Bilayer Electron System Research Articles

Nonequilibrium phenomena in bilayer electron systems

In the present Letter, we have used magnetocapacitance and magnetoresistance measurements to investigate nonequilibrium phenomena in a bilayer electron system based on GaAs/AlGaAs heterostructures. The magnetic field ramping drives the bilayer electron system out of equilibrium, leading to magnetoresistance hysteresis and spikes. Unlike magnetoresistance, magnetocapacitance results intriguingly show hysteresis even when both layers are in the quantum Hall state. The hysteresis is accompanied by interlayer charge transfer, but the disequilibrium is not limited to interlayer imbalance. Results show that the edge-bulk imbalance can be the initial ground for the appearance of hysteresis. In addition, the nonequilibrium states are observed in which the total, rather than individual, layer densities determine the magnetic field and gate voltage dependencies.

The stability of the quantum Hall state at ν = 1 in bilayer electron systems

The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in double quantum dots has been plotted for the Landau level filling factor ν=1. It has been shown that the quantum Hall state can be stable for a zero tunnel splitting. The influence of the impurity potential on the stability condition for the quantum Hall state has been analyzed.

Unconventional Fractional Quantum Hall States in a Wide Quantum Well

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.

The Stability of the Quantum Hall State at Ν = 1 in Bilayer Electron Systems

The Stability of the Quantum Hall State at Ν = 1 in Bilayer Electron Systems

Viscous magnetotransport and Gurzhi effect in bilayer electron system

We observe a large negative magnetoresistance and a decrease of resistivity with increasing temperature, known as the Gurzhi effect, in a bilayer (BL) electron system formed by a wide GaAs quantum well. A hydrodynamic model for the single fluid transport parameters in narrow channels is employed and successfully describes our experimental findings. We find that the electron-electron scattering in the bilayer is more intensive in comparison with a single-band well (SW). The hydrodynamic assumption implies a strong dependence on boundary conditions, which can be characterized by slip length, describing the behavior of a liquid near the edge. Our results reveal that slip length in a BL is shorter than in a SW, and that the BL system goes deeper into the hydrodynamic regime. This is in agreement with the model proposed where the slip length is of the order of the electron-electron mean free path.

Capacitive detection of magnetic field induced quantum phase transitions in an imbalanced bilayer electron system

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.

Magneto-Oscillations of the Charge of a Field-Effect Transistor That Are due to a Microwave-Induced Nonequilibrium Electron Energy Distribution

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.

Antiparallel spin Hall current in a bilayer with skew scattering

The spin Hall effect due to skew scattering is studied by solving the Boltzmann equation in a bilayer electron system with attractive impurity potentials in one layer and repulsive ones in the other. In such an impurity configuration, directions of the spin Hall current in two decoupled layers are antiparallel. An analytical formula for the magnitude of the antiparallel spin Hall current is derived in the crossover from the decoupled bilayer to the strongly coupled one with no spin Hall current with increasing ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SAS}}$, the energy separation between the symmetric and antisymmetric states of the motion perpendicular to the layer. When the impurity potential is short ranged and ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SAS}}\ensuremath{\ll}{\ensuremath{\varepsilon}}_{\mathrm{F}}$, with ${\ensuremath{\varepsilon}}_{\mathrm{F}}$ being the Fermi energy, the normalized antiparallel spin Hall conductivity is found to be ${[1+{(\ensuremath{\omega}{\ensuremath{\tau}}_{p})}^{2}]}^{\ensuremath{-}1}$, with $\ensuremath{\omega}={\mathrm{\ensuremath{\Delta}}}_{\mathrm{SAS}}/\ensuremath{\hbar}$ and ${\ensuremath{\tau}}_{p}$ being the momentum relaxation time at ${\ensuremath{\varepsilon}}_{\mathrm{F}}$. This formula is explained by extending the dynamics for the Hanle effect, which was originally developed for spin, to the pseudospin (layer) degree of freedom. The present finding suggests that the Hanle effect will be useful in understanding the pseudospin dynamics as well as the spin dynamics.

