This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.

A self-terminated electrochemical method was used to fabricate microscopic-scale contacts between two Au electrodes in a microfluidic channel. The conductance of contacts varies in a stepwise fashion showing quantization near the integer multiples of the conductance quantum ( ). The mechanism works by a pressure-driven flow parallel to a pair of Au electrodes with a gap on the order of micron in an electrolyte of HCl. When applying a bias voltage between two electrodes, metal atoms are etched off the anode and dissolved into the electrolyte as metal ions, which are then deposited onto the cathode. Consequently, the gap decreases to the atomic scale and then completely closes as the two electrodes form a contact. The electrochemical fabrication approach introduces large variance in the formation and location of individual junctions. Understanding and controlling this process will enable the precise positioning of reproducible geometries into nano-electronic devices.

This thesis deals with electron correlation effects within low-dimensional, mesoscopic systems. We study phenomena within two different types of system in which correlations play an important role. The first involves the spectra and spin structure of small symmetric quantum dots, or &quoteartificial atoms&quote. The second is the &quote0.7 structure&quote, a well-known but mysterious anomalous conductance plateau which occurs in the conductance profile of a quantum point contact. Artificial atoms are manufactured mesoscopic devices: quantum dots which resemble real atoms in that their symmetry gives them a &quoteshell structure&quote. We examine two-dimensional circular artificial atoms numerically, using restricted and unrestricted Hartree-Fock simulation. We go beyond the mean-field approximation by direct calculation of second-order correlation terms; a method which works well for real atoms but to our knowledge has not been used before for quantum dots. We examine the spectra and spin structure of such dots and find, contrary to previous theoretical mean-field studies, that Hund's rule is not followed. We also find, in agreement with previous numerical studies, that the shell structure is fragile with respect to a simple elliptical deformation. The 0.7 structure appears in the conductance of a quantum point contact. The conductance through a ballistic quantum point contact is quantised in units of 2e^2/h. On the lowest conductance step, an anomalous narrow conductance plateau at about G = 0.7 x 2e^2/h is known to exist, which cannot be explained in the non-interacting picture. Based on suggestive numerical results, we model conductance through the lowest channel of a quantum point contact analytically. The model is based on the screening of the electron-electron interaction outside the QPC, and our observation that the wavefunctions at the Fermi level are peaked within the QPC. We use a kinetic equation approach, with perturbative account of electron-electron backscattering, to demonstrate that these simple features lead to the existence of a 0.7-like structure in the conductance. The behaviour of this structure reproduces experimentally observed features of the 0.7 structure, including the temperature dependence and the behaviour under applied in-plane magnetic fields.

No description available.

<p>In this work, we study two important themes in the physics of the interacting one-dimensional (1D) electron gas: the transition from one-dimensional to higher dimensional behavior, and the role of inhomogeneity. The interplay between interactions, reduced dimensionality, and inhomogeneity drives a rich variety of phenomena in mesoscopic physics. In 1D, interactions fundamentally alter the nature of the electron gas, and the homogeneous 1D electron gas is described by Luttinger Liquid theory. We use Quantum Monte Carlo methods to study two situations that are beyond Luttinger Liquid theory --- the quantum phase transition from a linear 1D electron system to a quasi-1D zigzag arrangement, and electron localization in quantum point contacts. </p><p>Since the interacting electron gas has fundamentally different behavior in one dimension than in higher dimensions, the transition from 1D to higher dimensional behavior is of both practical and theoretical interest. We study the first stage in such a transition; the quantum phase transition from a 1D linear arrangement of electrons in a quantum wire to a quasi-1D zigzag configuration, and then to a liquid-like phase at higher densities. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition occurs even in narrow wires with strong quantum fluctuations, and that it has characteristics which are qualitatively different from the classical transition.</p><p>Experiments in quantum point contacts (QPC's) show an unexplained feature in the conductance known as the ``0.7 Effect''. The presence of the 0.7 effect is an indication of the rich physics present in inhomogeneous systems, and we study electron localization in quantum point contacts to evaluate several different proposed mechanisms for the 0.7 effect. We show that electrons form a Wigner crystal in a 1D constriction; for sharp constriction potentials the localized electrons are separated from the leads by a gap in the density, while for smoother potentials, the Wigner crystal is smoothly connected to the leads. Isolated bound states can also form in smooth constrictions if they are sufficiently long. We thus show that localization can occur in QPC's for a variety of potential shapes and at a variety of electron densities. These results are consistent with the idea that the 0.7 effect and bound states observed in quantum point contacts are two distinct phenomena.</p> / Dissertation

The electrical and thermal conductance and the Seebeck coefficient are calculated for one-dimensional systems, and their behavior as a function of temperature and chemical potential is investigated. It is shown that the conductances are proportional to an average of the transmission probability around the Fermi level with the average taken for the thermal conductance being over a wider range. This has the effect of creating less well-defined plateaus for thermal-conductance quantization experiments. For weak non-linearities, the charge and entropy currents across a quantum point contact are expanded as a series in powers of the applied bias voltage and the temperature difference. After that, the expansions of the Seebeck voltage in temperature difference and the Peltier heat in current are obtained. Also, it is shown that the linear thermal conductance of a quantum point contact displays a half-plateau structure, almost flat regions appearing around half-integer multiples of the conductance quantum. This structure is investigated for the saddle-potential model.

