Semiconductor–superconductor hybrid systems are promising candidates for the realization of Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the non-trivial phase. The transition between the trivial and nontrivial phase is reflected in the closing and reopening of an excitation gap. We show that the signatures of topological order are robust against details of the geometry, electrostatic disorder and the existence of additional subbands and only rely on the topology of the nanowire and the existence of a superconducting gap. Finally, we show that the coherence length in the non-trivial phase is much longer than in the trivial phase. This opens the possibility to coat the nanowire with superconducting nanograins and thereby significantly reduce the current due to cotunnelling of Cooper pairs and to enhance the Coulomb charging energy without destroying the superconducting gap.

Neste trabalho é apresentado o cálculo, pelo grupo de renormalização numérico, da condutância AC através de uma nanoestrutura acoplada a gases eletrônicos, a baixa temperatura e no regime de resposta linear. Este sistema apresenta a competição entre dois efeitos: blo¬queio Coulombiano e efeito Kondo. Nosso modelo considera gases eletrônicos unidimensionais que são unidos pelas extremidades para formar um anel, no qual a corrente é induzida por um fluxo magnético oscilante com freqüência . Nós partimos de um modelo tight-binding de vizinhos mais próximos para os gases eletrônicos e, deste modo, o potencial vetor é facilmente incorporado ao Hamiltoniano por condições de contorno torsionais. Uma barreira de potencial entre os gases eletrônicos e a nanoestrutura é simulada em termos de uma taxa de tunelamento entre a nanoestrutura e os sítios adjacentes menor que aquela entre entre sítios vizinhos no anel. A capacitância da nanoestrutura é pequena, o que implica que nós podemos considerar mudanças no número de elétrons dentro da mesma por apenas uma unidade. Como conseqüência, o Hamiltoniano é mapeado no Hamiltoniano de Anderson com correlação U entre os elétrons. Uma voltagem de gate controla a energia da impureza (da nanoestrutura), 0. Plotada como função de , a condutância mostra dois picos característicos do bloqueio Coulombiano, em freqüências correspondentes às energias para adicionar um elétron à nanoestrutura e para remover um elétron da nanoestrutura respectivamente. No regime Kondo, 0 > 0 > -U (ou seja, para voltagens de gate tais que a nanoestrutura isolada teria estado fundamental com degenerescência de spin), um pico (Kondo) adicional aparece próximo à = 0. Plotada como função de Vg, a condutância DC mostra um largo pico no regime Kondo, caindo rapidamente a zero para voltagens resultando em um estado fundamental não degenerado para a nanoestrutura isolada. Uma relação entre a condutância e a densidade espectral do nível da impureza é obtida e utilizada para interpretar os resultados numéricos. / In this work a renormalization-group calculation of the low-temperature AC conductance in the linear response regime through a nanostructure coupled to metallic leads is presented. This system shows a competition between two effects: the Coulomb blockade and the Kon¬do effect. Our model considers one-dimensional leads which are connected to form a ring, in which a current is induced by a magnetic flux oscillating at the frequency . We start from a nearest-neighbor tight-binding model for the leads and in this way the potential vector is easily incorporated in the model Hamiltonian by twisting boundary conditions. A potential barrier between the leads and the nanostructure is simulated in terms of a tunneling rate between the nanostructure and the adjacent sites in the leads, which is smaller than the one between neighbors sites in the leads. The capacity of the nanostructure is small, which implies that substantial energy changes are associated with each electron transfered to the nanostructure. As a consequence, the model Hamiltonian maps onto the spin-degenerate Anderson Hamiltoni¬an with correlation U between the electrons. A gate voltage Vg controls the impurity (i.e., nanostructure) energy 0. Plotted as a function of , the conductivity shows two Coulomb-blockade peaks, at the energy needed to add an electron to and to remove an electron from the nanostructure, respectively. In the Kondo regime 0 > 0 > -U (i.e., for gate voltages such that the isolated nanostructure would have a spin-degeneration ground state), an addition (Kondo) peak appears near = 0. Plotted as functions of Vg, the static conductivity shows a broad peak in the Kondo regime and drops rapidly to zero for voltages resulting in a non-degenerate nanostructure ground state. A relation between the conductance and the spectral density of the impurity is obtained and used to interpret the numerical results.

