[Truncated abstract] In this dissertation we present a theoretical study of electron transport through domain walls, with a particular focus on conductance properties, in order to understand various transport measurements that have been carried out recently on ferromagnetic nanowires. The starting point for our work is a ballistic treatment of transport through the domain wall. In this case conduction electrons are generally only weakly reflected by the domain wall, and the principal effect is a mixing of transmitted electron spins between up and down states. For small spin-splitting of conductance electrons the latter can be characterized by an appropriate adiabaticity parameter. We then incorporate the effect of spin-dependent scattering in the regions adjacent to the domain wall through a circuit model based on a generalization of the two-resistor theory of Valet and Fert. Within this model we find that the domain wall gives rise to an enhancement of resistance similar to the giant magnetoresistance effect found in ferromagnetic multilayer systems. The effect is largest in the limit of an abrupt wall, for which there is complete mistracking of spin, and decreases with increasing wall width due to the reduction of spin mistracking. For reasonable physical parameter values we find order-of-magnitude agreement with recent experiments. Going beyond the assumption of ballistic transport, we then consider the more realistic case of a domain wall subject to impurity scattering. A scattering matrix formalism is used to calculate conductance through a disordered region with either uniform magnetization or a domain wall. By combining either amplitudes or probabilities we are able to study both coherent and incoherent transport properties. The coherent case corresponds to elastic scattering by static defects, which is dominant at low temperatures, while the incoherent case provides a phenomenological description of the inelastic scattering present in real physical systems at room temperature. It is found that scattering from impurities increases the amount of spin mistracking of electrons travelling through a domain wall. This leads, in the incoherent case, to a reduction of conductance through the domain wall as compared to a uniformly magnetized region. In the coherent case, on the other hand, a reduction of weak localization and spin-reversing reflection amplitudes combine to give a positive contribution to domain wall conductance, which can lead to an overall enhancement of conductance due to the domain wall in the diffusive regime. A reduction of universal conductance fluctuations is found in a coherent disordered domain wall, which can be attributed to a decorrelation between spin-mixing and spin-conserving scattering amplitudes.

Les progrès des techniques de nanofabrication des dix dernières années ont permis la mise en place de protocoles visant à manipuler les charges uniques dans les nanostructures. Ces nouvelles techniques permettent d'envisager la réalisation d'expériences d'optique quantique avec des électrons. Cette thèse s'inscrit dans ce contexte. Le but de ce travail a été la construction d'un formalisme adapté à la description de telles expériences. Ce formalisme, construit en analogie avec la théorie de la cohérence quantique du champ électromagnétique de Glauber, souligne les similitudes et différences entre les photons se propageant dans le vide, et le transport électronique dans des conducteurs balistiques unidimensionnels. En particulier, il rend compte de la décohérence et de la relaxation en énergie des excitations électroniques en présence d'interactions. Un autre aspect de cette thèse a été la proposition de protocoles permettant de mesurer des quantités directement reliées aux propriétés de cohérence décrites par le formalisme de l'optique quantique électronique. En particulier, un protocole de tomographie quantique reposant sur l'effet Hanbury Brown et Twiss a été proposé pour reconstruire la cohérence à un corps d'une source monoélectronique. Ce protocole peut aussi être envisagé pour obtenir des informations sur les mécanismes de décohérence. / The last ten years saw tremendous progress in nanofabrication techniques. These progresses allowed the realization of experimental protocols aiming at the manipulation of single electrons in nanostructures. Thus, the advent of these technologies permit to envision the realization of electronic analogues of quantum optics experiments. This thesis is devoted to the theoretical study of quantum optics with electrons propagating in quantum Hall edge channels, in analogy with Glauber's theory for the quantum coherence of the electromagnetic field. The proposed formalism underlines the analogies and differences between photons propagating in the vacuum and electrons in ballistic conductors. In particular, it takes into account the decoherence and relaxation of electronic excitations under the influence of a linear electromagnetic environment. All along this thesis, efforts have been made to propose protocols aiming at accessing experimental quantities related to the coherence properties described by the electron quantum optics formalism. A particular example is a single electron quantum tomography protocol which reconstructs the single particle coherence from current noise measurements. This protocol can also be envisioned to probe decoherence mechanisms.

