Magnetic Field-Induced Quantum Phase Transitions in a Quasi-Two-Dimensional Electron System in GaAs Quantum Wells of Different Widths

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 ν_tot = 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 ν_tot ≈ 2, regardless of the electron density in the system and the quantum-well width. In the range of 1 < ν_tot < 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 ν_tot ≤ 2. In the 60-nm-wide well, for 1 < ν_tot < 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.