To study transport properties in single InAs nanowires (NW) with etched constrictions, a bunch of back-gated single InAs NW devices were made. The standard device contained a NW section with an etched constriction, placed between two pre-patterned side-gates. For comparison, devices either without etched constriction or without side-gates were also fabricated. Transport measurement results of three devices were presented and discussed. The device without side-gates exhibited Coulomb blockade due to electron tunneling through double quantum dots (QDs). The device without the etched constriction displayed conductance quantization. The standard device showed both Coulomb blockade (due to electron tunneling through either multiple QDs or single QD) and Fabry-Perot conductance oscillation at different gate bias regime. A 3-D electrostatic and 2-D eigenvalue coupled simulation was conducted to explain the observed conductance quantization. This model suggests that the nonuniform potential distribution in a thick NW dramatically modifies the confinement energies in the NW.

To study transport properties in single InAs nanowires (NW) with etched constrictions, a bunch of back-gated single InAs NW devices were made. The standard device contained a NW section with an etched constriction, placed between two pre-patterned side-gates. For comparison, devices either without etched constriction or without side-gates were also fabricated. Transport measurement results of three devices were presented and discussed. The device without side-gates exhibited Coulomb blockade due to electron tunneling through double quantum dots (QDs). The device without the etched constriction displayed conductance quantization. The standard device showed both Coulomb blockade (due to electron tunneling through either multiple QDs or single QD) and Fabry-Perot conductance oscillation at different gate bias regime. A 3-D electrostatic and 2-D eigenvalue coupled simulation was conducted to explain the observed conductance quantization. This model suggests that the nonuniform potential distribution in a thick NW dramatically modifies the confinement energies in the NW.

xvi, 116 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / This dissertation focuses on low-dimensional electron transport phenomena in devices ranging from semiconductor electron 'billiards' to semimetal atomic clusters to gold nanoparticles. In each material system, the goal of this research is to understand how carrier transport occurs when many elements act in concert. In the semiconductor electron billiards, magnetoconductance fluctuations, the result of electron quantum interference within the device, are used as a probe of electron transport through arrays of one, two, and three connected billiards. By combining two established analysis techniques, this research demonstrates a novel method for determining the quantum energy level spacing in each of the arrays. That information in turn shows the extent (and limits) of the phase-coherent electron wavefunction in each of the devices. The use of the following two material systems, the semimetal atomic clusters and the gold nanoparticles, is inspired by the electron billiard results. First, the output of the simple, rectangular electron billiards, the magnetoconductance fluctuations, is quite generally found to be fractal. This research addresses the question of what output one might expect from a device with manifestly fractal geometry by simulating the electrical response of fractal resistor networks and by outlining a method to implement such devices in fractal aggregates of semimetal atomic clusters. Second, in gold nanoparticle arrays, the number of array elements can increase by orders of magnitude over the billiard arrays, all with the potential to stay in a similar, phase-coherent transport regime. The last portion of this dissertation details the fabrication of these nanoparticle-based devices and their electrical characteristics, which exhibit strong evidence for electron transport in the Coulomb-blockade regime. A sketch for further 'off-blockade' experiments to realize magnetoconductance fluctuations, i.e. phase-coherent electron phenomena, is presented. / Committee in charge: Jens Noeckel, Chairperson, Physics; Richard Taylor, Member, Physics; Heiner Linke, Member, Physics; David Strom, Member, Physics; James Hutchison, Outside Member, Chemistry