Quantum Effects in the Capacitance of Field-Effect Transistors with a Double Quantum Well

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.

Fractional quantum Hall effects in In0.75Ga0.25As bilayer electron systems observed as \u201cFinger print\u201d

Observations of fractional quantum Hall (FQH) plateaus are reported in bilayer electron gas system in wide (>80 nm) In0.75Ga0.25As wells. Several q/p (p = 5, 3, and 2, q > 5) QH states are confirmed at high temperatures (~1.6 K) when the critical conditions including an electron density imbalance as well as a dynamical resistance behavior at the bilayer-monolayer transition are properly satisfied. The former leads to a quantum limit in either of the layers and the latter might bring a meta-stable nature into FQH phenomena. Such a behavior occurs as a probability process associating with impurities or defects in the wells, they inevitably reflect the local structural landscapes of each sample. This is verified by the new finding that the kinds of fractional plateaus (what set of fractional filling factors) appeared are different depending on the samples, that is, they are the “finger print” in each sample.

Characterization of individual layers in a bilayer electron system produced in a wide quantum well

Here, we report on a transparent method to characterize individual layers in a double-layer electron system, which forms in a wide quantum well, and to determine their electron densities. The technique relies on the simultaneous measurement of the capacitances between the electron system and gates located on either side of the well. Modifications to the electron wave function due to the population of the second subband and the appearance of an additional electron layer can be detected. The magnetic field dependence of these capacitances is dominated by quantum corrections caused by the occupation of Landau levels in the nearest electron layer. The technique should be equally applicable to other implementations of a double layer electron system.

Interaction-induced interlayer charge transfer in the extreme quantum limit

An interacting bilayer electron system provides an extended platform to study electron-electron interaction beyond single layers. We report here experiments demonstrating that the layer densities of an asymmetric bilayer electron system oscillate as a function of perpendicular magnetic field that quantizes the energy levels. At intermediate fields, this interlayer charge transfer can be well explained by the alignment of the Landau levels in the two layers. At the highest fields where both layers reach the extreme quantum limit, however, there is an anomalous, enhanced charge transfer to the majority layer. Surprisingly, when the minority layer becomes extremely dilute, this charge transfer slows down as the electrons in the minority layer condense into a Wigner crystal. Furthermore, by examining the quantum capacitance of the dilute layer at high fields, the screening induced by the composite fermions in an adjacent layer is unveiled. The results highlight the influence of strong interaction in interlayer charge transfer in the regime of very high fields and low Landau level filling factors.

Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal.

When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν≪1), its direct observation has been elusive. Here we present a new technique and experimental results directly probing the magnetic-field-induced WC. We measure the magnetoresistance of a bilayer electron system where one layer has a very low density and is in the WC regime (ν≪1), while the other ("probe") layer is near ν=1/2 and hosts a sea of composite fermions (CFs). The data exhibit commensurability oscillations in the magnetoresistance of the CF layer, induced by the periodic potential of WC electrons in the other layer, and provide a unique, direct glimpse at the symmetry of the WC, its lattice constant, and melting. They also demonstrate a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasiparticles of another many-body state.

Exciton Condensation in Bilayer Quantum Hall Systems

The condensation of excitons, bound electron-hole pairs in a solid, into a coherent collective electronic state was predicted more than 50 years ago. Perhaps surprisingly, the phenomenon was first observed in a system consisting of two closely spaced parallel two-dimensional electron gases in a semiconductor double quantum well. At an appropriate high magnetic field and low temperature, the bilayer electron system condenses into a state resembling a superconductor, only with the Cooper pairs replaced by excitons consisting of electrons in one layer bound to holes in the other. In spite of being charge neutral, the transport of excitons within the condensate gives rise to several spectacular electrical effects. This article describes these phenomena and examines how they inform our understanding of this unique phase of quantum electronic matter.

