In the first part of this work, we describe a theory of the ground states and charge gaps in the fractional quantum Hall states of graphene. The theory relies on knowledge of these properties for filling fractions smaller than one. Then, by the application of two mapping rules, one is able to obtain these properties for fractional quantum Hall states at arbitrary fillings, by conceiving the quantum Hall ferromagnets as vacua on which correlated electrons or correlated holes are added. The predicted charge gaps and phase transitions between different fractional quantum Hall states are in good agreement with recent experiments. In the second part, we investigate the low energy theory for the neutral Landau level of bilayer graphene. We closely analyze the way different terms in the Hamiltonian transform under the action of particle-hole conjugation symmetries, and identify several terms that are relevant in explaining the lack of such symmetry in experiments. Combining an accurate parametrization of the electronic structure of bilayer graphene with a systematic account of the impact of screening we are able to explain the absence of particle-hole symmetry reported in recent experiments. We also study the energetics of fractional quantum Hall states with coherence between n=0 and n=1 cyclotron quantum numbers, and obtain a general formula to map the two-point correlation function from their well-known counterparts made from only n=0 quantum numbers. Bilayer graphene has the potential for realizing these states which have no analogue in other two-dimensional electron systems such as Gallium Arsenide. We apply this formula to describe the properties of the n=0/n=1 coherent Laughlin state which displays nematic correlations. / text

Two dimensional (2D) systems with low carrier density is an outstanding platform for studying a wide spectrum of physics. These include both classical and quantum effects, arising from disorder, Coulomb interactions and even non-trivial topological properties of band-structure. In this thesis, we have explored the physics at low carrier number density in GaAs/AlGaAs heterostructure and bilayer graphene, by investigating in a larger phase space using a variety of electrical measurement tools. A two-dimensional electron system (2DES) formed in a GaAs/AlGaAs heterostructure offers an avenue to build a variety of mesoscopic devices, primarily because its surface gates can very effectively control its carrier density profile. In the first half of the thesis, we study the relevance of disorder in two kinds of devices made in a 2DES. A very strong negative gate voltage not only reduces the carrier density of the 2DES, but also drives it to a disordered state. In this state, we explore a new direction in parameter space by increasing in-plane electric field and investigating its magneto-resistance (MR). At sufficiently strong gate voltage and source-drain bias, we discover a remarkably linear MR. Its enormous magnitude and weak temperature dependence indicate that this is a classical effect of disorder. In another study, we examine a specially designed dual-gated device that can induce low number density in a periodic pattern. By applying appropriate gate voltages, we demonstrate the formation of an electrostatically tunable quantum dot lattice and study the impact of disorder on it. This work is important in paving way for solid state based platform for experimental simulations of artificial solids. The most striking property of bilayer graphene is the ability to open its band gap by a perpendicular electric field, giving the prospects of enabling a large set of de-vice applications. However, despite a band gap, a number of transport mechanisms are still active at very low densities that range from hopping transport through bulk to topologically protected 1D transport at the edges or along 1D crystal dislocations. In the second half of the thesis, we have used higher order statistical moment of resistance/conductance fluctuations, namely the variance of the fluctuations, to complement averaged resistance/conductance, and study and infer the dominant transport mechanism at low densities in a gapped bilayer graphene. Our results show possible evidence of percolative transport and topologically protected edge transport at different ranges of low number densities. We also explore the same phase space by studying its mesoscopic conductance fluctuations at very low temperatures. This is the first of its kind systematic experiment in a dual-gated bilayer graphene device. Its conductance fluctuations have several anomalous features suggesting non-universal behaviour which is at odds with conventional disordered systems.