Neste trabalho é apresentado o cálculo, pelo grupo de renormalização numérico, da condutância AC através de uma nanoestrutura acoplada a gases eletrônicos, a baixa temperatura e no regime de resposta linear. Este sistema apresenta a competição entre dois efeitos: blo¬queio Coulombiano e efeito Kondo. Nosso modelo considera gases eletrônicos unidimensionais que são unidos pelas extremidades para formar um anel, no qual a corrente é induzida por um fluxo magnético oscilante com freqüência . Nós partimos de um modelo tight-binding de vizinhos mais próximos para os gases eletrônicos e, deste modo, o potencial vetor é facilmente incorporado ao Hamiltoniano por condições de contorno torsionais. Uma barreira de potencial entre os gases eletrônicos e a nanoestrutura é simulada em termos de uma taxa de tunelamento entre a nanoestrutura e os sítios adjacentes menor que aquela entre entre sítios vizinhos no anel. A capacitância da nanoestrutura é pequena, o que implica que nós podemos considerar mudanças no número de elétrons dentro da mesma por apenas uma unidade. Como conseqüência, o Hamiltoniano é mapeado no Hamiltoniano de Anderson com correlação U entre os elétrons. Uma voltagem de gate controla a energia da impureza (da nanoestrutura), 0. Plotada como função de , a condutância mostra dois picos característicos do bloqueio Coulombiano, em freqüências correspondentes às energias para adicionar um elétron à nanoestrutura e para remover um elétron da nanoestrutura respectivamente. No regime Kondo, 0 > 0 > -U (ou seja, para voltagens de gate tais que a nanoestrutura isolada teria estado fundamental com degenerescência de spin), um pico (Kondo) adicional aparece próximo à = 0. Plotada como função de Vg, a condutância DC mostra um largo pico no regime Kondo, caindo rapidamente a zero para voltagens resultando em um estado fundamental não degenerado para a nanoestrutura isolada. Uma relação entre a condutância e a densidade espectral do nível da impureza é obtida e utilizada para interpretar os resultados numéricos. / In this work a renormalization-group calculation of the low-temperature AC conductance in the linear response regime through a nanostructure coupled to metallic leads is presented. This system shows a competition between two effects: the Coulomb blockade and the Kon¬do effect. Our model considers one-dimensional leads which are connected to form a ring, in which a current is induced by a magnetic flux oscillating at the frequency . We start from a nearest-neighbor tight-binding model for the leads and in this way the potential vector is easily incorporated in the model Hamiltonian by twisting boundary conditions. A potential barrier between the leads and the nanostructure is simulated in terms of a tunneling rate between the nanostructure and the adjacent sites in the leads, which is smaller than the one between neighbors sites in the leads. The capacity of the nanostructure is small, which implies that substantial energy changes are associated with each electron transfered to the nanostructure. As a consequence, the model Hamiltonian maps onto the spin-degenerate Anderson Hamiltoni¬an with correlation U between the electrons. A gate voltage Vg controls the impurity (i.e., nanostructure) energy 0. Plotted as a function of , the conductivity shows two Coulomb-blockade peaks, at the energy needed to add an electron to and to remove an electron from the nanostructure, respectively. In the Kondo regime 0 > 0 > -U (i.e., for gate voltages such that the isolated nanostructure would have a spin-degeneration ground state), an addition (Kondo) peak appears near = 0. Plotted as functions of Vg, the static conductivity shows a broad peak in the Kondo regime and drops rapidly to zero for voltages resulting in a non-degenerate nanostructure ground state. A relation between the conductance and the spectral density of the impurity is obtained and used to interpret the numerical results.

