This thesis is a study of the size effect. Improvements on both theoretical work and experimental design are involved in this thesis. The theoretical section focuses on the grain size effect, while the experimental section is related to the micro-foil bending test. Both classic experimental data and theories for the Hall-Petch relationship are reviewed comprehensively. The fitting of the datasets show that the inverse square-root dependence and simple inverse expressions are equally good. The fully Bayesian analysis strongly suggests that the latter is correct. Since the physical mechanism underlying the simple inverse dependence is a general size effect, the precise description of the Hall-Petch effect is that it is a manifestation of the general size effect, instead of having its own special character. Improvements on the classic Stolken and Evans' micro-foil bending experiments are also carried out in this thesis. The smart design of the new equipment eliminates the big risk of error in the classic experiment. By using the new device, precise datasets from the elastic region through the yield point and to high plastic strain area can be obtained. The initial results correspond well with the old published data.

Thesis (Ph.D.)--Boston University

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.

The "hall churches" of East Anglia, which number fewer than two dozen, were among the most distinctive of the thousands of parish churches built or rebuilt in England during the Late Middle Ages. Indeed, at the time of their construction, these buildings were nothing short of revolutionary since their open configurations upended centuries-old conventions of church planning. All medieval parish churches, by virtue of their function as spiritual centers for the common faithful, possessed two important ritual zones: the nave (traditionally maintained by the laity) and the chancel (traditionally maintained by the clergy). The vast majority treated these zones as semi-autonomous spaces. But a tiny minority, namely "hall churches," treated them as a single fully integrated volume of continuous extent and congruent design. Historians of art and architecture, in evaluating these one-of-a-kind structures, have been quick to praise their phenomenological homogeneity as architectural ensembles but slow to parse their ontological heterogeneity as composite spatial enclosures and conglomerate social enterprises. This dissertation seeks, in contrast, to investigate the implications of this productive tension between affect and reality via object-oriented methods derived from the spatial turn in the humanities. It argues—with special reference to three case study buildings in the cathedral city of Norwich—that the provocative contradictions of late medieval parish “hall churches” enabled parishioners to problematize identity by exploiting the fundamentally pliable relationship between form and meaning in architectural production.

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

Medidas de resistividade elétrica, magnetorresistência e efeito Hall em amostras de grafite modificadas por implantação iônica são apresentadas e discutidas nesta Tese. As experiências de resistividade foram realizadas em função da temperatura com corrente aplicada paralelamente aos planos de grafeno. Medidas de magneto-transporte, na orientação planar, foram realizadas no limite de baixas temperaturas, em campos magnéticos de amplitude – 9 T < B < 9 T aplicados perpendicularmente aos planos de grafeno. Amostras de grafite de diferentes origens foram estudadas. Em conformidade com o fornecedor, tais amostras são eventualmente denominadas GW, ZYA, SPi-I, Kish e Natural. As três primeiras são grafites pirolíticas altamente orientadas (HOPG) e as duas últimas são monocristalinas. Nestas amostras foram feitas implantações com Al, P, Na, Ga e As em até três fluências distintas. Na primeira etapa deste trabalho, foram implantados, em diferentes amostras de grafite SPi-I, íons de alumínio, fósforo e sódio. Diferentes fluências foram empregadas. Medidas de magneto-transporte foram realizadas nesta etapa em cinco temperaturas fixas: T = 2 K, 4 K, 8 K, 12 K e 25 K. Na segunda etapa do trabalho, amostras de todas as grafites foram submetidas à implantação de Ga e As. As medidas de magneto-transporte foram executadas nas temperaturas fixas de T = 2 K, 3 K, 5 K, 7 K e 10 K. Oscilações de Shubnikov-de Haas (SdH) foram observadas tanto nas medidas de magnetorresistência quanto nas medidas de resistividade Hall. Análises desses resultados por meio de transformações de Fourier levaram à obtenção das frequências fundamentais de oscilação e das massas efetivas para elétrons e lacunas tanto no estado puro quanto nos estados implantados de todas as amostras investigadas. As oscilações SdH observadas não revelam efeitos notáveis produzidos por implantação em nenhum dos casos investigados. Medidas de resistividade Hall mostraram variações significativas por efeito de implantação nas amostras: (i) SPi-I irradiadas com Al e P, (ii) GW irradiadas com Ga e As e (iii) Grafite Natural irradiada com As. Em baixos campos magnéticos, efeitos sistemáticos foram observados na resistividade Hall da grafite SPi-I implantada com Al e da grafite GW implantada com As. Para interpretação destes resultados foi proposto um modelo de condução por duas correntes em que a implantação modifica as mobilidades de elétrons e lacunas. A resistividade Hall das amostras GW e ZYA mostra uma reversão de sinal, passando de negativa para positiva em altos campos aplicados. / An experimental study of electrical resistivity, magnetoresistance and Hall Effect in graphite samples modified by ionic implantation is presented in this Thesis. The resistivity measurements were carried out as a function of the temperature with current applied parallel to the graphene sheets. The magneto transport measurements were performed at low temperatures in magnetic fields in the interval -9 T < B < 9 T applied perpendicular to the graphene sheets. Graphite samples from different sources were studied. In accordance to the supplier, these samples are named GW, ZYA, SPi-I, Kish and Natural. The first three samples are highly oriented pyrolytic graphites (HOPG) and the last ones are monocrystaline. In these samples were carried out implantations with Al, P, Na, Ga and As in three different fluences at most. In the first part of this study, aluminum, phosphorous and sodium were implanted in SPi-I graphite samples. Magneto transport measurements were then performed at five fixed temperature, T = 2 K, 4 K, 8 K, 12 K e 25 K. In the second part, the HOPG, Kish and Natural graphite samples were investigated. All of them were submitted to Ga and As implantation. Magnetotransport experiments were carried out in five fixed temperatures, T = 2 K, 3 K, 5 K, 7 K e 10 K. Shubnikov-de Haas oscillations (SdH) were observed in the magnetoresistance as well as in Hall resistivity measurements. Results were analyzed using fast Fourier Transform. Quantum fundamental frequencies and effective masses for electrons and holes were obtained in the pure and implanted states of all investigated samples. The SdH oscillations didn’t reveal significant effects from implantation in all investigated samples. Hall resistivity measurements showed a significative variation upon irradiation in: (i) SPi-I graphite irradiated with Al and P, (ii) GW samples irradiated with Ga and As and (iii) Natural graphite irradiated with As. Systematic effects could be seen in the low field Hall resistivity of SPi-I graphite irradiated with Al and GW irradiated with As. These results were described by a simple twoband model where implantation modifies the electron and hole mobilities. The Hall resistivity of the HOPG GW and ZYA samples revealed a signal reversal in high applied fields.