This thesis consists of two parts. The first part considers the effect of microwave radiation on magnetotransport in high quality GaAs/AlGaAs heterostructure two dimensional electron systems. The effect of microwave (MW) radiation on electron temperature was studied by investigating the amplitude of the Shubnikov de Haas (SdH) oscillations in a regime where the cyclotron frequency $\omega_{c}$ and the MW angular frequency $\omega$ satisfy $2\omega \leq \omega_{c} \leq 3.5\omega$. The results indicate negligible electron heating under modest MW photoexcitation, in agreement with theoretical predictions. Next, the effect of the polarization direction of the linearly polarized MWs on the MW induced magnetoresistance oscillation amplitude was investigated. The results demonstrate the first indications of polarization dependence of MW induced magnetoresistance oscillations. In the second part, experiments on the magnetotransport of three dimensional highly oriented pyrolytic graphite (HOPG) reveal a non-zero Berry phase for HOPG. Furthermore, a novel phase relation between oscillatory magneto- and Hall- resistances was discovered from the studies of the HOPG specimen.

Electrical transport in materials is typically diffusive, due to dominant momentum-relaxing scattering of carriers with the phonons or defects. In ultraclean material systems such as GaAs/AlGaAs or graphene/hBN heterostructures, momentum-relaxing can be suppressed, leading to the onset of non-diffusive transport regimes, where Ohm's law is no longer valid. Within these non-diffusive regimes, the hydrodynamic regime occurs when momentum-conserving electron-electron scattering length scale is smaller than the device length scale (usually at intermediate temperatures). On the other hand, weak electron-electron scattering (at low temperatures) results in ballistic transport, commonly understood using the familiar single-particle framework of injected carriers travelling in straight line trajectories with intermittent reflections off device boundaries. Both the ballistic and hydrodynamic regimes can exhibit a emph{negative} nonlocal resistance, and collective behaviour such as the formation of current vortices. In this work, we study nonlocal current-voltage characteristics in mesoscopic devices fabricated from a GaAs/AlGaAs heterostructure that hosts a two-dimensional electron system in a GaAs quantum well. First, we report a quadratic non-linearity in the nonlocal current-voltage characteristics that manifests in any device where a nonlocal voltage measurement is possible. Using measurements at low temperatures ($sim$ 4 K) across multiple devices and considering various contact configurations for each device, we show that the non-linearity is universal. We apply the non-linearity to rectification and frequency multiplication. We also report on a periodic peaks in the nonlocal voltage vs. magnetic field, in an enclosed mesoscopic geometry in which transverse magnetic focusing (TMF) is typically studied. These peaks occur at weak magnetic fields, are independent of the source-detector separation and are distinct from TMF. Our experimental findings are backed by an extensive set of simulations using in both the semiclassical as well as quantum-coherent transport models. / Master of Science / Current is made up of charged particles such as electrons moving through a material. Typically, current is proportional to the applied voltage and flows from higher to lower potential within the device with the potential decreasing monotonically as we move from the source contact to the drain contact irrespective of the path taken through the device. This is commonly known as Ohm's law, and is followed in most materials we come across. The motion of electrons carrying this current is akin to the motion of balls inside a pinball machine, their momentum randomized by intermittent collisions due to lattice vibrations, defects and impurities present in the material. In ultraclean two-dimensional materials at low-intermediate temperatures (where lattice vibration is weak), these collisions become sparse. Collisions of electrons with other electrons now become important. When electron-electron collisions are frequent, the electrons collectively behave like a fluid, giving rise to so called hydrodynamic transport. On the other hand, when electron-electron collisions are sparse as well, electrons move unhindered in ballistic straight line trajectories until they reflect off the device boundaries. This is known as ballistic transport. Under both these transport regimes, Ohm's law breaks down, leading to interesting physical phenomena such as the formation of current whirlpools. In this work, we study the voltage measured at a point in the device which is distinct from the point where current is injected or extracted. This is commonly known as the nonlocal voltage. We explore the relationship between the nonlocal voltage and the injected current and find it to be significantly different from predictions made by Ohm's law. We use this novel current-voltage relationship to build a rectifier and frequency multiplier - two devices commonly used in high-frequency detection, radar systems and telecommunications. We also report previously unseen periodic oscillations in the nonlocal voltage when the magnetic field perpendicular to the device is varied. Using high-resolution simulations, we show the these oscillations can not be explained by looking at individual electron paths, and arise due to contribution from all electrons that travel through the device.