Cette thèse consiste en une étude de jonctions tunnels à Quantum Dot (QD) unique. Le second chapitre présentera une introduction aux concepts fondamentaux nécessaires à la description d’une telle jonction. Dans le troisième chapitre, je décrirais les méthodes de fabrications et de mesures. Dans le quatrième chapitre, je décrirais une étude par spectroscopie tunnel de QDs PbS. Trois signatures distinctes du couplage électron-phonon sont observées dans le spectre tunnel. Dans le régime de « remplissage de couches », la dégénérescence d’ordre 8 des états est levée par les interactions de Coulomb et permet l’observation des sous-bandes de phonons résultant de l’émission de phonons optiques. A faible tension, une bande interdite (gap) est observée dans le spectre, laquelle ne peut être fermée avec la tension de grille, ce qui est une signature caractéristique du blocage de France-Condon. A partir de ces données, un facteur de Huang-Rhys de l’ordre de S~1.7-2.5 est obtenu. Finalement, dans le régime de « shell-tunneling », les phonons optiques apparaissent dans le spectre tunnel inélastique d2I/dV2. Dans le cinquième chapitre, je présente une étude du spectre tunnel de QDs HgSe. En appliquant une tension de grille, différents niveaux d’occupation du QD peuvent être atteints. La valeur de la bande interdite change avec le niveau d’occupation. Une valeur de 0.9 eV est observée pour l’inter-bande (QD vide), une valeur de 0.2 eV est observée pour l’intra-bande (QD occupé par 2 e). Sous illumination, un photocourant peut être mesuré en utilisant une technique de démodulation. De cette mesure, une durée de vide τ ~ 65 μs est extraite pour la paire électron-trou photo-générée. / My PhD work consists in a study of single Quantum Dot (QD) tunnel junctions. Following the introduction chapter, the second chapter will present the fundamental concepts needed to describe a single QD junction, such as quantum confinement and Coulomb blockade. In the third chapter, I will describe the sample fabrication methods and the measurement setups. In the fourth chapter, I will describe a tunneling spectroscopy study of single PbS QDs. Three distinct signatures of strong electron-phonon coupling are observed in the Electron Tunneling Spectrum (ETS) of these QDs. In the shell-filling regime, the 8 times degeneracy of the electronic levels is lifted by the Coulomb interactions and allows the observation of phonon sub-bands that result from the emission of optical phonons. At low bias, a gap is observed in the spectrum that cannot be closed with the gate voltage, which is a distinguishing feature of the Franck-Condon blockade. From the data, a Huang-Rhys factor in the range S~ 1.7 - 2.5 is obtained. Finally, in the shell tunneling regime, the optical phonons appear in the inelastic ETS d2I/dV2. In the fifth chapter, I present a tunnel spectroscopy study of single HgSe QDs. Upon tuning the gate voltage, different occupation levels of the QD can be reached. The gap observed in the ETS changes with the occupation level. A large inter-band gap, 0.9~eV, is observed for the empty QDs, and an intra-band gap 0.2~eV is observed for the doubly occupied QD. Upon illuminating the QD, a photocurrent can be measured using an especially designed demodulation technique. From this measurement, the lifetime τ ~65 μs is extracted for the photogenerated electron-hole in the QD.

[pt] Neste trabalho estudamos as propriedades eletrônicas e de transporte de uma molécula artificial diatômica que consiste de dois pontos quânticos conectados a dois contatos submetidos a um potencial externo. Cada ponto quântico é descrito por um nível de energia no qual os elétrons estão fortmente correlacionados pela interação Coulombiana no interior e entre os pontos quânticos. Duas topologias são consideradas para o sistema: uma corresponde aos dois pontos dispostos numa linha de condução e o outro a uma configuração em paralelo. O problema é tratado com as funções de Green obtidas a partir do formalismo de Keldysh para o sistema fora do equilíbrio. Estas funções permitem o cálculo da carga nos pontos quânticos e da corrente elétrica no sistema. A física do sistema é controlada principalmente pelas várias interações Coulombianas. Para a configuração em paralelo existem dois canais interferindo para a propagação do elétron pelo sistema, cujas propriedades dependem do estado de carga de cada ponto quântico. Para a configuração em série a corrente é controlada pela possibilidade da carga ser drenada de um ponto quântico ao outro. O estado de carga em cada ponto quântico e a corrente elétrica são discutidos em detalhe para as duas configurações e para diferentes valores dos parâmetros que definem o sistema. / [en] In this work we study the electronic and transport properties of an artificial diatomic molecule consisting of two quantum dots connected to two leads under the effect of an applied potential. Each dot is described by one energy level in which the electrons are supposed to be strongly correlated due to intra-dot and inter-dot Coulomb interaction. Two topologies are considered for the system: one corresponds to two dots along a conducting line and the other in a parallel configuration. The problem is treated using the out-of-equilibrium Green function Keldysh formalism. The Green functions permit the calculation of the charge in the dots and the electronic current of the system. The physics is controlled mainly by the various Coulomb interactions. For the parallel configuration there are two interfering channels for the electron to go along the system, which properties depend upon the state of charge of each dot. For the serial configuration the current is controlled by the possibility of the charge to be drained from one dot to the other. The state of charge at each dot and the electronic current are discussed in detail for the two configurations and for different values of the parameters that define the system.

