Hall Plateaus Research Articles

Correlated electron states at level crossings of bilayer two-dimensional electron systems in tilted magnetic fields

We have measured the energy-level structure of high mobility, strongly coupled bilayer two-dimensional electron systems in tilted magnetic fields by means of magnetotransport experiments. At tilt angles where single-particle levels with opposite spin and symmetry cross, we observe a surprising sudden broadening of the quantum Hall plateaus and a deepening of the Shubnikov–de Haas minima. This observation is explained by an interaction-induced rearrangement of the energy level structure which strongly increases the energetic splitting of two (anti-)crossing levels.

Hall plateau diagram for the Hofstadter butterfly energy spectrum

We extensively study the localization and the quantum Hall effect in the Hofstadter butterfly, which emerges in a two-dimensional electron system with a weak two-dimensional periodic potential. We numerically calculate the Hall conductivity and the localization length for finite systems with the disorder in general magnetic fields, and estimate the energies of the extended levels in an infinite system. We obtain the Hall plateau diagram on the whole region of the Hofstadter butterfly, and propose a theory for the evolution of the plateau structure with increasing disorder. There we show that a subband with the Hall conductivity $n e^2/h$ has $|n|$ separated bunches of extended levels, at least for an integer $n \leq 2$. We also find that the clusters of the subbands with identical Hall conductivity, which repeatedly appear in the Hofstadter butterfly, have a similar localization property.

Study of persistent photoconductivity and subband electronic properties of the two-dimensional electron gas in modulation doped GaAs/AlGaAs structure

We obtained the high mobility of μ2K=1.78×106 cm2/V·s in Si-doped GaAs/AlGaAs two-dimensional electron gas (2DEG) structures . After the sample was illuminated by a light-emitting diode in magnetic fields up to 6 T at T=2K, we did observe the persistent photoconductivity effect and th e electron density increased obviously. The electronic properties of 2DEG have b een studied by Quantum-Hall-effect and Shubnikov-de Haas (SdH) oscillation measu rements. We found that the electron concentrations of two subbands increase simu ltaneity with the increasing total electron concentration, and the electron mobi lity also increases obviously after being illuminated. At the same time, we also found that the electronic quantum lifetime becomes shorter, and a theoretical e xplunation is given through the widths of integral quantum Hall plateaus.

Transport between edge states in multilayer integer quantum Hall systems: Exact treatment of Coulomb interactions and disorder

A set of stacked two-dimensional electron systems in a perpendicular magnetic field exhibits a three-dimensional version of the quantum Hall effect if interlayer tunneling is not too strong. When such a sample is in a quantum Hall plateau, the edge states of each layer combine to form a chiral metal at the sample surface. We study the interplay of interactions and disorder in transport properties of the chiral metal, in the regime of weak interlayer tunneling. Our starting point is a system without interlayer tunneling, in which the only excitations are harmonic collective modes: surface magnetoplasmons. Using bosonization and working perturbatively in the interlayer tunneling amplitude, we express transport properties in terms of the spectrum for these collective modes, treating electron-electron interactions and impurity scattering exactly. We calculte the conductivity as a function of temperature, finding that it increases with increasing temperature as observed in recent experiments. We also calculate the autocorrelation function of mesoscopic conductance fluctuations induced by changes in a magnetic field component perpendicular to the sample surface, and its dependence on temperature. We show that conductance fluctuations are characterised by a dephasing length that varies inversely with temperature.

Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the nu=5/2 state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by quasiparticle braiding. Using the measured excitation gap at nu=5/2, we estimate the error rate to be 10(-30) or lower.

Aharonov–Bohm-type Effects in Triangular Antidot Lattice

Three kinds of Aharonov–Bohm (AB)-type oscillation have been investigated in triangular antidot lattice fabricated from a GaAs/AlGaAs two-dimensional electron gas sample. The oscillation periods of Altshuler–Aronov–Spivak (AAS) effect and AB-type effect near zero magnetic field are determined by the unit cell area, whereas those of AB-type oscillations in the quantum Hall plateau transition regime are governed by the effective area of antidot. The evolution of the high-field AB-type oscillation as a function of gate voltage gives infomation on the profile of the self-consistent potential associated with compressible edge channels formed around antidot. The temperature dependences and decoherence mechanisms of the AAS and AB-type oscillations near zero magnetic field as well as the high-field AB-type oscillation are discussed.

Interactions suppress quasiparticle tunneling at Hall bar constrictions.

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly pinched quantum-point-contact constrictions in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.

Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) “cloud-chamber” orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both “canonical” and “magnetic” angular momentum components, which add together to form the invariant “kinematic” angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the un,l eigenstates un,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of ν = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.