No description available.

It is well known from Mermin-Wagner theorem that a two dimensional(2D) system with continuous symmetry can have no long-range order at finite temperature. However such systems can undergo a transition from a low temperature phase with quasi-long range order to a disordered phase at high temperatures. This is known as Berezinskii Kosterlitz Thouless (BKT) transition. The BKT transition is characterized by the presence of bound vortex pairs at low temperature which dissociate into free vortices above the critical temperature and has been observed in thin superconducting films, 2D superfluids, 2D liquid crystals etc. In this thesis work, we have used resistance/current fluctuations (low frequency/shotnoise) as a probe to investigate the BKT transition in different 2D systems. This work can be divided into three parts: In the first part, we probe the ground state of interacting electrons in 2D in the presence of disorder. We show that at low enough temperatures (~ 270mK),the conductivity tends to zero at a nonzero carrier density with a BKT-like transition. Our experiments with many two dimensional electron systems in GaAs/AlGaAs heterostructures suggest that the charge transport at low carrier densities is due to the melting of an underlying ordered ground state through proliferation of topological defects. Independent measurement of low-frequency conductivity noise supports this scenario. In the second part, we probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultrathin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and BKT type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depends strongly on the roughness and structural inhomogeneity of the superconducting films. In the final part of the thesis, we explore the transport mechanism in disordered 2D superconductors using shot noise. The resistivity shows an activated transport in the patterned ultrathin films of NbN at low temperatures signifying the presence of large scale inhomogeneities in the sample. The measurement of current fluctuations yield a giant excess noise at low temperatures which eventually decreases below the measurement background at a temperature corresponding to the normal state of the original sample(before patterning). We attribute the enhancement in the shot noise to a possible occurrence of multiple Andreev reflections occurring in a network of SNS(superconductor-normal-superconductor) junctions formed due to the interplay of disorder and superconducting fluctuations.

Les matériaux dans lesquels des interactions à plusieurs particules, un confinement de faible dimension et/ou un fort couplage spin-orbite sont présents témoignent d’une grande variété de phénomènes, mais sont encore mal compris. Des informations essentielles sur l’origine de tels phénomènes peuvent être obtenues en mesurant leur structure électronique. Cette thèse présente une étude expérimentale de la structure électronique de matériaux de faible dimension et/ou fortement corrélés présentant un intérêt fondamental actuel, en utilisant la spectroscopie par photoémission résolue en angle et en spin (ARPES et SARPES).Dans la partie introductive, je présente mon travail sur deux exemples de type "livre de texte", mais innovants, montrant comment les interactions affectent la structure de bande d'un matériau: le couplage des électrons avec des phonons dans une distribution de Debye dans un système électronique à deux dimensions (2DES) dans ZnO, semi-conducteur à oxyde à bande interdite large utilisé dans les applications photovoltaïques, et le dédoublement induit par un fort couplage spin-orbite (SOC) dans la bande de valence du ZnTe, un autre semi-conducteur important utilisé dans les dispositifs optoélectroniques. Ensuite, dans la suite de cette thèse, je discute de mes résultats originaux dans trois systèmes différents de basse dimensionnalité et d'intérêt actuel en recherche : 1.La réalisation d'un 2DES à la surface (110) de SnO₂, le premier du genre dans une structure rutile. L'ajustabilité de la densité de ses porteurs au moyen de la température ou du dépôt d'Eu, et la robustesse vis-à-vis les reconstructions de surface et l'exposition aux conditions ambiantes rendent ce 2DES prometteur pour les applications. Au moyen d'une simple réaction redox à la surface, ces travaux ont prouvé que les lacunes en oxygène pouvaient doper la bande de conduction à la surface de SnO₂, résolvant ainsi un problème longtemps débattu concernant le rôle desdites lacunes dans le dopage de type n dans SnO₂. 2.L'étude des états de surface topologiques dans M₂Te₂X (avec M = Hf, Zr ou Ti; et X = P ou As), une nouvelle famille de métaux topologiques en trois dimensions, provenant du SOC et étant protégés par la symétrie du renversement du temps. Leur structure électronique et leur texture de spin, étudiées par ARPES et SARPES, révèlent la présence de fermions de Dirac sans masse donnant naissance à des arcs de nœuds de Dirac. 