La miniaturisation des composants, qui s’est engagée depuis l’avènement de l’électronique il y a plus de 50 ans, atteint aujourd’hui la dimension nanométrique, ouvrant la porte aux phénomènes quantiques. Ultime étape de cette miniaturisation, la boîte quantique, dans laquelle les électrons sont confinés dans les trois directions de l’espace, présente des propriétés remarquables, telles que l’augmentation du gap entre la bande de conduction et la bande de valence, ou la discrétisation des niveaux d’énergies. Autre conséquence du confinement, la forte interaction électron-électron régnant au sein de la boîte conduit à une énergie de charge importante, susceptible de bloquer l'entrée d'un électron dans la boîte sans apport d'énergie extérieur. Ce phénomène de blocage des charges est appelé blocage de Coulomb. Le transistor à un électron (SET), dispositif élémentaire tirant profit de ce phénomène, est pressenti pour quelques applications, comme la réalisation de fonctions logiques ou la détection de charge. Parmi les domaines concernés, la thermoélectricité, c’est-à-dire la possibilité de créer du courant électrique à partir d’une différence de température, s’intéresse de près aux dispositifs à un électron en raison de leurs niveaux d’énergie discrets qui conduisent à une très faible conductivité thermique. Ce travail présente le simulateur SENS (Single-Electron Nanodevice Simulation) développé dans l’équipe, et dont j’ai réalisé la partie destinée à la simulation du SET. Il s’appuie sur la résolution des équations couplées de Poisson et Schrödinger, nécessaire à la détermination des fonctions d’onde dans la boîte de silicium, elles-mêmes dépendantes des tensions appliquées aux électrodes. Les fréquences de transition tunnel sont ensuite calculées par la règle d’or de Fermi. L’étude approfondie du courant dans les SET permet d’extraire des diagrammes de stabilité en diamant, et démontre l’importance de paramètres tels que la taille de l’îlot, la dimension des barrières tunnel, la température et le nombre d’électrons occupant la boîte. L’étude du courant électronique et du courant de chaleur en présence d’une différence de température aux électrodes du SET est également faite pour juger de la pertinence de l’utilisation d’un SET en tant que générateur thermoélectrique, mais aussi comme étalon pour déterminer le coefficient Seebeck. Enfin, une étude du bruit de grenaille dans la double-jonction tunnel (SET sans la grille) est faite, démontrant le fort lien entre taux de transfert tunnel et bruit. En particulier, selon l’évolution des taux des transferts tunnel d’entrée et de sortie de l'îlot, pour un nombre d’électrons supérieur 2, il est possible d’observer une augmentation importante du bruit, qui devient alors super-Poissonien. L’étude de l’influence des paramètres géométriques démontre que le bruit de grenaille dépend essentiellement de la différence des épaisseurs de barrière tunnel. / After a continuous reduction which has begun 50 years ago, the feature size of electronic devices has now reached the nanometer scale, opening the door to quantum phenomena. The final stage of this miniaturization, the quantum dot, in which the electrons are confined in all three directions of space, has remarkable properties, such as an increase of the bandgap between the conduction band and the valence band, and the discretization of energy levels. Another consequence of confinement, the strong electron-electron interaction occurring in the dot induces a significant charging energy which may prevent an electron entering the dot if an external energy is not provided to the system. This charge blocking is called Coulomb blockade. The single electron transistor (SET), the elementary device taking advantage of Coulomb blockade, is slated for some applications, such as the realization of digital functions or charge sensors. Among the areas concerned, the thermoelectricity, i.e., the possibility of creating an electrical current from a temperature gradient, is very interested in single-electron devices due to their discrete energy levels which lead to a very low thermal conductivity.This thesis presents the simulator SENS (Single-Electron Nanodevice Simulation) developed in the team and the part I have developed specifically for the simulation of SET. It is based on a 3D solver of Poisson and Schrödinger coupled equations, necessary for the determination of the wave functions in the case of silicon, and dependent on voltages applied to the electrodes. Tunnel transfer rates are then calculated by Fermi's golden rule. In-depth study of the current in the SETs gives access to diamond stability diagrams, and demonstrates the importance of parameters such as dot size, tunnel the barriers thicknesses, the temperature and the number of electrons occupying the dot. The study of the electron current and the heat flow in the presence of a temperature difference at the electrodes of an SET is also made to consider the suitability of the use of an SET as thermoelectric generator, but also as a standard for determining the Seebeck coefficient.Finally, a study of shot noise in double-tunnel junction (SET without the gate) is made, demonstrating the strong link between tunnel transfer rate and shot noise. In particular, according to the evolution of in- and out – tunnel transfer rates, for a number of electrons in the dot greater than 2, it is possible to observe a significant increase in noise, which becomes super-Poissonian. The study of the influence of geometrical parameters shows that the shot noise depends mainly on the difference of the tunnel barrier thicknesses.