Orientador: Peter Alexander Bleinroth Schulz / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T18:57:51Z (GMT). No. of bitstreams: 1 AndradeNeto_ManuelAlmeida_D.pdf: 3363262 bytes, checksum: 2dd774f6d30a270dde0494748ef784be (MD5) Previous issue date: 1997 / Resumo: Neste trabalho discutimos as propriedades eletrônicas de um sistema bidimensional com modulação periódica de potencial na presença de um campo magnético perpendicular ao plano do sistema. Trata-se de um problema acadêmico estudado desde os primórdios da Mecânica Quântica, envolvendo espectros de energia auto-similares. A existência de várias questões em aberto e o avanço recente de técnicas experimentais, para fabricação desses sistemas com parâmetro de rede da modulação arbitrário, reforçam o interesse no problema nos últimos anos. Apresentamos um modelo que possibilita estudar unificadamente os regimes de modulação fraca e forte e a transição entre eles. Efeitos de borda em cristais são analisados. Os diferentes limites do problema, bem como a caracterização de estados de um sistema específico (bilhar de Sinai periódico) são discutidos. Finalmente, apresentamos algumas condições mínimas necessárias para a observação experimental desses espectros de energia auto-similares (Borboletas de Hofstadter acopladas) / Abstract: In this work we discuss the electronic properties of a bidimensional system with periodic potential modulation in the presence of a magnetic field perpendicular to the plane of the system. It consist of an academic problem which has been studied since the early days of Quantum Mechanics involving autosimilar energy spectra. The existence of many open questions and the recent advance in experimental techniques, opening the possibility of manufacturing of these systems with arbitrary lattice parameter, have reinforced the interest in the problem in the past years. We present a model that make possible to study in a unified picture the weak modulation regime, the strong modulation regime and the transition between them. Edge effects in crystals were analyzed. The different limits of the problem, and also the characterization of the states of an specific system (Sinai's periodic bilhar) are discussed. Finally, we present some minimal and necessary conditions to observe these autosimilar energy spectra experimentally (coupled Hofstadter's butterfly) / Doutorado / Física / Doutor em Ciências

