In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

This dissertation reports on the synthesis, structural and thermal characterization and electrical and thermal transport properties of a variety of strongly correlated spinels. General structure property relationships for electrical and thermal transport are discussed. However, the relationship between thermopower and features of the crystal structure such as spin, crystal field, anti-site disorder, and structural distortions are explored in depth. The experimental findings are reported in the context of improving existing oxide thermoelectric materials, screening for new materials or using thermopower as a unique characterization tool to determine the cation distribution in spinels. The need for improved n-type oxide thermoelectric materials has led researchers to consider mixed valence \((+3/+4)\) manganese oxides. Contrary to previous findings we report herein that the \(LiMn_2O_4\) compound reaches the relatively large n-type thermopower of \(-73 \mu V/K\) which is three times larger than the value observed in other manganese oxides, \(-25 \mu V/K\). The cause of this increase in thermopower is shown to be the absence of a Jahn-Teller distortion on the \(Mn^{3+}\) ions in \(LiMn_2O_4\). By avoiding this structural distortion the orbital degeneracy is doubled and the Koshibae et al.’s modified Heikes formula predicts a thermopower of \(-79 \mu V/K\) in good agreement with the experiment. Altering the \(Mn^{3+/4+}\) ratio via aliovalent doping did not affect the thermopower and is a second evidence of universal charge transport first reported by Kobayashi et al. The role of anti-site disorder was further examined in \(Fe_xMn_{1-x}NiCrO_4\) x=0, ½, ¾, 1 spinels but the effect on thermopower was inconclusive due to the presence of impurity phases. Next, the thermopower as a function of temperature in \(Co_3O_4\) was investigated as a means whereby the Wu and Mason’s 30 year old model for using thermopower to calculate cation distribution in spinels could be revisited. We report evidence that Wu and Mason’s original model using the standard Heikes formula and considering octahedral sites alone leads to a stoichiometrically inconsistent result at high temperatures. Alternate models are evaluated considering Koshibae et al.’s modified Heikes formula and accounting for tetrahedral site contributions. Furthermore, the effect of a possible spin state transition is considered. / Engineering and Applied Sciences

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

Ce travail présente l'étude du transport électronique à l'interface entre deux oxydes isolants le SrTiO3 et le LaTiO3. Lorsqu'une interface polaire est réalisée à la surface d'un substrat de SrTiO3 non dopé, il se forme un gaz d'électrons bi-dimensionnel confiné près de l'interface. Ce phénomène a été mis en évidence pour différents oxydes isolants formant l'interface (LaAlO3, LaVO3, LaGaO3,...). Nous nous sommes intéressés en particulier à l'interface avec l'isolant de Mott LaTiO3. Nous avons montré que le gaz d'électrons présent à cette interface a un comportement métallique et est supraconducteur à très basse température. Nous avons également pu contrôler les propriétés de transport du gaz par effet de champ électrostatique. L'analyse de l'effet Hall à haut champ magnétique a montré que le gaz est composé de deux types de porteurs : une majorité de porteurs de faible mobilité, et une minorité de porteurs de mobilité plus importante. En accord avec un modèle de courbure de bande développé au cours de cette thèse, nous avons montré que les porteurs majoritaires sont confinés près de l'interface dans les sous-bandes les plus profondes, alors que les porteurs minoritaires sont contrôlés par le remplissage et le déconfinement de sous-bandes plus élevées en énergie. La supraconductivité est intrinsèquement liée à la présence de ces derniers. L'analyse du comportement critique de la transition supraconducteur-isolant en champ magnétique révèle que ces porteurs sont spatialement groupés en flaques de tailles mésoscopiques. Les mesures de magnetorésistance mettent en évidence la présence d'un fort couplage spin-orbite de type Rashba qu'il est possible de moduler par effet de champ électrostatique.