Coherence of two-dimensional electron-hole systems: Spontaneous breaking of continuous symmetries: A review

The spontaneous breaking of the continuous symmetries of a two-dimensional electron-hole system in a strong magnetic field perpendicular to the plane leads to the formation of new ground states and determines the energy spectrum of collective elementary excitations that appear above these new ground states. In this review, the main attention is paid to the electron-hole system formed from coplanar magnetoexcitons under conditions of Bose-Einstein condensation in the ground state with the wave vector k = 0 taking into account the influence of excited Landau levels, when exciton-type elementary excitations coexist with plasmon-type oscillations. At the same time, the properties of a two-component system consisting of a two-dimensional electron gas and a two-dimensional hole gas spatially separated in a double quantum well under conditions of the fractional quantum Hall effect are of great interest, because these properties can affect the quantum states of magnetic excitons that are formed when the distance between the layers tends to zero. Bilayer electron systems are also considered under conditions of the fractional quantum Hall effect with the one-half filling factor for each layer and the total filling factor equal to unity for both layers. The coherence between the electron states in the two layers is equivalent to the formation of excitons in a macroscopic coherent state. This makes it possible to compare the energy spectrum of collective elementary excitations of Bose-Einstein condensed excitons under conditions of the quantum Hall effect and coplanar magnetoexcitons. The breaking of the global gauge symmetry or of the continuous rotational symmetry leads to the formation of a gapless spectrum of the Nambu-Goldstone type, whereas the breaking of the local gauge symmetry is accompanied by the appearance of a gap in the energy spectrum (Higgs phenomenon). These phenomena are equivalent to the formation of massless and massive particles in the relativistic physics. The application of the Nielsen-Chadha theorem, which determines the number of Nambu-Goldstone modes as a function of the number of broken symmetry operators, is demonstrated using the example of Bose-Einstein condensation of spinor atomic gases in an optical trap. This example is presented for a better understanding of the results obtained in the case of a Bose-Einstein condensation of coplanar magnetoexcitons. The Higgs phenomenon leads to the formation of composite particles under conditions of the fractional quantum Hall effect. Their description is given in terms of the Ginzburg-Landau theory. The possibilities for the appearance of spontaneous coherence in a system of indirect excitons in structures with a double quantum well are analyzed. The experimental attempts to create these conditions, the main results obtained in this field, and the accumulated knowledge are reviewed. The basic properties of the energy spectrum of magnetoexciton polaritons in a microcavity are formulated. A hypothesis is put forward about the possibility of forming two-dimensional magnetoexcitons and two-dimensional magnetoexciton polaritons of high density with attached point quantum vortices, i.e., about the possibility of forming new composite particles.

Spontaneous Symmetry Breaking and Coherence in Two-Dimensional Electron–Hole and Exciton Systems

The spontaneous breaking of the continuous symmetries of the two-dimensional(2D) electron-hole systems in a strong perpendicular magnetic field leads to the formation of new ground states and determines the energy spectra of the collective elementary excitations appearing over these ground states. In this review the main attention is given to the electron-hole systems forming coplanar magnetoexcitons in the Bose-Einstein condensation(BEC) ground state with the wave vector k=0, taking into account the excited Landau levels, when the exciton-type elementary excitations coexist with the plasmon-type oscillations. At the same time properties of the two-dimensional electron gas(2DEG) spatially separated as in the case of double quantum wells(DQWs) from the 2D hole gas under conditions of the fractional quantum Hall effect(FQHE) are of great interest because they can influence the quantum states of the coplanar magnetoexcitons when the distance between the DQW layers diminishes. We also consider in this review the bilayer electron systems under conditions of the FQHE with the one half filling factor for each layer and with the total filling factor for two layers equal to unity because the coherence between the electron states in two layers is equivalent to the formation of the quantum Hall excitons(QHExs) in a coherent macroscopic state. The breaking of the global gauge symmetry as well as of the continuous rotational symmetries leads to the formation of the gapless Nambu-Goldstone(NG) modes while the breaking of the local gauge symmetry gives rise to the Higgs phenomenon characterized by the gapped branches of the energy spectrum. The conditions in which the spontaneous coherence could appear in a system of indirect excitons in a double quantum well structures are discussed. The experimental attempts to achieve these conditions, the main results and the accumulated knowledge are reviewed.

