Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [95]-100).

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008. / Minqiang Li, Committee Member ; Constantine Yannouleas, Committee Member ; Michael Pustilnik, Committee Member ; Mei-Yin Chou, Committee Member ; Uzi Landman, Committee Member.

No description available.

The integer and fractional quantum Hall effects arise in two-dimensional electron systems subject to low temperature and high perpendicular magnetic field. The phenomenology of these two effects is rich and provides interesting insight into quantum physics. We present two experimental studies of phenomena in the fractional quantum Hall regime. The first examines the tunneling conductance of quasiparticles at filling factor 5/2. This state is of significant interest because it lies outside the traditional Jain hierarchy of fractional quantum Hall states and because it may be the first physical system found to exhibit non-abelian particle statistics. A quantum point contact is used to bring edge states on opposite sides of the system in proximity to each other, allowing quasiparticles to tunnel between the edge states. By annealing the gates forming the quantum point contact at different voltages we control the tunneling strength for fixed temperature and bias. We demonstrate a transition from strong to weak tunneling controlled in this manner. In the weak tunneling regime, the DC bias and temperature dependence of the tunneling conductance is fit to a theoretical form, resulting in values for the quasiparticle charge \(e*\) and the interaction parameter \(g\). The values of these parameters are used to help distinguish between proposed candidate states for the 5/2 wave function. Quantitative and qualitative results are most consistent with the abelian 331 state. Our second main focus is the breakdown of the fractional quantum Hall states at filling factors 4/3 and 5/3. Breakdown of integer and fractional quantum Hall states is known to occur when the Hall and longitudinal resistances deviate from their ideal values at nonzero critical currents. Although multiple studies of breakdown in the integer quantum Hall regime have been reported, corresponding results for the fractional regime are scarce. We observe breakdown over a range of integer states that is consistent with previous results. However, breakdown in the fractional regime is found to exhibit markedly different behavior. In particular, the magnitude of the critical current decreases with increased sample width. This behavior is opposite that observed for integer filling factors and does not seem to be explicable based on current theories of breakdown. / Physics

The quantum Hall effect occurs when a conductor carrying a current is placed in a perpendicular magnetic field. If certain conditions are met, such as strong magnetic field and low temperature, the resistivity becomes quantised, taking values of integer or fractional multiples of h/e2. By analysing the movement of electrons in a magnetic field classically and quantum mechanically information about the integer quantum Hall effect and the fractional quantum Hall effect can be gathered, using the two different gauge potentials of Landau gauge and Symmetric gauge. Resistance Metrology is one field of study that the quantum Hall effect has greatly impacted by providing a way to universally maintain the ohm, with significantly less uncertainty than previously. / Den kvantmekaniska hall-effekten uppstår när en strömbärande ledare placeras i ett vinkelrätt magnetfält. Om vissa villkor är uppfyllda, såsom starkt magnetfält och låg temperatur, blir resistiviteten kvantiserad. Given av heltal (integer) eller fraktions-(fractional) multiplar av h/e2. Genom att analysera elektroners rörelse i ett magnetfält klassiskt och kvantmekaniskt fås information om Hall-effekterna; integer quantum Hall effect och fractional quantum Hall effect, med hjälp av de två gauge potentialerna Landau gauge och Symmetrisk gauge. Resistansmetrologi är ett forskningsområde som kvant Hall-effekten har starkt påverkat genom att tillhandahålla ett sätt att universellt upprätthålla ohm-enheten med betydligt mindre osäkerhet än tidigare.

This thesis scrutinizes the condensed matter physics phenomenon known as the fractional quantum Hall effect (FQHE), in particular fractional quantum Hall effects occurring in multicomponent systems. Broadly speaking, the FQHE can be defined as a many-electron quantum phenomenon, driven by strong interactions, that occurs in two-dimensional electron gasses in the presence of a perpendicular external magnetic field (and it is also predicted to occur for any two-dimensional particles, such as confined cold atoms, in an external gauge field). Multicomponent systems are systems where the constituent particles (such as electrons or cold atoms) possess internal degrees of freedom, for instance a spin or valley index. These internal degrees of freedom are often overlooked when modeling the FQHE. Taking into account the multicomponent degree of freedom yields an abundance of possibilities for the intellection of new types of so-called “topological phases of matter”, which are ubiquitously associated with the FQHE. In this thesis several different cases are considered. The first topic discussed herein is a study of phase transitions that can take place between FQHE phases with different net values of their multicomponent degrees of freedom. Examples are phase transitions between phases of different uniform net spin polarization, tunable as a function of certain system parameters. Some significant technical refinements are made to a previous model and comparisons are made with a variety of different experiments. The results are relevant for multicomponent FQHEs occurring in GaAs,AlAs and SiGe semiconductor systems where the electronic structure is confined to two dimensions, as well as in two-dimensional materials such as graphene. The second topic discussed herein is the introduction of the multiparticle multicomponent pseudopotential formalism. This methodology is oriented towards considerably expanding an existing framework for the construction of exactly solvable FQHE models by parameterizing multicomponent interactions. The final topic is the first example application of this new formalism to the construction of an exactly solvable FQHE model.