La technique de la microscopie à grille de balayage (SGM) consiste à mesurer la conductance d'un gaz bidimensionnel d'électrons (2DEG) sous l'influence d'une pointe balayant la surface de l'échantillon. Dans ce travail, une approche analytique complétée par des simulations numériques est développée pour étudier la relation entre les mesures SGM et les propriétés électroniques locales dans des systèmes mésoscopiques. La correspondance entre la réponse SGM et la densité locale partielle (PLDOS) est étudiée pour un contact quantique entouré d’un 2DEG en présence ou en absence de désordre, pour une pointe perturbative ou non perturbative. Une correspondance SGM-PLDOS parfaite est trouvée pour des transmissions entières et des pointes locales. La dégradation de la correspondance en dehors de cette situation est étudiée. D’autre part, la liaison entre la réponse SGM et la transformée de Hilbert de la densité locale est discutée. Pour étudier le rôle de la force de la pointe sur la conductance SGM, une formule analytique donnant la conductance totale est obtenue. Dans le cas d'une pointe à taille finie nous proposons une méthode basée sur les fonctions de Green permettant de calculer la conductance en connaissant les propriétés non-perturbées. En plus, nous avons étudié la dépendance des branches de la PLDOS en fonction de l’énergie de Fermi. / The scanning gate microscopy (SGM) technique consists in measuring the conductance of a two dimensional electron gas (2DEG) under the influence of a scanning tip. In this work, an analytical approach complemented by numerical simulations is developed to study the connection between SGM measurements and local electronic properties in mesoscopic devices. The connection between the SGM response and the partial local density of states (PLDOS) is studied for the case of a quantum point contact surrounded by clean or disordered 2DEG for perturbative or non-perturbative, local or extended tips. An SGM-PLDOS correspondence is found for integer transmissions and local tips. The degradation of this correspondence out of these conditions is studied. Moreover, a presumed link between the SGM response and the Hilbert transform of the LDOS is discussed. To study the role of the tip strength, an analytical formula giving the full conductance in the case of local tips is obtained. Furthermore, a Green function method enabling to calculate the quantum conductance in the presence of a finite size tip in terms of the unperturbed properties is proposed. Finally the dependence of the PLDOS branches on the Fermi energy is studied.

This work is concerned with the theoretical description of the Scanning Gate Microscopy (SGM) in general and with solving particular models of the quantum point contact (QPC) nanostructure, analytically and numerically. SGM is an experimental technique, which measures the conductance of a nanostructure, while a charged AFM tip is scanned above its surface. It gives many interesting results, such as lobed and branched images, interference fringes and a chequerboard pattern. A generally applicable theory, allowing for unambiguous interpretation of the results, is still missing. Using the Lippman-Schwinger scattering theory, we have developed a perturbative description of non-invasive SGM signal. First and second order expressions are given, pertaining to the ramp- and plateau-regions of the conductance curve. The maps of time-reversal invariant (TRI) systems, tuned to the lowest conductance plateau, are related to the Fermi-energy charge density. In a TRI system with a four-fold spatial symmetry and very wide leads, the map is also related to the current density, on any plateau. We present and discuss the maps calculated for two analytically solvable models of the QPC and maps obtained numerically, with Recursive Green Function method, pointing to the experimental features they reproduce and to the fundamental difficulties in obtaining good plateau tuning which they reveal.

Ce travail porte sur la description théorique de la microscopie à grille locale (SGM) et sur la résolution de modèles particuliers de contacts quantiques (QPC), analytiquement et numériquement. SGM est une technique expérimentale, qui mesure la conductance d'une nanostructure, lorsqu'une pointe de microscope a force atomique chargée balaye la surface, sans contacter cette dernière. Les images de SGM révèlent de nombreuses traits intéressants, tels que des lobes, des branches, des franges d'interférence et des motifs de damier. Aucune théorie généralement applicable, donnant une interprétation univoque, n’est disponible à ce jour. En utilisant la théorie de la diffusion de Lippman–Schwinger, nous avons développé une description perturbative de signal de SGM non invasive. Les expressions du premier et du second ordre ont été données, se rapportant aux régions de marche et de plateau de la courbe de conductance. Dans les systèmes invariants par renversement du temps (TRI), adaptés au premier plateau de conductance, les images SGM sont liées à la densité de charge à l`énergie de Fermi. Dans un système TRI, avec une symétrie spatiale centrale et de très larges contacts, les images sont aussi liées à la densité de courant, quelque soit le plateau. Nous présentons et discutons les images calculées pour deux modèles analytiques de QPC et les images obtenues numériquement avec la méthode des fonctions de Green récursives, reproduisant certains motifs observés expérimentalement, et pointant les difficultés fondamentales a se bien positionner sur le plateau de conductance. / This work is concerned with the theoretical description of the Scanning Gate Microscopy (SGM) in general and with solving particular models of the quantum point contact (QPC) nanostructure, analytically and numerically. SGM is an experimental technique, which measures the conductance of a nanostructure, while a charged AFM tip is scanned above its surface. It gives many interesting results, such as lobed and branched images, interference fringes and a chequerboard pattern. A generally applicable theory, allowing for unambiguous interpretation of the results, is still missing. Using the Lippman-Schwinger scattering theory, we have developed a perturbative description of non-invasive SGM signal. First and second order expressions are given, pertaining to the ramp- and plateau-regions of the conductance curve. The maps of time-reversal invariant (TRI) systems, tuned to the lowest conductance plateau, are related to the Fermi-energy charge density. In a TRI system with a four-fold spatial symmetry and very wide leads, the map is also related to the current density, on any plateau. We present and discuss the maps calculated for two analytically solvable models of the QPC and maps obtained numerically, with Recursive Green Function method, pointing to the experimental features they reproduce and to the fundamental difficulties in obtaining good plateau tuning which they reveal.