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.

A Aproximação de Massa Efetiva para a função evnvelope multi-componente, na presença de uma interface, desenvolvida por Marques e Sham, será utilizada aqui, para materiais de gap estreito do grupo II-VI, da seguinte maneira: A) A forte interação entre bandas de condução e valência, nestes materiais, é justificada em um Hamiltoniano de Kane (6x6) modificado, contendo todas as ondas de Bloch propagantes e evanescentes. Na presença de uma interface, a função de onda eletrônica, &#936, é composta de uma onda de Bloch incidente, uma refletida e duas evanescentes, com a mesma energia E e momento paralelo k. Já que a estrutura da maioria dos isolantes utilizados são desconhecidos, a interface semicondutor-isolante por ser considerada como uma barreira infinita, de modo que, &#936, se anule na interface. Existe uma fina região de espessura &#945 na interface, onde o decaimento das ondas evanescentes é indispensável. Distante desta região, as ondas evanescentes possuem um papel insignificante e eventualmente anulam-se. O limite de &#945 &#8594 0 determina as condições de contorno para cada componente da função de onda envelope na interface. B) As condições de contorno são usadas para computar a estrutura de subbandas e o potencial auto-consistente para o Hg1-xCdxTe. A mais interessante característica é o afastamento dos estados de spin duplamente degenerados. Estes resultados serão utilizados para encontrarmos a dependência da energia das subbandas com um campo magnético perpendicular à interface. C) A magneto-condutividade longitudinal é calculada como função do campo magnético B &#8869. Efeitos das interações elétron-elétron e elétrons-impureza são levadas em conta nas aproximações de Hartee-Foch e auto-consistente de Born, respectivamente. Para uma interação elétron-impureza finita, encontram-se fatores de preenchimentos críticos dos níveis de Landau, onde transições de fase são observadas. Estes resultados explicam as descontinuidades presentes, em medidas experimentais, na magneto-resistividade longitudinal e transversal (Hall), em MISFET de Hg (Cd)Te. / The Effective Mass Approximation for multi-component envelope wave function in the presence of an interface in the MOSFET system, developed by Marques and Sham, will be used here, for II-VI narrow-gap semiconductors, in the following way: A) The strong interaction between conduction and valence bands, in these materials, is justified. The (6x6) Kane type modified Hamiltonian is used and the total wave function contains every propagating and evanescent waves. For an interface, the total function, &#936, is composed of one incident and one reflected and two evanescent Bloch waves, with energy E and parallel wave-vector k. Since the band structure of the most used insulators is usually not well known, the insulator-semiconductor interface can be assumed as an infinite barrier; therefore, the total wave-function there can set to zero. The semiconductor evanescent Bloch waves are indispensable in a thin layer, of thickness &#945, close to this region. Far away from the interface their role are insignificant and can be neglected. In the limit &#945 &#8594 0, the boundary condition for each the limit the total Bloch wave function, are derived. B) These boundary conditions are used to calculate the self-consistent electric subband and potential for MISFET of Hg1-xCdxTe. The subbands present a very important spin splitting, due to the internal electric field. C) The effect of a perpendicular magnetic field is also studied and the longitudinal magneto-conductivity are calculated. The effect of electron-electron and electron-impurity interactions are respectively accounted for in the Hartee-Fock and self-consistent Born approximations. For critical electron-impurity interaction, the Landau level filling shows a phase transition at a given fractional occupation (or magnetic field). These results are experimentally observed in both longitudinal and transverse (Hall) magneto-resistance for Hg(Cd)Te.

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.

Yuen Chi Yan = 有關光折變晶體中空間孤子、偏振轉動以及霍爾效應的研究 / 阮志仁. / Thesis submitted in: July 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 81-82). / Text in English; abstracts in English and Chinese. / Yuen Chi Yan = You guan guang zhe bian jing ti zhong kong jian gu zi, pian zhen zhuan dong yi ji Huoer xiao ying de yan jiu / Ruan Zhiren. / Acknowledgments --- p.i / Abstract --- p.ii / Table of Contents --- p.v / Chapter Chapter 1 --- Photorefractive Spatial Soliton --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Bright Spatial Soliton --- p.3 / Chapter 1.2.1 --- Experiment --- p.4 / Chapter 1.2.2 --- Results and Discussion --- p.6 / Chapter 1.2.2.1 --- Expansion --- p.6 / Chapter 1.2.2.2 --- Contraction --- p.10 / Chapter 1.3 --- Dark Spatial Soliton --- p.15 / Chapter 1.3.1 --- Experiment --- p.15 / Chapter 1.3.2 --- Results and Discussion --- p.20 / Chapter Chapter 2 --- Polarization Rotation --- p.23 / Chapter 2.1 --- Introduction --- p.23 / Chapter 2.2 --- Experiment --- p.24 / Chapter 2.3 --- Results and Discussion --- p.30 / Chapter 2.3.1 --- Effect of varying pump beam power --- p.30 / Chapter 2.3.2 --- Effect of different polarizations of signal beam --- p.41 / Chapter 2.3.3 --- Effect of signal beam size --- p.43 / Chapter 2.3.4 --- Effect of applied E-field --- p.46 / Chapter 2.3.5 --- Effect of signal beam and pump beam separation and perpendicularly --- p.52 / Chapter 2.3.6 --- Investigation of Δne using interferometer --- p.60 / Chapter 2.3.7 --- Computer Simulation --- p.69 / Chapter Chapter 3 --- Hall Effect --- p.72 / Chapter 3.1 --- Introduction --- p.72 / Chapter 3.2 --- Experiment --- p.75 / Chapter 3.3 --- Results and Discussion --- p.76 / Conclusion and Possible Further Works --- p.79 / References --- p.81

