Induction kinetics in 2D electron systems at the Hall plateaus

Specific features of the induction excitation of 2D electron systems at the Hall plateaus are discussed. The corresponding kinetics is shown to have several frequency regimes. In the region ω ? ω_D, where ω_D is the frequency characteristic of the kinetics at the Hall plateaus, an induction-caused variation of electron density follows the magnetic-field variation with time. For the frequencies ω ≤ ω_D, a noticeable relaxation of the electron disturbance appears, and the induction polarization of 2D samples at the Hall plateaus noticeably decreases as compared to the maximum possible polarization. Finally, in the limit ω ≤ ω_slow, where ω_slow corresponds to another characteristic time of the quantum Hall effect, the so-called adiabatic approximation takes place with the 2D system responding to the derivative of magnetic field dH/dt rather than to the magnetic field itself H(t). The results of calculations are compared with the experimental data reported in the literature.     

Critical width of Hall incompressible strips in regularly nonuniform 2D electron systems

A formalism for determining the critical width of Hall incompressible strips, which arise in regularly nonuniform 2D electron systems in the presence of a magnetic field, is proposed. Under equilibrium conditions, this width is determined by competition between the cyclotron and Coulomb energies at distances of about the critical width of a channel with integer filling factor. The calculations are applied to interpretation of available experimental data.     

Integer and fractional quantum Hall effects in bilayer electron systems

Integer and fractional quantum Hall (QH) effects are studied in bilayer electron systems both theoretically and experimentally, especially, at ν=2 and 2/3. Due to the spin and layer degrees of freedom, the SU(4) symmetry underlies the integer QH states, where quantum coherence develops spontaneously and quasiparticles are coherent excitations. It is intriguing that a pair of skyrmions makes one quasiparticle at ν=2. In the fractional QH regime, on the other hand, the composite-fermion cyclotron gap competes with the Zeeman and tunneling gaps, bringing in new phases and excitations. At ν=2/3 our experimental data suggest that a quasiparticle is not a coherent excitation but simply a composite fermion.     

Hall coefficient of the 2D electron system in silicon MOSFETs

Hall coefficient measurements are reported for the two-dimensional electron system in silicon MOSFETs for densities throughout the metallic phase and very near the transition to insulating behavior.     

Collective excitations in low-density 2D electron systems

We report the observation of sharp plasmon and magnetoplasmon modes in ultra-low-density 2D electron systems. Well defined dispersions for the modes are observed at densities as low as 1.1×10⁹ cm⁻² and with excitation wave vectors as large as 1.2×10⁵ cm⁻¹. Interestingly, both modes are found to be more easily measured in low-density systems than in high-density systems. The strength of the light scattering cross-sections at low density suggests potential applications to the study of quantum phase transitions at large r_s.     

Photoconductivity of 2D electron systems in magnetic field

According to recent photoconductivity measurements in 2D electron semiconductor systems in magnetic fields normal to the 2D plane, the photoconductivity as a function of magnetic field exhibits oscillations in the region of fields much weaker than those necessary for the observation of the Shubnikov-de Haas effect. In this paper, the aforementioned oscillations are interpreted as a two-dimensional analogue of magnetophoton (phonon) oscillations studied in detail by different authors on 3D samples.     

Hierarchy of quantized Hall states in double-layer electron systems

The hierarchy of fractionally quantized Hall states of Haldane and Halperin is extended to the case of double-layer electron systems. Recursion relations for the filling fractions and flux shifts in the spherical geometry are derived and used to elaborate simple cases, including quasiparticle condensates with opposite charges in different layers. Extensive numerical studies are presented, which provide evidence for many of our predictions.     

Universal magnetoluminescence kinetics in magnetically frozen 2D electron systems

The kinetics of recombination of electrons and acceptor-bound holes in AlGaAs-GaAs heterostructure obey a single-exponential decay in the liquid phase of 2D electrons, whereas localization gives rise to a broad spectrum of recombination rates, especially in the magnetic freeze-out regime. This results in a power-law dependence I(t)∝(τ/t)^α in the tail of the recombination kinetics, with the universal exponent α=(1−ν)⁻¹ at ν<1 for all the samples examined experimentally in this work. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 118–122 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Multichannel Kondo models in non-Abelian quantum Hall droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction nu=2+k/(k+2) or its particle-hole conjugate at nu=2+2/(k+2). The k-channel Kondo model is channel isotropic even without fine-tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of k=2, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction nu=5/2.     

Nonmonotonic temperature dependence of the Hall resistance of a 2D electron system in silicon

For a 2D electron system in silicon, the temperature dependence of the Hall resistance ρ_xy(T) is measured in a weak magnetic field in the range of temperatures (1–35 K) and carrier concentrations n where the diagonal resistance component exhibits a metallic-type behavior. The temperature dependences ρ_xy(T) obtained for different n values are nonmonotonic and have a maximum at T_max ～ 0.16T_F. At lower temperatures T < T_max, the change δρ_xy(T) in the Hall resistance noticeably exceeds the interaction quantum correction and qualitatively agrees with the semiclassical model, where only the broadening of the Fermi distribution is taken into account. At higher temperatures T > T_max, the dependence ρ_xy(T) can be qualitatively explained by both the temperature dependence of the scattering time and the thermal activation of carriers from the band of localized states.     

“Soft” edge states in inhomogeneous 2D electron systems

The structural details of an edge electronic state in external-field-bounded 2D charged (electron or hole) systems at the zero boundary density of the mobile charge carriers are discussed. It is shown that the so-called “soft” edge electronic states (SESs) appear along these boundaries. The details of their structure and spectrum are analyzed, and the possible effects with the SESs are outlined.     

Theoretical approach to microwave-radiation-induced zero-resistance states in 2D electron systems

We present a theoretical model in which the existence of radiation-induced zero-resistance states is analyzed. An exact solution for the harmonic oscillator wave function in the presence of radiation, and a perturbation treatment for elastic scattering due to randomly distributed charged impurities, form the foundations of our model. Following this model most experimental results are reproduced, including the formation of resistivity oscillations, their dependence on the intensity and frequency of the radiation, temperature effects, and the locations of the resistivity minima. The existence of zero-resistance states is thus explained in terms of the interplay of the electron microwave-driven orbit dynamics and the Pauli exclusion principle.     

Width effect on the magnetoconductivity of 2D electron systems

Based on a parabolic well model, it is shown that the magnetoconductivity of narrow 2D electron systems is characterized by a modified cyclotron frequency and a crossover parameter which is a ratio of the cyclotron frequency to the curvature of the parabolic potential. Explicit results are derived for systems with finite width under the assumption that quantum oscillations are small.     

Droplet state and the compressibility anomaly in dilute 2D electron systems

We investigate the space distribution of carrier density and the compressibility of two-dimensional (2D) electron systems by using the local density approximation. The strong correlation is simulated by the local exchange and correlation energies. A slowly varied disorder potential is applied to simulate the disorder effect. We show that the compressibility anomaly observed in 2D systems which accompanies the metal-insulator transition can be attributed to the formation of the droplet state due to a disorder effect at low carrier densities.     

Anomalous giant piezoresistance in AlAs 2D electron systems with antidot lattices

An AlAs two-dimensional electron system patterned with an antidot lattice exhibits a giant piezoresistance effect at low temperatures, with a sign opposite to the piezoresistance observed in the unpatterned region. We suggest that the origin of this anomalous giant piezoresistance is the nonuniform strain in the antidot lattice and the exclusion of electrons occupying the two conduction-band valleys from different regions of the sample. This is analogous to the well-known giant magnetoresistance effect, with valley playing the role of spin and strain the role of magnetic field.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.