Nous avons étudié la dynamique des électrons dans des réseaux de nanoparticules métalliques. Nous avons d'abord considéré le réseau le plus simple, c'est-à-dire le dimère de nanoparticules. Nous avons trouvé des fréquences propres du dimère hétérogène et ensuite nous avons appliqué l'approche du système quantique ouvert pour décrire les processus d’amortissement présents dans le système. Nous avons étudié deux processus d’amortissement qui dépendent de la taille des nanoparticules constituant le dimère: l'amortissement de Landau avec une proportionnalité inverse à la taille du système, et l’amortissement radiatif, proportionnel au volume du système. En utilisant les résultats de l'étude des dimères, nous avons étendu notre approche du système quantique ouvert pour étudier des chaînes de nanoparticules unidimensionnelles. Nous avons dérivé une équation maîtresse qui a été utilisée pour étudier la propagation des plasmons le long de la chaîne. Nous avons constaté que la propagation du plasmon est limitée que par les sources non radiatives d'amortissement. Enfin, nous avons dérivé l'expression analytique de la longueur de propagation d'un plasmon dans une chaîne de nanoparticules. / We studied the electron dynamics in metallic nanoparticle arrays. We first considered the simplestarray i.e. a nanoparticle dimer. We found the eigenfrequencies of the heterogeneous dimer andthen we applied the open quantum system approach to describe the decay processes present inthe system. We investigated two decay processes which depend on the size of the nanoparticlesbuilding up the dimer : the Landau damping, inversly proportional to the system-size, and radiationdamping, proportional to the volume of the system. Using the results of the dimer study weextended our open quantum system approach to study one-dimensional nanoparticle chains. Wederived a master equation and used it to investigate the propagation of plasmons along the chain.We found that the propagation of the plasmon is limited by the non-radiative sources of damping.Finally we derived an analytical expression for the propagation length of a plasmon in ananoparticle chain.

La supraconductivité par effet de proximité est un phénomène apparaissant à basse températures qui confère des propriétés supraconductrices à un métal normal cohérent de phase connecté à des électrodes supraconductrices. C'est aussi un outil puissant de la physique mésoscopique, car il est sensible aux différents régimes de transport à basse température. En particulier, nous avons utilisé cet effet afin de révéler les propriétés électroniques spéciales de nanofils de Bi monocrystallins. Dans ce système, le transport est dominé par la surface. De plus, la présence de fort couplage spin-orbite dans le Bi à basse dimension influence profondément sa structure de bande : la bicouche de Bi orienté selon la direction (111) a été prédite d'être isolante dans le volume, mais conductrice sur les bords. Cet effet, appelé l'effet Hall quantique de spin donne lieu a deux états chiraux contra-propageants, qui sont insensibles au désordre tant que la symétrie par renversement du temps est préservée.A travers l'observation de la robustesse du courant critique à fort champ magnétique dans plusieurs échantillons, en même temps que des intérférences de type SQUID à bas champ magnétique, nous avons montré l'existence d'états de bord 1D portant le supercourant. La mesure de la relation courant-phase grâce à la technique de SQUID asymétrique sur un nanofil caractérisé auparavant a été réalisée et démontre que ces canaux sont en fait balistiques. Ces résultats sont compatibles avec des simulations de type liaisons fortes, qui étendent les résultats connus pour la bicouche de Bi (111) aux systèmes de type nanofil. L'ajout d'un champ Zeeman dans le plan permet d'observer des transitions 0-π, révélant ainsi des croisements de niveaux induits par la séparation en spin des états d'Andreev. Enfin, des mesures de la susceptibilité dynamique de ce système via des mesures de spectroscopie micro-onde ont été mises en place, et pourraient démontrer de manière univoque la propriété de protection topologique contre le désordre, d'après nos simulations numériques. / The superconducting proximity effect is a phenomenon occurring at low temperatures that conveys superconducting properties to a phase coherent normal metal sample connected to superconducting electrodes. It is also a powerful tool in mesoscopic physics because it is sensitive to different transport regimes at low temperatures. In particular, we have used this effect to reveal the special electronic transport properties of single crystal Bi nanowires. In this system, the transport is dominated by surface states. Moreover, the presence of strong spin-orbit coupling in Bi at low dimensions deeply influences its electronic structure : it was predicted that (111) oriented Bi bilayer are insulating in the bulk, but conducting along the edges. This so called Quantum Spin Hall Effect (QSHE), gives rise to counterpropagating chiral edge states, that are protected against disorder as long as time reversal symmetry is present.Through the observation of the resilience of the critical current in several samples at high magnetic field, along with SQUID-like interference pattern at low magnetic field, we showed the existence of supercurrent carrying 1D edge states. The measurement of the current-phase relation using the asymetric SQUID technique on a previously characterized nanowire was realized and further demonstrates that these edge states are ballistic. These findings are consistent with tight-binding simulations that extend the known results for (111) Bi bilayer to nanowire-like system. The addition of an in-plane Zeeman field allows one to observe 0-π transitions, thereby revealing spin-splitting induced Andreev level crossings. Finally, microwave spectroscopy measurement of the dynamical susceptibility in this system are initiated, that could reliably demonstrate the property of protection against disorder according to numerical simulations.By exploring Bi at low dimensions, this thesis paves the way towards the exploration of electronic states fully protected from disorder.