[pt] Investigamos as propriedades de transporte de spin polarizado através de um ponto quântico conectado a dois terminais. A corrente elétrica que circula em nosso sistema pode ter sua polarização modulada através de um potencial de porta que controla o acoplamento spin-órbita (efeito Rashba). Nós estudamos o efeito de polarização do spin em um transistor constituído por um ponto quântico em que suas energias podem ser controladas através de um outro potencial de porta que opera apenas na região de confinamento. O alto grau de confinamento e correlação entre as cargas dão origem a fenômenos físicos interessantes que descreveremos neste trabalho. Nós demonstramos que através da manipulação de um potencial externo é possível controlar de uma maneira extremamente eficiente a intensidade e a polarização da corrente através do sistema. Outro parâmetro importante que iremos manipular para uma compreensão detalhada do sistema é o campo elétrico externo. Na segunda parte deste trabalho estudamos a evolução temporal da função de onda, suposta inicialmente como um pacote de onda circulando nosso sistema composto por um ponto quântico. Podemos comprovar efeitos de tunelamento ressonante e efeitos de interferência de nosso pacote inicial ao longo do tempo e, além disso, estudamos também efeitos de interação spin- órbita na polarização de nosso pacote de onda. / [en] We investigated spin polarized transport properties through a quantum dot connected with two terminals. An electric current that circulates in our system can have its polarization modulated with an external potential that controls the spin orbit coupling (Rashba effect). We studied the effect of spin polarization n a transistor constituted by a quantum dot where its energies can be controlled with a gate potential that operates only in the confinement region. The high confinement and correlation between the charges give rises to interesting phenomena that we describe in this work. We demonstrate that tuning an external potential it is possible to control with a extremely efficient precision the intensity and the polarization of the current through this system. Another important parameter that we used to better understand this system was the external electric field. In the second part of this work, we studied the time evolution of a wave function supposed to be initially a wave package circulating our system composed by a quantum dot. We can prove resonant tunneling effects and interference effects in such a wave package as time goes by and we also studied spin orbit interaction effects on the polarization of the carrier.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

Cette thèse est consacrée à l'étude des phases de Mott isolantes des systèmes unidimensionnels d'atomes froids fermioniques à plusieurs composantes. La première partie de ce travail consiste en l'étude du modèle des atomes froids de type alcalinoterreux de spin nucléaire I=1/2. Ces atomes possèdent un état excité métastable offrant à ces atomes un degré de liberté orbital supplémentaire et en fait des fermions à quatre composantes. L'étude est menée au demi-remplissage, aux forts et aux faibles couplages par des moyens analytiques (théorie conforme, bosonisation, refermionisation, groupe de renormalisation); elle conduit à un diagramme de phase très riche. Il comporte sept phases isolantes de Mott dont trois sont particulièrement intéressantes, car elles présentent un ordre caché qui s'apparente à la physique de Haldane de la chaîne antiferromagnétique de spin-1. Ces conclusions sont mises en regard avec des simulations numériques exécutées avec l'algorithme du groupe de renormalisation de la matrice densité (DMRG), pour un régime de couplages intermédiaires. La comparaison montre une continuité adiabatique entre les différents régimes de couplages. Une étude similaire d'un modèle d'atomes froids de spin-3/2 met en évidence la physique de Haldane dans le secteur de charge des degrés de liberté, avec pour modèle effectif une chaîne de (pseudo-)spin-1. L'étude nous permet également l'investigation des propriétés de température nulle de la chaîne bilinéaire et biquadratique de Heisenberg SO(5). On montre qu'elle présente deux phases gappées : l'une dimerisée et l'autre possédant une symétrie cachée (Z_2xZ_2)² et des états de bords de spin-3/2, séparées par un point critique appartenant à la classe d'universalité SO(5)_1. Enfin, une étude de systèmes d'atomes froids de spins demi-entiers (à 2N composantes) généralise les résultats obtenus pour les spins-3/2. Cela nous conduit en particulier à mettre en évidence un effet pair/impair suivant N, en tout point similaire à l'effet pair/impair des chaînes de spin, découvert par Haldane en 1983. / This thesis is devoted to the investigation of the Mott insulating phases arising in onedimensionalmulticomponent fermionic cold atoms systems. The first part of this work isthe study of a model with alkaline-earth cold atoms with nuclear spin I = 1/2. Thoseatoms enjoy an additional orbital degree of freedom, due to the presence of a metastableexcited state ; they thus have a total of four components. Our investigation is carried athalf-filling, at strong and at weak couplings by means of analytic methods (conformaltheory, bononization, refermionization, renormalisation group). We found that the zerotemperature phase diagram of the system is very rich : it contains seven Mott insulatingphases, among which three are particularly interesting, since they display a hiddenorder, related to the Haldane physics of the antiferromagnetic spin-1 Heisenberg chain.Our conclusions are checked against numerical simulations, that were carried out with thedensity matrix renormalization group (DMRG) algorithm for intermediate couplings. Thecomparison shows an adiabatic continuity between the different regimes. A similar studyfor a model of cold atoms with hyperfine spin-3/2 highlights the Haldane physics in thecharge sector of the degrees of freedom, with an effective model given by an antiferromagneticpseudo-spin-1 chain. This analysis provides us an opportunity to investigate thezero temperature properties of the SO(5) bilinear-biquadratic Heisenberg chain. We showthe presence of two gapped phases : one is dimerized, the other has a hidden symmetry(Z2 × Z2)2 and spin-3/2 edge states, and they are separated by a critical point that belongsto the SO(5)1 universality class. Finally, we investigate half-integer hyperfine spincold atoms systems with 2N components which generalized the results obtained for thehyperfine spin-3/2 model. This leads us to find an even/odd effect according to the parityof N, very similar to the even/odd effect of spin chains, discovered by Haldane in 1983.