Orientador: Peter Alexander Bleinroth Schulz / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-10-02T13:05:57Z (GMT). No. of bitstreams: 1 Pereira_AnaLuizaCardoso_M.pdf: 4257154 bytes, checksum: 90636b5d5531fba3a44e56bcb2542f53 (MD5) Previous issue date: 2001 / Resumo: Neste trabalho é investigada numericamente a questão da levitação de estados estendidos em sistemas eletrônicos bidimensionais submetidos a campo magnético. Poucos anos após a descoberta do Efeito Hall Quântico, Laughlin e Khmelnitskii propuseram que os estados estendidos do centro das bandas de Landau deveriam levitar em energia, ultrapassando o nível de Fermi, à medida que o campo magnético tendesse a zero ou a desordem no sistema fosse suficientemente aumentada. Esta proposta de levitação implica em importantes conseqüências para as propriedades de transporte destes sistemas, em particular prevendo transições de fase tipo metal-isolante induzidas por campo magnético. Entretanto, trata-se apenas de uma conjectura, que apesar de estar sendo bastante discutida nos últimos anos, ainda envolve muitas controvérsias e o entendimento da questão ainda contém diversos pontos em aberto. Este trabalho vem dar algumas contribuições para o entendimento deste problema. As simulações numéricas utilizadas envolvem um modelo de rede bidimensional tratada na aproximação tight-binding, considerando elétrons não-interagentes. O grau de localização dos estados eletrônicos é inferido através do cálculo da Razão de Participação. Foi possível identificar claramente a ocorrência do processo de levitação dos estados estendidos, para ambos os modelos de desordem estudados: desordem não-correlacionada tipo ruído branco e desordem correlacionada. Foram obtidas expressões para a dependência da magnitude de levitação observada em função da variação da desordem ou do campo magnético. Estas análises quantitativas permitiram estabelecer comparações quanto à levitação, entre os diferentes modelos de desordem e também entre diferentes bandas de Landau. Os resultados obtidos contribuem para a montagem do real Diagrama de Fases para o Efeito Hall Quântico Inteiro / Abstract: In this work the Ievitation of extended states in two dimensional electron systems in the presence of magnetic field is numerically investigated. Few years after the discovery of the Quantum Hall Effect, Laughlin and Khmelnitskii conjectured that the extended states at the Landau level centers shouId levitate in energy, rising above the Fermi energy, for vanishing magnetic field or sufficiently increasing disorder. This hypothesis Ieads to important consequences to the transport properties of the system, particularly on the magnetic field induced metal-insulator transitions in two dimensions. This conjecture, however, involves many controversial points and, although intensively investigated in the past few years, many open questions remain unanswered. The present work gives some contributions for understanding the problem. The numerical approach uses two dimensional Iattice models treated in a tight-binding framework, considering non interacting electrons. The degree of Iocalization of the electronic states is inferred from Participation Ratios calculations. It was possible to clearly identify the Ievitation of extended states for both disorder models studied: uncorreIated white-noise like and gaussian correlated disorder. Simple expressions for the magnitude of Ievitation as a function of either magnetic field or disorder could be obtained. These quantitative analysis Iead to comparisons among different disorder models, as well as Landau band indexes, concerning the Ievitation. The present results shed some Iight on the building of the actual Phase Diagram for the Quantum HalI Effect / Mestrado / Física / Mestra em Física

Studien utgår från ett projekt som initierats av en förskola där vi som examensarbetesskribenter har haft som uppgift att titta på pedagogernas roll ur ett utomstående perspektiv. Det relationella perspektivet har fått en betydande roll genom hela studien då just mötet mellan pedagog och barn varit i fokus. Syftet med studien är att iaktta pedagogernas bemötande av barnen i hallen ur ett jämlikhetsperspektiv. Första mötet i hallen på morgonen kan ha en varierande betydelse för varje individ. För vissa barn betyder det att man får springa in och leka med kompisar och för andra är det en ledsam stund där man måste lämna sina vårdnadshavare. Därför är hallen intressant att undersöka närmre för att få inblick i hur pedagogerna arbetar när de möter barnen i hallen på morgonen. Studien baseras på semistrukturerade observationer där ett observationsschema följts. Reflekterande samtal har därefter förts med pedagogerna på avdelningen med utgångspunkt i den insamlade empirin från observationerna. Empirin har varit ett verktyg för pedagogerna att bli självmedvetna och uppmuntra till självreflektion kring sin progression. Resultatet visar att pedagogerna ger barn den tid som behövs för en god lämning samt ett bemötande som är anpassat efter varje enskild individ. Detta kan tolkas som att pedagogerna utgår från ett jämlikhetsperspektiv i mötet med barn i hallen.