Nambu-Goldstone modes of the two-dimensional Bose-Einstein condensed magnetoexcitons

The collective elementary excitations of two-dimensional magnetoexcitons in a Bose-Einstein condensate (BEC) with wave vector k = 0 were investigated in the framework of the Bogoliubov theory of quasiaverages. The Hamiltonian of the electrons and holes lying in the lowest Landau levels (LLLs) contains supplementary interactions due to virtual quantum transitions of the particles to the excited Landau levels (ELLs) and back. As a result, the interaction between the magnetoexcitons with k = 0 does not vanish and their BEC becomes stable. The equations of motion for the exciton operators d(P) and d†(P) are interconnected with equations of motion for the density operators ρ(P) and D(P). Instead of a set of two equations of motion, as in the case of usual Bose gas, corresponding to normal and abnormal Green’s functions, we have a set of four equations of motion. This means we have to deal simultaneously with four branches of the energy spectrum, the two supplementary branches being the optical plasmon branch represented by the operator ρ(P) and the acoustical plasmon branch represented by the operator D(P). The perturbation theory on the small parameter v2(1 − v2), where v2 is the filling factor and (1 − v2) is the phase space filling factor was developed. The energy spectrum contains only one gapless, true Nambu-Goldstone (NG) mode of the second kind with dependence ω(k) ≈ k2 at small values k describing the optical-plasmon-type oscillations. There are two exciton-type branches corresponding to normal and abnormal Green’s functions. Both modes are gapped with roton-type segments at intermediary values of the wave vectors and can be named as quasi-NG modes. The fourth branch is the acoustical plasmon-type mode with absolute instability in the region of small and intermediary values of the wave vectors. All branches have a saturation-type dependencies at great values of the wave vectors. The number and the kind of the true NG modes is in accordance with the number of the broken symmetry operators. The comparison of the results concerning two Bose-Einstein condensates namely of the coplanar magnetoexcitons and of the quantum Hall excitons in the bilayer electron systems reveals their similarity.

Zero-resistance states in bilayer electron systems induced by microwave irradiation

We experimentally demonstrate the existence of microwave-induced zero-resistance states (ZRS) in bilayer electron systems created in wide quantum wells. In contrast to single-layer two-dimensional electron systems, ZRS are developed from the strongest magneto-intersubband oscillation peaks inverted by microwave radiation. Our experimental work is discussed within the theories of microscopic mechanisms of photoresistance, and the calculations reveal that the condition for absolute negative resistivity correlates with the appearance of ZRS.

Density-Imbalance Stability Diagram of the νT = 1 Bilayer Electron System at Full Spin Polarization

We investigate the evolution of the total Landau level filling factor νT = 1 bilayer quantum Hall (QH) state versus density imbalance at full spin polarization under a tilted magnetic field. When the system is well below the compressible-incompressible transition point at the balanced density, the νT = 1 QH state extends widely versus density imbalance, continuously merging into the single-layer ν = 1 QH state. In the vicinity of the transition point, the νT = 1 QH state is only weakly developed at small imbalance but increases in strength toward νT = 1/3 + 2/3, where it is clearly separated from the single-layer ν = 1 QH state. These results suggest that the system at the imbalance of Δν = 1/3 undergoes a transition from the correlated νT = 1 QH state to single-layer fractional QH states with increasing density.

Microwave-induced Hall resistance in bilayer electron systems

The influence of microwave irradiation on dissipative and Hall resistance in high-quality bilayer electron systems is investigated experimentally. We observe a deviation from odd symmetry under magnetic field reversal in the microwave-induced Hall resistance $\Delta R_{xy}$ whereas the dissipative resistance $\Delta R_{xx}$ obeys even symmetry. Studies of $\Delta R_{xy}$ as a function of the microwave electric field and polarization exhibit a strong and non-trivial power and polarization dependence. The obtained results are discussed in connection to existing theoretical models of microwave-induced photoconductivity.