Role of Si-doped Al0.3Ga0.7As layers in the high-frequency conductivity of GaAs/Al0.3Ga0.7As heterostructures under conditions of the quantum hall effect

The complex high-frequency conductivity of GaAs/Al0.3Ga0.7As heterostructures that are δ-doped and modulation-doped with silicon was investigated by acoustic methods under conditions of the integer quantum Hall effect. Both the real (σ1) and imaginary (σ2) parts of the complex conductivity σ(ω, H)=σi−iσ2 were determined from the dependences of the absorption and velocity of surface acoustic waves on magnetic field. It is shown that, in the heterostructures with electron density ns=(1.3–7)×1011 cm−2 and mobility μ=(1–2)×105 cm2/(V s), the high-frequency conductivity near the centers of the Hall plateau is due to electron hopping between localized states. It is established that, with filling numbers 2 and 4, the conductivity of the Al0.3Ga0.7As:Si layer efficiently shunts the high-frequency hopping conductivity of the two-dimensional interface layer. A method of separating the contributions of the interface and Al0.3Ga0.7As:Si layers to the hopping conductivity σ(ω, H) is developed. The localization length of electrons in the interface layer is determined on the basis of the nearest neighbor hopping model. It is shown that, near the centers of the Hall plateau, both σ(ω, H) and ns depend on the cooling rate of a GaAs/Al0.3Ga0.7As sample. As a result, the sample “remembers” the cooling conditions. Infrared light and static strain also change both σ(ω, H) and ns. We attribute this behavior to the presence of two-electron defects (so-called DX− centers) in the Al0.3Ga0.7As:Si layer.

The Width of AC Quantum Hall Plateaus

The quantum Hall effect in GaAs heterostructures is investigated with alternating currents in the kilohertz frequency range. The width of the plateau shows no significant frequency dependence and is determined by an effective temperature. This effective temperature is higher than the bath temperature by an amount which depends on the current and the bath temperature. Whereas the electron temperature determined by other measurements of the dc conductivity shows a clear divergence toward the centre of the Landau levels, the effective temperature determined from the ac plateau width does not depend on the noninteger fraction of the filling factor [1], [2]. This unexpected result is now explained as a matter of the definition of the effective temperature and not of unexpected physics.

A new quantum Hall effect in the two-dimensional organic conductor, τ-(EDO-S,S-DMEDT-TTF)2(AuBr2)1+y

In the two-dimensional organic conductor, τ-(EDO-S,S-DMEDT-TTF)2(AuBr2)1+y, we have observed Shubnikov de Hass oscillations with Landau level down to n=2 in field up to 27 T. Motivated with this result, we extended to Hall effect study in pulsed magnetic field up to 60 T as well as in dc field up to 45 T and found Hall resistance plateau above 40 T (n=1). Since this system consists of two two-dimensional Fermi surface pockets, and larger pocket has a large effective mass compared with the smaller one, larger Fermi pocket behaves as a reservoir for the smaller pocket to be well-separated into completely filled and completely empty Landau levels in a certain range of temperature and magnetic field. The interpretation of realizing the Hall plateau can be understood as a new mechanism for QHE, but is quite different neither from localization nor field induce spin density wave state in organic TMTSF salts.

Long time relaxation phenomena of a two-dimensional electron system within integer quantum Hall plateau regimes after magnetic field sweeps

For investigating a two-dimensional electron system (2DES) in high magnetic fields and at temperatures below 0.1 K a single electron transistor (SET) is directly fabricated on top of a GaAs/AIGaAs heterostructure containing the 2DES underneath the surface. By using the SET as a highly sensitive electrostatic potential probe, the variation of the local electrostatic potential in the 2DES under the SET can be observed. Sweeping the magnetic field over a Hall plateau regime, a characteristic hysteresislike dependence of the local electrostatic potential between up and down sweep is observed indicating a nonequilibrium state for the 2DES. Stopping the magnetic field in a Hall plateau regime, the relaxation of the nonequilibrium potential distribution within the 2DES into the thermodynamic equilibrium at very low temperatures can elapse over several hours. The hysteresis effect is interpreted as the fingerprints of eddy currents which are driven by induced electrochemical potential gradients across the incompressible regions of the 2DES.

Screening and dissipation at the superconductor-insulator transition induced by a metallic ground plane

We study localization phenomena in two dimensional systems of charged particles in the presence of a metallic ground plane with particular focus on the superconductor-insulator transition. The ground plane introduces a screening of the long-range Coulomb interaction, and provides a source of dissipation due to the gapless diffusive electrons. The interplay of these two effects leads to interesting physical phenomena which are analyzed in detail in this paper. We argue that the generic superconductor-insulator transition of charged particles in the presence of the ground plane may be controlled by a fixed line with variable critical exponents. This is illustrated by an explicit calculation in an appropriate e expansion. In contrast, the universal properties of the superconductor-Mott insulator transition in the clean limit at commensurate densities are shown to be unmodified by either the metal or the long-range Coulomb interaction. A similar fixed line can arise in the presence of a metallic ground plane for quantum Hall plateau transitions. Implications for experiments on Josephson-junction arrays and quantum Hall systems are described.