3.L'étude du matériau YbNi₄P₂ à fermions lourds quasi unidimensionnel, qui présente une transition de phase quantique de second ordre d’une phase ferromagnétique à une phase paramagnétique de liquide de Fermi lors de la substitution partielle du phosphore par l'arséniure. Une telle transition ne devrait se produire que dans les systèmes zéro ou unidimensionnels, mais la mesure directe de la structure électronique des matériaux ferromagnétiques quantiques critiques faisait jusqu'à présent défaut. Grâce à une préparation et nettoyage méticuleux in situ de la surface des monocristaux YbNi₄P₂, qui sont impossibles à cliver, leur structure électronique a été mesurée avec succès au moyen de l'ARPES, dévoilant ainsi le caractère quasi-1D, nécessaire à la compréhension de la criticité quantique ferromagnétique, dans YbNi₄P₂. Le protocole utilisé pour rendre ce matériau accessible à l'ARPES peut être facilement généralisé à d'autres matériaux exotiques dépourvus de plan de clivage. / Materials in which many-body interactions, low-dimensional confinement, and/or strong spin-orbit coupling are present show a rich variety of phenomena, but are still poorly understood. Essential information about the origin of such phenomena can be obtained by measuring their electronic structure. This thesis presents an experimental study of the electronic structure of some low-dimensional and/or strongly correlated materials of current fundamental interest, using angle- and spin-resolved photoemission spectroscopy (ARPES and SARPES). In the introductory part, I present my work on two innovative textbook examples showing how interactions affect the band structure of a material: the coupling of electrons with phonons in a Debye distribution in a two-dimensional electron system (2DES) in ZnO, a wide-band-gap oxide semiconductor used in photovoltaic applications, and the splitting induced by strong spin-orbit coupling (SOC) in the bulk valence band of ZnTe, another important semiconductor used in optoelectronic devices. Then, in the rest of this thesis, I discuss my original results in three different low-dimensional systems of current interest: 1.The realisation of a 2DES at the (110) surface of SnO₂, the first of its kind in a rutile structure. Tunability of its carrier density by means of temperature or Eu deposition and robustness against surface reconstructions and exposure to ambient conditions make this 2DES promising for applications. By means of a simple redox reaction on the surface, this work has proven that oxygen vacancies can dope the conduction band minimum at the surface of SnO₂, solving a long-debated issue about their role in n-type doping in SnO₂. 2.The study of topological surface states in M₂Te₂X (with M = Hf, Zr, or Ti; and X = P or As), a new family of three-dimensional topological metals, originating from SOC and being protected by time-reversal symmetry. Their electronic structure and spin texture, studied by ARPES and SARPES, reveal the presence of massless Dirac fermions giving rise to Dirac-node arcs. 3.The investigation of the quasi-one-dimensional heavy-fermion material YbNi₄P₂, which presents a second-order quantum phase transition from a ferromagnetic to a paramagnetic phase upon partial substitution of phosphorous by arsenide. Such a transition is expected to occur only in zero- or one-dimensional systems, but a direct measurement of the electronic structure of ferromagnetic quantum-critical materials was missing so far. By careful in-situ preparation and cleaning of the surface of YbNi₄P₂ single crystals, which are impossible to cleave, their electronic structure has been successfully measured by ARPES, thus effectively unveiling the quasi-one-dimensionality of YbNi₄P₂. Moreover, the protocol used to make this material accessible to ARPES can be readily generalised to other exotic materials lacking a cleavage plane.