Des états électroniques localisés apparaissent dans les liens faibles entre électrodes supraconductrices : les états d’Andreev. Les expériences présentées dans cette thèse explorent les propriétés de cohérence quantique de ces états, en utilisant comme liens faibles des contacts à un atome entre des électrodes d’aluminium. Les contacts atomiques sont intégrés dans une cavité microonde qui permet à la fois de les isoler et de les sonder.Dans une première série d’expériences, il est montré qu’on peut utiliser les états d’Andreev pour définir un bit quantique, le « qubit d’Andreev », qu’on contrôle à l’aide d’impulsions micro-onde.Les mesures des temps de vie de cohérence de ce qubit sont analysées en détail.Dans une deuxième série d’expérience,l’interaction entre le qubit d’Andreev et le résonateur micro-onde est utilisée pour quantifier le nombre de photons présents dans le résonateur en fonction de la puissance d’impulsions microonde à sa fréquence propre.Enfin, des sauts quantiques et des sauts de parités ont observés dans des mesures continues de l’état du qubit d’Andreev. / Localized electronic states, called Andreev bound states, appear in weak-links placed between superconducting electrodes. The experiments presented in this thesis explore the coherence properties of these states. Single atom contacts between aluminum electrodes are used as weak links. In order to isolate and probe these states, the atomic contacts are integrated in amicrowave cavity.In a first series of experiments, it is shown that Andreev states can be used to define a quantumbit, “the Andreev qubit”, which is controlled using microwave pulses.Measurements of the lifetime and coherence time of this qubit are thoroughly analyzed.In a second series of experiments, the interaction between the Andreev qubit and the microwave cavity are used to determine the number of photons present in the cavity as a function of the power of microwave pulses at its eigenfrequency.Finally, quantum and parity jumps are observed in continuous measurements of the state of the Andreev dot.

No description available.

We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents: We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase. Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm. By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates. Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices. Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk.