Upshift of the fractional quantum Hall plateaux: evidence for repulsive scattering for composite fermions

It is now established that if there are an equal number of positively and negatively charged impurities, the quantum Hall plateaux in ρ xy ( B) are expected to be centred about the classical value ρ xy = B/( en) where n is the 2D carrier density. It has also been shown that when repulsive or attractive scattering centres are deliberately introduced close to a two-dimensional electron gas (2DEG), the centres of the quantum Hall plateaux are shifted to higher or lower magnetic field, respectively. In this paper, we present magneto transport measurements on a high-quality GaAs electron system. We extend this concept to the composite fermions where each electron is bound to two magnetic flux quanta. We provide compelling evidence that the dominant scattering for the composite fermions is different from that for electrons. This is supported by studying the upshift of the ν=1 quantum Hall plateau within the composite fermion picture.

On the Theory of Electric DC‐Conductivity: Linear and Non‐linear Microscopic Evolution and Macroscopic Behavior

We consider the Schrödinger time evolution of charged particles subject to a static substrate potential and to a homogeneous, macroscopic electric field (a magnetic field may also be present). We investigate the microscopic velocities and the resulting macroscopic current. We show that the microscopic velocities are in general non‐linear with respect to the electric field. One kind of non‐linearity arises from the highly non‐linear adiabatic evolution and (or) from an admixture of parts of it in so‐called intermediate states, and the other kind from non‐quadratic transition rates between adiabatic states. The resulting macroscopic dc‐current may or may not be linear in the field. Three cases can be distinguished: (a) the microscopic non‐linearities can be neglected. This is assumed to be the case in linear response theory (Kubo formalism, …). We give arguments which make it plausible that often such an assumption is indeed justified, in particular for the current parallel to the field. (b) The microscopic non‐linearities lead to macroscopic non‐linearities. An example is the onset of dissipation by increasing the electric field in the breakdown of the quantum Hall effect. (c) The macroscopic current is linear although the microscopic non‐linearities constitute an essential part of it and cannot be neglected. We show that the Hall current of a quantized Hall plateau belongs to this case. This illustrates that macroscopic linearity does not necessarily result from microscopic linearity. In the second and third cases linear response theory is inadequate. We elucidate also some other problems related to linear response theory.

25 Years quantum Hall effect: how it all came about

The quantum Hall effect (QHE) was discovered by Klaus von Klitzing in the spring of 1980. However, the plateaus in the Hall resistance of silicon metal oxide semiconductor devices which can be observed in high magnetic fields at low temperatures showed up several years earlier. The world wide research, which eventually culminated in the discovery, is briefly reviewed. The QHE was not predicted by theory, there were only approximate indications of quantization of the Hall resistance in whole fractions of h/ e 2. The exceptional precision of the resistance values of the Hall plateau led very soon to a new resistance standard.

Spatial distribution of edge states in the quantum Hall plateaus investigated by magnetocapacitance

The spatial distribution of the edge states in the quantum Hall (QH) regime has been investigated by the magnetocapacitance measured with the multigate of thin wires along the sample boundary. We have observed the compressible electronic states which exist within about $1\ensuremath{\mu}\mathrm{m}$ along the sample boundary in the QH regime. The edge states become broad by more than a few microns when the negative side gate bias is applied to the outermost gate wire.

Critical currents of ideal quantum Hall superfluids

Filling factor $\nu=1$ bilayer electron systems in the quantum Hall regime have an excitonic-condensate superfluid ground state when the layer separation $d$ is less than a critical value $d_c$. On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents, and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking inter-layer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange inter-layer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as $(d_c-d)^{1/2}$ when $d$ approaches $d_c$ from below. For large inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.

Phase diagram for quantum hall bilayers at nu=1.

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.

Deconstructing the Liouvillian approach to the quantum Hall plateau transition

We examine the Liouvillian approach to the quantum Hall plateau transition, as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62}, 2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87}, 046801 (2001)]. We show that, despite appearances to the contrary, the Liouvillian approach is not specific to the quantum mechanics of particles moving in a single Landau level: we formulate it for a general disordered single-particle Hamiltonian. We next examine the relationship between Liouvillian perturbation theory and conventional calculations of disorder-averaged products of Green functions and show that each term in Liouvillian perturbation theory corresponds to a specific contribution to the two-particle Green function. As a consequence, any Liouvillian approximation scheme may be re-expressed in the language of Green functions. We illustrate these ideas by applying Liouvillian methods, including their extension to $N_L > 1$ Liouvillian flavors, to random matrix ensembles, using numerical calculations for small integer $N_L$ and an analytic analysis for large $N_L$. We find that behavior at $N_L > 1$ is different in qualitative ways from that at $N_L=1$. In particular, the $N_L = \infty$ limit expressed using Green functions generates a pathological approximation, in which two-particle correlation functions fail to factorize correctly at large separations of their energy, and exhibit spurious singularities inside the band of random matrix energy levels. We also consider the large $N_L$ treatment of the quantum Hall plateau transition, showing that the same undesirable features are present there, too.