Cette thèse traite des systèmes de Hall quantiques en deux dimensions, dans lesquels les électrons peuvent porter plusieurs degrés de liberté discrets différents. Le ferromagnétisme de Hall quantique fournit une manière de traiter ces degrés de liberté électroniques comme des spins et isospins effectifs des électrons. Les différentes phases du système correspondent alors à différents ordres de spin ou d'isospin. En exploitant cette analogie, nous explorons différents aspects des systèmes bi-dimensionnels dans le régime de Hall quantique en étudiant la structure correspondante des spins et isospins. Ce travail consiste en trois parties qui analysent différents matériaux bi-dimensionnels dans le régime de l'effet Hall quantique. Dans chaque projet, nous utilisons la théorie de Hartree-Fock pour étudier le système à plusieurs composantes de spin et d'isospin dans l'approximation de champ moyen. Toutes nos considérations sont directement stimulées par des résultats expérimentaux. Notre motivation principale est d'obtenir une compréhension plus profonde des processus physiques et des mécanismes qui déterminent les propriétés des matériaux à partir d'investigations exclusivement théoriques de modèles abstraits. Nous espérons que cela permettra par la suite de tirer des conclusions sur les expériences, de donner des explications aux phénomènes observés ainsi que de donner des perspectives pour des investigations futures. / The present thesis deals with two-dimensional quantum Hall systems in which the electrons may be endowed with multiple discrete degrees of freedom. Quantum Hall ferromagnetism provides a framework to treat these electronic degrees of freedom as effective spins and isospins of the electrons. Different orderings of the electronic spins and isospins then characterise different possible phases of the system. Using this analogy, various aspects of the two-dimensional systems in the quantum Hall regime are explored theoretically by studying the corresponding spin and isospin structure. The work consists of three parts in which different two-dimensional materials are investigated in the quantum Hall regime. In any of the three projects presented within this thesis, Hartree Fock theory is employed to study the multicomponent spin and isospin system at the mean field level. All our considerations are stimulated directly by experimental results. We draw our main motivation from the key idea that purely theoretical investigations of abstract models may us allow to obtain deeper insights into the physical processes and mechanisms that determine the properties of the materials. This, in turn, we hope to allow conclusions about the experiments by providing possible explanations of the phenomena observed, as well as prospects for future investigations.

Although band theory is about a century old, it remains relevant today as a tool for the treatment of electrons in solids. The confluence of mathematical ideas like geometry and topology with band theory has proven to be a ripe avenue for research in the past few decades. The importance of Fermi surface geometry, especially in conjunction with electronic correlation, has been well recognized. One particular thread in this direction is probing the occurrence of non-trivial Fermi surface geometry, and its influence on macroscopic properties of materials. A notable example of exotic Fermi surface geometry arises from singular points of the dispersion, and these have been known since 1953. The investigation into these was reignited recently, culminating in the work presented in this thesis. In this dissertation, I investigate two broad categories of singular points in bands. At a singular point, either the dispersion or the Fermi surface fail to be smooth. This may cause distinct signatures in transport and spectroscopic properties when the singular point occurs close to the Fermi level. In the two dimensional setting, I classify using catastrophe theory, the point singularities arising from higher order saddles of the dispersion. These are the more exclusive cousins of the regular van Hove saddle that cause, among other things, a power law divergence in the density of states. The role of lattice symmetries in aiding or preventing the occurrence of these singularities is also carefully explored. In the case of three dimensional bands, I investigate the spectroscopic properties of the nodal point singularity, arising from a linear band crossing. In particular, I determine the distinct signature of nodal points in the analytic, momentum resolved, joint density of states (JDOS) and the numerically calculated resonant inelastic x-ray scattering (RIXS) spectrum, within the fast collision approximation that ignores core hole effects. The results presented here will be the stepping stone towards a careful future calculation, incorporating the potential edge singularity effects through core hole potential. Such a calculation may be directly comparable with ongoing experiments.