With the advance in nanotechnology, we are more interested in the "smaller worlds". One of the practical applications of this is to measure a very small displacement or the mass of a nano-mechanical object. To measure such properties, one needs a very sensitive detector. A quantum point contact (QPC) is one of the most sensitive detectors. In a QPC, electrons tunnel one by one through a tunnel junction (a "hole"). The tunnel junction in a QPC consists of a narrow constriction (nm-wide) between two conductors. To measure the properties of a nano-mechanical object (which acts as a harmonic oscillator), we couple it to a QPC. This coupling effects the electrons tunneling through the QPC junction. By measuring the transport properties of the tunneling electrons, we can infer the properties of the oscillator (i.e. the nano-mechanical object). However, this coupling introduces noise, which reduces the measurement precision. Thus, it is very important to understand this source of noise and to study how it effects the measurement process. We theoretically study the transport properties of electrons through a QPC junction, weakly coupled to a vibration mode of a nano-mechanical oscillator via both the position and the momentum of the oscillator. %We study both the position and momentum based coupling. The transport properties that we study consist of the average flow of current through the junction, given by the one-time correlation of the electron tunneling event, and the current noise given by the two-time correlation of the average current, i.e, the variance. The first comprehensive experimental study of the noise spectrum of a detector coupled to a QPC was performed by the group of Stettenheim et al. Their observed spectral features had two pronounced peaks which depict the noise produced due to the coupling of the QPC with the oscillator and in turn provide evidence of the induced feedback loop (back-action). Benatov and Blencowe theoretically studied these spectral features using the Born approximation and the Markovian approximation. In this case the Born approximation refers to second order perturbation of the interaction Hamiltonian. In this approximation, the electrons tunnel independently, i.e., one by one only, and co-tunneling is disregarded. The Markovian approximation does not take into account the past behavior of the system under time evolution. These two approximations also enable one to study the system analytically, and the noise is calculated using the MacDonald formula. Our main aim for this thesis is to find a suitable theoretical model that would replicate the experimental plots from the work of Stettenheim et al. Our work does not use the Markovian approximation. However, we do use the Born approximation. This is justified as long as the coupling between the oscillator and QPC is weak. We first obtain the non-Markovian unconditional master equation for the reduced density matrix of the system. Non-Markovian dynamics enables us to study, in principle, the full memory effects of the system. From the master equation, we then derive analytical results for the current and the current noise. Due to the non-Markovian nature of our system, the electron tunneling parameters are time-dependent. Therefore, we cannot study the system analytically. We thus numerically solve the current noise expression to obtain the noise spectrum. We then compare our noise spectrum with the experimental noise spectrum. We show that our spectral noise results agree better with the experimental evidence compared to the results obtained using the Markovian approximation. We thus conclude that one needs non-Markovian dynamics to understand the experimental noise spectrum of a QPC coupled to a nano-mechanical oscillator. / Physics

The first part of this thesis deals with the study of mesoscopic fluctuations of the Coulomb drag resistance in double-layer GaAs/AlGaAs heterostructures, both in weak magnetic fields and strong magnetic fields. In the second part, measurements are made in a monolayer graphene structure, specifically of the quantum lifetime, and the mesoscopic resistance fluctuations at quantising magnetic fields.

<p>This thesis addresses electron spin phenomena in semi-conductor quantum dots/anti-dots from a computational perspective. In the first paper (paper I) we have studied spin-dependent transport through open quantum dots, i.e., dots strongly coupled to their leads, within the Hubbard model. Results in this model were found consistent with experimental data and suggest that spin-degeneracy is lifted inside the dot – even at zero magnetic field.</p><p>Similar systems were also studied with electron-electron effects incorporated via Density Functional Theory (DFT) in paper III. Within DFT we found a significant spin-polarisation in the dot at low electron densities. As the electron density increases the spin polarisation in the dot gradually diminishes. These findings are consistent with available experimental observations. Notably, the polarisation is qualitatively different from the one found in the Hubbard model – this indicates that the simplified approach to electronelectron interaction in the Hubbard model might not always be reliable.</p><p>In paper II we propose a spin-filter device based on resonant backscattering of edge states against a quantum anti-dot embedded in a quantum wire. A magnetic field is applied and the spin up/spin down states are separated through Zeeman splitting. Their respective resonant states may be tuned so that the device can be used to filter either spin in a controlled way.</p> / Report code: LIU-Tek-Lic 2005:65