Electron-electron (e-e) interactions in 2-dimensional electron gases (2DEGs) can lead to many-body correlated states such as the the fractional quantum Hall effect (FQHE), where the Hall conductance quantization appears at fractional filling factors. The experimental discovery of an anomalous integer quantum Hall effect in graphene has faciliated the study of the interacting electrons which behave like massless chiral fermions. However, the observation of correlated electron physics in graphene is mostly hindered by strong electron scattering caused by charge impurities. We fabricate devices, in which, electrically contacted and electrostatically gated graphene samples are either suspended over a SiO₂ substrate or deposited on a hexagonal boron nitride layer, so that a drastic suppression of disorder is achieved. The mobility of our graphene samples exceeds 100,000 cm²/Vs. This very high mobility allows us to observe previously inaccessible quantum limited transport phenomena. In this thesis, we first present the transport measurements of ultraclean, suspended two-terminal graphene (chapter 3), where we observe the Fractional quantum Hall effect (FQHE) corresponding to filling fraction ν=1/3 FQHE state, hereby supporting the existence of interaction induced correlated electron states. In addition, we show that at low carrier densities graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields. Since the quantitative characterization of the observed FQHE states such as the FQHE energy gap is not straight-forward in a two-terminal measurement, we have employed the four-probe measuremt in chapter 4. We report on the multi-terminal measurement of integer quantum Hall effect(IQHE) and fractional quantum Hall effect (FQHE) states in ultraclean suspended graphene samples in low density regime. Filling factors corresponding to fully developed IQHE states, including the ν±1 broken-symmetry states and the ν=1/3 FQHE state are observed. The energy gap of the 1/3 FQHE, measured by its temperature-dependent activation, is found to be much larger than the corresponding state found in the 2DEGs of high-quality GaAs heterostructures, indicating that stronger e-e interactions are present in graphene relative to 2DEGs. In chapter 5, we investigate the e-e correlations in graphene deposited on hexagonal boron nitride using the thermopower measurements. Our results show that at high temperatures the measured thermopower deviates from the generally accepted Mott's formula and that this deviation increases for samples with higher mobility. We quantify this deviation using the Boltzmann transport theory. We consider different scattering mechanisms in the system, including the electron-electron scattering. In the last chapter, we present the magnetothermopower measurements of high quality graphene on hexagonal boron nitride, where we observe the quantized thermopower at intermediate fields. We also see deviations from the Mott's formula for samples with low disorder, where the interaction effects come into play . In addition, the symmetry broken quantum Hall states due to strong electron-electron interactions appear at higher fields, whose effect are clearly observed in the measured in mangeto-thermopower. We discuss the predicted peak values of the thermopower corresponding to these states by thermodynamic arguments and compare it with our experimental results. We also present the sample fabrication methods in chapter 2. Here, we first explain the fabrication of the two-terminal and multi-terminal suspended graphene and the current annealing technique used to clean these samples. Then, we illustrate the fabrication of graphene on hexagonal boron nitride as well as encapsulated graphene samples with edge contacts. In addition, the thermopower measurement technique is presented in Appendix A, in which, we explain the temperature calibration, DC and AC measurement techniques.

