Exact results for systems of electrons in the fractional quantum Hall regime

There has been a great deal of interest over the last two decades on the fractional quantum Hall effect, a novel quantum many-body liquid state of strongly correlated two-dimensional electronic systems in a strong perpendicular magnetic field. The most pronounced fractional quantum Hall states occur at odd denominator filling factors of the lowest Landau level and are described by the Laughlin wave function. It is well known that exact closed-form solutions for many-body wave functions, including the Laughlin wave function, are generally very rare and hard to obtain. In this work we present some exact results corresponding to small systems of electrons in the fractional quantum Hall regime at odd denominator filling factors. Use of Jacobi coordinates is the key tool that facilitates the exact calculation of various quantities. Expressions involving integrals over many variables are considerably simplified with the help of Jacobi coordinates allowing us to calculate exactly various quantities corresponding to systems with several electrons.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Tilt-induced localization and delocalization in the second Landau level

We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at nu=2+1/5 and 2+4/5 and the solid phases at nu=2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through the melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.     

Electronic correlation in the quantum Hall regime

Two‐dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many‐particle ground state and its excitations are studied in detail at fractional filling factors for spin‐polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.     

Pairing of spin excitations in lateral quantum dots

We demonstrate the existence of correlated electronic states as paired spin excitations of lateral quantum dots in the integer quantum Hall regime. Starting from the spin-singlet filling-factor nu=2 droplet, by increasing the magnetic field we force the electrons to flip spins and increase the spin polarization. We identify the second spin-flip process as one accompanied by correlated, spin depolarized phases, interpreted as pairs of spin excitons. The correlated states are identified experimentally in few-electron lateral quantum dots using high source-drain voltage spectroscopy.     

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.     

Vanishing hall coefficient in the extreme quantum limit in photocarrier-doped SrTiO3

We explore the extreme quantum limit of photogenerated electrons in quantum paraelectric SrTiO3. This regime is distinct from conventional semiconductors, due to the large electron effective mass and large dielectric constant. At low temperature, the magnetoresistance and Hall resistivity saturate at a high magnetic field, deviating from conventional behavior. As a result, the Hall coefficient vanishes on the scale of the ratio of the Landau level splitting to the thermal energy, indicating the essential role of lowest Landau level occupancy, as limited by thermal broadening.     

Enhancement of valley splitting in (100) Si MOSFETs at high magnetic fields

We report the density and magnetic field dependence of the valley splitting of two-dimensional electrons in (100) Si metal–oxide–semiconductor field-effect transistors, as determined via activation measurements in the quantum Hall regime. We find that the valley activation gap can be greatly enhanced at high magnetic fields as compared to the bare valley splitting. The observation of strong dependence of the valley activation gap on orbital Landau level occupancy and similar behavior of nearby spin gaps suggest that electron–electron interactions play a large role in the observed enhancement.     

Observation of a quantized hall resistivity in the presence of mesoscopic fluctuations

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level, we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its nu=1 value, h/e(2). This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.     

Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.     

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.     

Resonant rayleigh scattering from bilayer quantum Hall phases

We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor nu = 1. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.     

Pinning mode resonances of new phases of 2D electron systems in high magnetic fields

A striking rf or microwave resonance is a generic feature of electron solid phases of two-dimensional electron systems. These resonances have served to identify and characterize such solids, in the insulator that terminates the series of fractional quantum Hall effects at high magnetic field, in the range of the integer quantum Hall effect, and in bubble phases in the first excited and higher Landau levels.     

Observation of collapse of pseudospin order in bilayer quantum Hall ferromagnets

The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor nu=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at nu=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic fields.     

Quantum corrections to the electrical conduction in an AlGaN/GaN heterostructure

A new method for magneto-transport characterisation of semiconductor heterostructures is presented. The classical model of mixed conduction, modified by corrections resulting from quantum effects, has been used in the analysis of the conductivity-tensor components, magnetoresistance, and Hall coefficient in n-type Al_0.85Ga_0.15N/GaN in magnetic fields up to 12 T, in the temperature range from 2 to 295 K. The mixed conduction is due to high-mobility carriers in the conduction band in the interface and to low-mobility carriers in the conduction band in the GaN layer and in an impurity band. The corrections to the conduction of high-mobility carriers result from quantum effects: negative magnetoresistance, extraordinary Hall effect, and freeze-out of electrons. Negative magnetoresistance is due to localisation of electrons and to increasing tunnel coupling between electron states in different minima of a random potential, due to interface roughness. The extraordinary Hall effect has been explained by interaction of electrons with magnetic moments of dislocations in the interface. Decreasing concentration of electrons is probably due to Landau quantisation of the conduction band in the interface of the heterostructure. Received: 27 November 2000 / Accepted: 18 December 2000 / Published online: 3 April 2001     

Intrinsic gap of the nu=5/2 fractional quantum Hall state

The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The nu=5/2 excitation gap at 2.63 T is measured to be 262+/-15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.     

Novel optical probe for quantum Hall system

Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.     

Zener tunneling between the landau levels in quasi-two-dimensional electronic Corbino disks at large filling factors

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E _dc. It is shown that the observed oscillations are related to the Zener tunneling induced by E _dc. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field.