In this PhD thesis, the fingerprints of geometry and topology on low dimensional mesoscopic systems are investigated. In particular, holographic non-equilibrium transport properties of the quantum spin Hall phase, a two dimensional time reversal symmetric bulk insulating phase featuring one dimensional gapless helical edge modes are studied. In these metallic helical edge states, the spin and the direction of motion of the charge carriers are locked to each other and counter-propagating states at the same energy are conjugated by time reversal symmetry. This phenomenology entails a so called topological protection against elastic single particle backscattering by time reversal symmetry. We investigate the limitations of this topological protection by studying the influence of inelastic processes as induced by the interplay of phonons and extrinsic spin orbit interaction and by taking into account multi electron processes due to electron-electron interaction, respectively. Furthermore, we propose possible spintronics applications that rely on a spin charge duality that is uniquely associated with the quantum spin Hall phase. This duality is present in the composite system of two helical edge states with opposite helicity as realized on the two opposite edges of a quantum spin Hall sample with ribbon geometry. More conceptually speaking, the quantum spin Hall phase is the first experimentally realized example of a symmetry protected topological state of matter, a non-interacting insulating band structure which preserves an anti-unitary symmetry and is topologically distinct from a trivial insulator in the same symmetry class with totally localized and hence independent atomic orbitals. In the first part of this thesis, the reader is provided with a fairly self-contained introduction into the theoretical concepts underlying the timely research field of topological states of matter. In this context, the topological invariants characterizing these novel states are viewed as global analogues of the geometric phase associated with a cyclic adiabatic evolution. Whereas the detailed discussion of the topological invariants is necessary to gain deeper insight into the nature of the quantum spin Hall effect and related physical phenomena, the non-Abelian version of the local geometric phase is employed in a proposal for holonomic quantum computing with spin qubits in quantum dots. / In dieser Doktorarbeit wird der Zusammenhang zwischen den mathematischen Bereichen der modernen Differentialgeometrie sowie der Topologie und den physikalischen Eigenschaften niedrigdimensionaler mesoskopischer Systeme erläutert. Insbesondere werden Phänomene des holographischen Quantentransportes in Quanten Spin Hall Systemen fernab des thermodynamischen Gleichgewichtes untersucht. Die Quanten Spin Hall Phase ist ein zweidimensionaler, zeitumkehrsymmetrischer elektrisch isolierender Zustand, dessen charakteristische Eigenschaft eindimensionale metallische Randzustände sind. Diese im Englischen als “helical edge states” bezeichneten Randkanäle zeichnen sic h dadurch aus, dass Spin und Bewegungsrichtung der Ladungsträger fest miteinander verknüpft sind und zwei Zustände mit gleicher Energie aber unterschiedlicher Bewegungsrichtung stets durch die Symmetrieoperation der Zeitumkehr zusammenhängen. Diese Phänomenologie bedingt einen sogenannten topologischen Schutz durch Zeitumkehrsymmetrie gegen elastische Einteilchenrückstreuung. Wir beschäftigen uns mit den Grenzen dieses Schutzes, indem wir inelastische Rückstreuprozesse in Betracht ziehen, wie sie etwa durch das Wechselspiel von extrinsischer Spin-Bahn Kopplung und Gitterschwingungen induziert werden können, oder aber indem wir Mehrteilchen-Streuprozesse untersuchen, welche die Coulomb-Wechselwirkung ermöglicht. Desweiteren werden Anwendungen aus dem Gebiet der Spintronik vorgeschlagen, welche auf einer dem Quanten Spin Hall Effekt eigenen Dualität zwischen dem Spin und dem Ladungsfreiheitsgrad beruhen. Diese Dualität existiert in einem aus zwei Randzuständen mit entgegengesetzter Helizität zusammengesetzten System, wie etwa durch zwei gegenüberliegende Ränder einer streifenförmigen Probe im Quanten Spin Hall Zustand realisiert. Konzeptionell gesehen ist der Quanten Spin Hall Zustand das erste experimentell nachgewiesene Beispiel eines symmetriegeschützten topologischen Zustandes nichtwechselwirkender Materie, also eines Bandisolators, welcher eine antiunitäre Symmetrie besitzt und sich von einem trivialen Isolator mit gleicher Symmetrie aber ausschliesslich lokalisierten und daher voneinander unabhängigen atomaren Orbitalen topologisch unterscheidet. Im ersten Teil dieser Dissertation geben wir eine Einführung in die theoretischen Konzepte, welche dem Forschungsgebiet der nichtwechselwirkenden topologischen Zustände zugrunde liegen. In diesem Zusammenhang werden die topologischen Invarianten, welche diese neuartigen Zustände charakterisieren, als globales Analogon zur lokalen geometrischen Phase dargestellt, welche mit einer zyklischen adiabatischen Entwicklung eines physikalischen Systems verknüpft ist. Während die ausführliche Diskussion der globalen Invarianten einem tieferen Verständnis des Quanten Spin Hall Effektes und damit verwandten physikalischen Phänomenen dienen soll, wird die nicht-Abelsche Variante der lokalen geometrischen Phase für einen Vorschlag zur Realisierung von holonomiebasierter Quanteninformationsverarbeitung genutzt. Das Quantenbit der von uns vorgeschlagenen Architektur ist ein in einem Quantenpunkt eingesperrter Spinfreiheitsgrad.