L’effet Hall quantique (EHQ), observé par exemple dans des gaz bidimensionnels d’électrons (2DEGS) à basse température et sous fort champ magnétique, a révolutionné la métrologie des résistances car il permet d’obtenir un étalon quantique de résistance qui ne dépend que de e et h (respectivement la charge de l’électron et la constante de Planck). Une des missions des métrologues est de développer les étalons en améliorant leurs performances ou en les rendant plus facile à mettre en oeuvre (travaillant à plus haute température ou plus faible champ magnétique). Dans ce contexte, la physique du graphène suscite l’intérêt pour une application en métrologie. Une monocouche de graphène est une feuille d’un seul atome d’épaisseur constituée d’atomes de carbone disposés en nid d’abeille. Une bicouche de graphène est formée par empilement de deux monocouches. Les écarts en énergie entre les premiers niveaux de Landau dans la monocouche et dans la bicouche sont supérieurs par rapport à ceux dans GaAs ce qui rend l’EHQ dans le graphène plus robuste et laisse envisager le développement d’un étalon plus pratique. Durant ma thèse, nous avons mis en place un protocole de fabrication de barres de Hall en graphène exfolié comprenant un repérage optique, des lithographies électroniques, la métallisation, la gravure plasma… L’utilisation de substrat de silicium oxydé en surface rend possible l’utilisation d’une grille en face arrière. En outre la géométrie des échantillons répond au mieux aux critères métrologiques (canal central large, prises de tension bien définies, …). A basse température, le dopage résiduel obtenu après le recuit in situ est de l’ordre de 3-4x1011 cm-2. Les mobilités sont proches de 3000 cm2/(V.s) et 4000 cm2/(V.s) respectivement pour les échantillons monocouche et bicouche à la fois pour les électrons et les trous. Le transport mésoscopique a été caractérisé à basse température par des mesures de localisation faible et de fluctuations universelles de conductance. La longueur de cohérence que nous avons extraite est de l’ordre de 0.5 µm à 1.5 K. La résistance des contacts mesurée en régime d’EHQ est plutôt faible (typiquement quelques ohms). L’EHQ a été étudié en détail à basse température (300 mK < T <1.5 K) et sous fort champ magnétique (jusqu’à 18.5T) à la fois dans la monocouche et la bicouche en mesurant de manière précise la résistance de Hall (RH) et la résistance longitudinale (Rxx). Les mesures fines de RH sont réalisées à l’aide d’un pont de comparaison basé sur un Comparateur Cryogénique de Courant ; elles consistent à comparer indirectement l’EHQ dans l’échantillon de graphène à l’EHQ obtenu dans une barre de Hall en GaAs/AlGaAs qui est supposée fournir la valeur exacte RH/2. Nos mesures révèlent un accord entre la résistance de Hall dans le graphène et la valeur attendue avec une incertitude de quelques 10-7. Au plus faible courant et dans l’état de dissipation minimale (Rxx→0), nous avons obtenu un accord avec une incertitude relative de 3.10-7. Ce niveau de précision est principalement limité par la petite taille de nos échantillons et par les inhomogénéités de la densité qui y sont présents, ces deux caractéristiques amenant de faibles courants de rupture de l’EHQ (1-2 µA). Toutefois, nos résultats sont à ce jour les tests les plus précis concernant l’EHQ dans du graphène exfolié et les premiers tests sur une bicouche. Ils confirment le potentiel de l’EHQ dans le graphène pour une application en métrologie. / The quantum Hall effect (QHE) observed in two dimensional electron gases (2DEGs) at low temperature and under high magnetic induction, has revolutionized the resistance metrology because it leads to a universal and very reproducible quantum resistance standard only dependent on e and h (respectively the electron charge and Planck's constant). One of the metrologists' missions is to develop standards with improved performances and to notably make them more practical, working for example at higher temperature or lower magnetic induction. In this context, graphene physics could be very interesting for metrological applications. Monolayer graphene is a one atom thick layer of carbon atoms condensed in a honeycomb lattice. A bilayer graphene consists in two stacked monolayers. Larger energy spacings between the first Landau Levels in monolayer and in bilayer than in GaAs make the QHE in graphene more robust and give hope that more practical standards could be developed. During the PhD, we have set a protocol up in order to fabricate exfoliated graphene based Hall bars, including location with an optical microscope, e-beam lithography, metallization, plasma etching… Backgated using oxidized silicon wafers the devices were designed to fulfill at best the metrological requirements (large conduction channel, well defined voltage probes…). At low temperature, the typical charge carrier residual doping obtained after the annealing process was 3-4x1011 cm-2. Mobilities were close to 3000 cm2/(V.s) and 4000 cm2/(V.s) respectively for the monolayer and the bilayer based device both for holes and electrons. Mesoscopic transport was characterized at low temperature by weak localization and universal conductance fluctuations (UCF) measurements. The phase coherence length deduced was about 0.5 µm below 1.5 K. The resistance of the contacts, measured in the QHE regime, appeared to be rather low (typically few ohms). The QHE was investigated in details at low temperature (300 mK < T <1.5 K) and high magnetic field (up to 18.5 T) in both monolayer and bilayer graphene by refined measurements of the Hall resistance (RH) and also of the longitudinal resistance (Rxx). The accurate measurements of RH were performed using a Cryogenic Current Comparator based resistance bridge. They consist in an indirect comparison between the QHE in graphene and the QHE obtained in a GaAs based Hall bar, supposed to deliver the expected value RH/2. Our measurements showed an agreement of the Hall resistance in graphene with the expected value within some parts in 107. At the lowest biasing current and in the lowest dissipation state (where Rxx→0) it is possible to demonstrate an agreement within an uncertainty of 3 parts in 107. That accuracy is essentially limited by the small size, and the poor homogeneity of the carrier density of the graphene electronic systems, both acting for a very reduced breakdown current of the QHE (1-2 µA). Nevertheless these results are the most accurate tests of the QHE performed in exfoliated graphene and the first universality test of the QHE with bilayer graphene. They confirm the potential of the QHE in graphene for the metrological application.

No description available.

Using the method of breaking circular symmetry and the subsequent symmetry restoration via projection techniques, we calculate the ground-state energies and excitation spectra of N-electrons confined in parabolic quantum dots in strong magnetic fields in the medium-size range 10<=N <=30. The physical picture is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. A derived analytic expression for the energetics is applicable to arbitrary sizes given the corresponding ring configuration of classical point charges. Also by exact diagonalization (EXD) method, we show the spectrum and structure of few electrons, 2<=N<=3, confined in elliptical dots at finite magnetic field. The results suggest the formation of a state of Wigner-molecular properties with spin associated, which has great instructions for the development of quantum register in quantum computing.