Magnetic field-induced quantum phase transitions in a quasi-two-dimensional electron system in GaAs quantum wells of different widths

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Using the original magnetocapacitance technique based on simultaneous measurements of magnetocapacitances between a quasi-two-dimensional electron system in a single GaAs quantum well and two gates placed on its opposite sides we have studied magnetic field induced quantum phase transitions between double-layer and single-layer-like states of the system. The measurements have been performed with samples of quantum well width 50 and 60 nm. The double-layer state was composed of layers of two-dimensional electrons confined near the opposite walls of the quantum well. It is characterized by the quantum magneto-oscillations of the compressibility of each of the layers with a frequency determined by the density of electrons in the corresponding layer. In a single-layer-like state, the compressibility minima have been observed only when all electrons occupied one or two spin sublevels of the lowest Landau level (when the total filling factor νtot = 1 and 2), and the ratio of the measured capacitances in this state was characteristic of the case when only one electronic layer existed between the gates. It has been found that the first transition from a double-layer to a single-layer-like state took place when the quantum limit was reached, i.e. when νtot ≈ 2, independent of either the density of electrons in the system or the quantum well width. A different behavior of electronic systems has been found in wells of different widths in the region 1 < νtot < 2. In a 50 nm well, the single-layer-like state existed in the whole studied region of filling factors νtot ≤ 2. In a 60 nm well, a double-layer region has been observed within 1 < νtot < 2 accompanied by an incompressible state of electrons in the layer with the largest density at filling factor unity in this layer. As a result, three magnetic-filed-induced quantum phase transitions have been observed in samples with 60 nm quantum well width, whereas only one quantum phase transition has been observed in a sample with 50 nm quantum well width. Such a dependence of the character of the quantum phase transition on the quantum well width is supposedly caused by the different tunneling strength between the layers. The formation of magnetic-field-induced compressible single-layer-like state in a nominally double-layer electronic system has been discovered.

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А. Kapustin

Osipyan Institute of Solid State Physics, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: kapustin@issp.ac.ru
俄罗斯联邦, Chernogolovka

S. Dorozhkin

Osipyan Institute of Solid State Physics, Russian Academy of Sciences

Email: kapustin@issp.ac.ru
俄罗斯联邦, Chernogolovka

I. Fedorov

Osipyan Institute of Solid State Physics, Russian Academy of Sciences

Email: kapustin@issp.ac.ru
俄罗斯联邦, Chernogolovka

参考

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2. Fig. 1. Dependences of the magnetocapacitance, normalized to the value at νtot = 3⁄2 (marked with a vertical dash), measured in a QW of width w = 50 nm between the electron system and the front (Cn,FG, dark lines) and back (Cn,BG, light lines) gates, on the inverse fill factor , which is proportional to the magnetic field B and corresponds to the total electron concentration. All curves were obtained for the voltage at the front gate VFG = 0, temperature T = 3 (solid curves) and 0.5 K (dashed curves), voltage at the back gate VBG and the corresponding electron concentration in the nearest layer nBL: VBG = 0.2 V, nBL = 0 (1); VBG = 1.2 V, nBL = 0.22×1011 cm–2 (2); VBG = 1.8 V, nBL = 0.74×1011 cm–2 (3); VBG = 2.4 V, nBL = 0.90×1011 cm–2 (4). The regions in which the electron system is in the two-layer (2L) and “single-layer” (1L) states are marked; the vertical dashed line marks the boundary of these regions near νtot ≈ 2. The arrows mark the most pronounced features of the normalized magnetocapacitances in the two-layer state (minima Cn,FG and the corresponding maxima Cn,BG).

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3. Fig. 2. Dependences of magnetocapacitance, normalized to the value at νtot = 3⁄2 (marked with a vertical dash), measured in a QW of width w = 60 nm between the electron system and the front (Cn,FG, dark lines) and back (Cn,BG, light lines) gates, on the inverse fill factor . All curves were obtained at a voltage on the front gate VFG = –0.2 V, temperature T = 1.5 K, voltage on the back gate VBG and the corresponding electron concentration in the nearest layer nBL: VBG = 0.8 V, nBL = 0.56×1011 cm–2 (1); VBG = 1 V, nBL = 0.69×1011 cm–2 (2). The regions in which the electron system is in the two-layer (2L) and “single-layer” (1L) states are marked; The vertical dashed line marks the boundary of these regions near νtot ≈ 2. The arrows mark the most pronounced features of the normalized magnetocapacitances in the two-layer state (minima Cn,FG and the corresponding maxima Cn,BG). The triangles highlight the minima corresponding to the incompressible state in the front electron layer with a filled Landau sublevel vFL = 1.

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4. Fig. 3. Dependence of magnetocapacitances between the electron system and the front (CFG, dark lines, left) and back (CBG, light lines, right) gates on the inverse filling factor in a quantum well of width w = 60 nm at T = 1.5 (solid curves) and 0.5 K (dashed curves). The curves were obtained at a voltage on the front gate VFG = –0.2 V, and a voltage on the back gate VBG = 0.8 V. The triangles mark the CFG minima corresponding to integer filling factors in the front electron layer vFL = 1; 2; 4 (on the graph, respectively).

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