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.

This dissertation presents the design, control, and implementation of a compact highprecision multidimensional positioner. This precision-positioning system consists of a novel concentrated-field magnet matrix and a triangular single-moving part that carries three 3-phase permanent-magnet planar-levitation-motor armatures. Since only a single levitated moving part, namely the platen, generates all required fine and coarse motions, this positioning system is reliable and potentially cost-effective. The three planar levitation motors based on the Lorentz-force law not only produce the vertical force to levitate the triangular platen but also control the platen's position and orientation in the horizontal plane. Three laser distance sensors are used to measure vertical, x-, and yrotation motions. Three 2-axis Hall-effect sensors are used to determine lateral motions and rotation motion about the z-axis by measuring the magnetic flux density generated by the magnet matrix. This positioning system has a total mass of 1.52 kg, which is the minimized mass to produce better dynamic performance. In order to reduce the mass of the moving platen, it is made of Delrin with a mass density of 1.54 g/cm3 by Computer Numerical Controlled (CNC) machining. The platen can be regarded a pure mass, and the spring and damping effects are neglected except for the vertical dynamic. Single-input single-output (SISO) digital lead-lag controllers and a multivariable Linear Quadratic Gaussian (LQG) controller were designed and implemented. Real-time control was performed with the Linux-Ubuntu operating system OS. Real Time Application Interface (RTAI) for Linux works with Comedi and Comedi libraries and enables closed-loop real-time control. One of the key advantages of this positioning stage with Hall-effect sensors is the extended travel range and rotation angle in the horizontal mode. The maximum travel ranges of 220 mm in x and 200 mm in y were achieved experimentally. Since the magnet matrix generates periodical sinusoidal flux densities in the x-y plane, the travel range can be extended by increasing the number of magnet pitches. The rotation angle of 12 degrees was achieved in rotation around z. The angular velocities of 0.2094 rad/s and 4.74 rad/s were produced by a 200-mm-diameter circular motion and a 30-mm-diameter spiral motion, respectively. The maximum velocity of 16.25 mm/s was acquired from over one pitch motion. The maximum velocity of 17.5 mm/s in a 8-mm scanning motion was achieved with the acceleration of 72.4 m/s2. Step responses demonstrated a 10-um resolution and 6-um rms position noise in the translational mode. For the vertical mode, step responses of 5 um in z, 0.001 degrees in roation around x, and 0.001 degrees in rotation around y were achieved. This compact single-moving-part positioner has potential applications for precisionpositioning systems in semiconductor- manufacturing.

This dissertation focuses on the study of spin-dependent transport in systems with strong spin-orbit coupling within their band structure. In particular we focus on the anomalous Hall effect, the spin Hall effect, and the Aharonov-Casher effect whose origins, are linked to the presence of spin-orbit coupling. Given the theoretical controversy surrounding these effects we further simplify our studies to semiconductor systems where the band structure is much simpler than in metallic systems with heavy elements. To obtain finite analytical results we focus on reduced dimensions (two and one dimensions) which can be explored experimentally. To set the stage, we discuss the origins of the strong spin-orbit coupling in semiconductors deriving the effective interaction from the Dirac equation. We discuss in detail the skew scattering contribution to the anomalous Hall effect in two-dimensional systems, which is dominant for systems with low impurity concentrations, and find that it is reduced when the two chiral subbands are partially occupied in an electron gas and vanishes for a hole gas, regardless of the band filling. We also present calculations for all contributing mechanisms. We propose a device to test this prediction and study the crossover from the intrinsic to the extrinsic anomalous Hall effect. We calculate all contributions to the anomalous Hall effect in electron systems using the Kubo-Streda formalism. We find that all contributions vanish when both subbands are occupied and that the skew scattering contribution dominates when only the majority subband is occupied. We calculate the interference effects due to spin-orbit interaction in mesoscopic ring structures patterned from HgTe quantum wells related to the Aharonov-Casher effect and the spin Hall effect. We find that the transport properties are affected by the carrier density as well as the spin orbit interaction. We find that the conductivity is larger in hole gas systems. We also show that devices with inhomogenous spin orbit interaction exhibit an electrically controlled spin-flipping mechanism.

No description available.