La r eduction (\scaling") continue des dimensions des transistors MOS- FET nous a conduits a l' ere de la nano electronique. Le transistor a ef- fet de champ multi-grilles (MultiGate FET, MuGFET) avec l'architecture \nano l canal" est consid er e comme un candidat possible pour le scaling des MOSFET jusqu' a la n de la roadmap. Parall element au scaling des CMOS classiques ou scaling suivant la loi de Moore, de nombreuses propo- sitions de nouveaux dispositifs, exploitant des ph enom enes nanom etriques, ont et e faites. Ainsi, le transistor mono electronique (SET), utilisant le ph enom ene de \blocage de Coulomb", et le transistor a atome unique (SAT), en tant que transistors de dimensions ultimes, sont les premiers disposi- tifs nano electroniques visant de nouvelles applications comme la logique a valeurs multiples ou l'informatique quantique. Bien que le SET a et e ini- tialement propos e comme un substitut au CMOS (\Au-del a du dispositif CMOS"), il est maintenant largement consid er e comme un compl ement a la technologie CMOS permettant de nouveaux circuits fonctionnels. Toutefois, la faible temp erature de fonctionnement et la fabrication incompatible avec le proc ed e CMOS ont et e des contraintes majeures pour l'int egration SET avec la technologie FET industrielle. Cette th ese r epond a ce probl eme en combinant les technologies CMOS de dimensions r eduites, SET et SAT par le biais d'un sch ema d'int egration unique a n de fabriquer des transistors \Trigate" nano l. Dans ce travail, pour la premi ere fois, un SET fonction- nant a temp erature ambiante et fabriqu es a partir de technologies CMOS SOI a l' etat de l'art (incluant high-k/grille m etallique) est d emontr e. Le fonctionnement a temp erature ambiante du SET n ecessite une le (ou canal) de dimensions inf erieures a 5 nm. Ce r esultat est obtenu grce a la r eduction du canal nano l "trigate" a environ 5 nm de largeur. Une etude plus ap- profondie des m ecanismes de transport mis en jeu dans le dispositif est r ealis ee au moyen de mesures cryog eniques de conductance. Des simula- tions NEGF tridimensionnelles sont egalement utilis ees pour optimiser la conception du SET. De plus, la coint egration sur la m^eme puce de MOS- FET FDSOI et SET est r ealis ee. Des circuits hybrides SET-FET fonction- nant a temp erature ambiante et permettant l'ampli cation du courant SET jusque dans la gamme des milliamp eres (appel e \dispositif SETMOS" dans la litt erature) sont d emontr es de m^eme que de la r esistance di erentielle n egative (NDR) et de la logique a valeurs multiples. Parall element, sur la m^eme technologie, un transistor a atome unique fonc- tionnant a temp erature cryog enique est egalement d emontr e. Ceci est obtenu par la r eduction de la longueur de canal MOSFET a environ 10 nm, si bien qu'il ne comporte plus qu'un seul atome de dopant dans le canal (dif- fus ee a partir de la source ou de drain). A basse temp erature, le trans- port d' electrons a travers l' etat d' energie de ce dopant unique est etudi e. Ces dispositifs fonctionnent egalement comme MOSFET a temp erature am- biante. Par cons equent, une nouvelle m ethode d'analyse est d evelopp ee en corr elation avec des caract eristiques a 300K et des mesures cryog eniques pour comprendre l'impact du dopant unique sur les caracteristiques du MOSFET a temp erature ambiante.