level energy on magnetic field has been suggested, and a formula for the position of nodes in two-dimensional electron systems with a Bychkov–Rashba spectrum has been derived on its basis. The formula has been used to treat early observations of beats in p-channel field-effect transistors. This formula has been found to adequately describe experimental data for electrons in InGaAs quantum wells, which indicates the dominance of spin splitting due to potential well asymmetry (Bychkov–Rashba mechanism). Evidence has been obtained that the absence of the center of inversion in the bulk material also contributes to the spin splitting in InAs quantum wells (Dresselhaus mechanism). It has been shown that the widely used Fourier-transform-based method for processing oscillation beat data fails in correctly determining the parameter of spin-orbit interaction in two-dimensional electron system with the Bychkov–Rashba spectrum.

The dispersion laws ω( k ) of Bernstein modes are calculated for ungated 2D electron systems, as well as those incorporated in the channel of a field-effect transistor. These modes represent the general type of magnetoplasma oscillations in such systems. The peculiarities of the dispersion laws are established, including their parametrization in ( kR c , ω/ω c ) coordinates and nonmonotonic dependence with universal positions of the minima, determined by the zeros of the Bessel functions and integers. Here, ω is the angular frequency of the mode, ω c is the electron cyclotron frequency, k is the magnetoplasmon wave vector, and R c is the electron cyclotron radius. The calculation results qualitatively agree with the presented experimental data on resonant microwave absorption induced in a 2D electron system of the GaAs/AlGaAs heterostructure by surface acoustic waves. The calculated dispersion laws are compared with the well-known magnetoplasmon spectrum and their partial coincidence is noted. It is shown that the absorption of electromagnetic waves with the wave vector k lying in the plane of the 2D system has maxima on the dispersion lines of Bernstein modes, and these maxima have the largest amplitudes in the regions of dispersion branches close to the magnetoplasmon spectrum.

The calculations and measurements of quantum corrections to the capacitances between the gates of a field-effect transistor and its channel located between these gates are performed. The cases when the channels are formed by one or two layers of two-dimensional electrons are studied. Qualitatively similar results are obtained for samples with a channel in wide and double quantum wells. Coincidence is established for the normalized values of the magnetocapacitances measured between different gates and the channel in the case when one electron layer in the channel is filled. Some specific features of the capacitance associated with the negative compressibility of electrons are revealed and explained in the case when two layers with different densities of electrons are filled.

The magnetic field dependence of the amplitudes of Shubnikov–de Haas oscillations in GaAs/AlGaAs heterostructure samples with a two-dimensional electron system irradiated by microwave radiation in the range of 130–170 GHz has been studied. Two features of the radiation-induced suppression of amplitudes of oscillations having a field-resonance character have been revealed. One of the resonances appears in a magnetic field corresponding to the second harmonic of the cyclotron resonance, whereas the dependence of the existence, position, and amplitude of the second resonance on the radiation frequency is more complex. The detected resonance absorption of radiation at the second harmonic is apparently responsible for an anomalous peak of the magnetoresistance recently observed near this harmonic. The detected resonances can be explained by the excitation of standing magnetoplasma waves in a confined sample with the same the wavenumber but corresponding to different regions of their dispersion relation: an almost dispersionless region of the Bernstein mode and a cyclotron magnetoplasma mode.

The observation of microwave-induced changes in the charge of a field effect transistor with a channel formed by a bilayer electron system has confirmed that microwave radiation induces a nonequilibrium electron energy distribution function, which generates magneto-oscillations of the resistance of two-dimensional electron systems. The observed periodicity and beating of magneto-oscillations of the charge have been explained by the redistribution of electrons between the layers, which occurs because of the corresponding nonequilibrium occupation of electronic states.

Ground states that appear in a quantizing magnetic field in an imbalanced bilayer electron system hosted by a dual-gated, wide GaAs quantum well are explored with a magnetocapacitance technique that enables detection of the compressibility of each layer separately, the characterization of the charge distribution, as well as the distinction of single- or double-layer-like behavior. Magnetic field induced reentrant quantum phase transitions are observed between a compressible double-layer ground state and a single-layer-like incompressible phase for both total fillings 1 and 2. The transitions are accompanied by a charge redistribution across the well. Our observations indicate for both incompressible states easy-plane pseudospin ferromagnetism as the origin.

We present an experimental study on microwave illuminated high mobility MgZnO/ZnO based two-dimensional electron systems with different electron densities and, hence, varying Coulomb interaction strength. The photoresponse of the low-temperature dc resistance in perpendicular magnetic field is examined in low and high density samples over a broad range of illumination frequencies. In low density samples a response due to cyclotron resonance (CR) absorption dominates, while high-density samples exhibit pronounced microwave-induced resistance oscillations (MIRO). Microwave transmission experiments serve as a complementary means of detecting the CR over the entire range of electron densities and as a reference for the band mass unrenormalized by interactions. Both CR and MIRO-associated features in the resistance permit extraction of the effective mass of electrons but yield two distinct values. The conventional cyclotron mass representing center-of-mass dynamics exhibits no change with density and coincides with the band electron mass of bulk ZnO, while MIRO mass reveals a systematic increase with lowering electron density consistent with renormalization expected in interacting Fermi liquids.

The compressibility of electrons in a bilayer electron system implemented in a GaAs double quantum well is investigated. Manifestations of the negative compressibility of a low-density two-dimensional electron system in zero and quantizing magnetic fields are observed. It is found that the magnetic field ranges where incompressible phases at the spin-resolved Landau level filling factors of 2 and 1 exist in the layer with the higher electron density are broadened considerably upon the filling of the other layer. The effect is explained by the stabilization of the quantum Hall effect states owing to the transfer of electrons from the layer with the lower density. The magnitude of jumps in the chemical potential for the corresponding quantum Hall effect states is estimated.

The temperature dependence of microwave absorption minima observed at cyclotron resonance harmonics in a two-dimensional electron system implemented in a GaAs/AlGaAs heterostructure has been studied. The coexistence of this effect with the temperature-dependent giant negative magnetoresistance has been revealed. A possible explanation of the results by the effect of electron-electron scattering on the non-Markovian electron kinetics has been discussed.