Dissertations / Theses on the topic 'Quantum Transport'

Within the framework of the quantum transport theory based on the Wigner transform of the density matrix I study first in non-relativistic and subsequently in relativistic formulation a number of applications. I also develop further the recently proposed relativistic theory: the classical limit is carefully derived and the integral equations of the relativistic Wigner function derived explicitly. I show how it is possible to obtain the Schwinger like particle production rate from relativistic quantum transport equations. Noteworthy numerical results address the shape of the relativistic Wigner function of a given quantum state. Other numerical studies are primarily oriented towards the time evolution of the Wigner function--I can presently solve only the nonrelativistic case in which there is no mixing between particle production and flow phenomena: I consider numerically the fate of the muon after muon catalyzed fusion.

Il ditellurio di tungsteno (WTe2) appartiene alla classe dei dicalcogenuri di metalli di transizione (TMDs), che rappresentano attualmente i materiali più promettenti, insieme al grafene, nel campo di ricerca dei cristalli bidimensionali (2D). Grazie ad una caratteristica struttura stratificata, con differenti piani atomici legati da forze di van der Waals, mediante esfoliazione è possibile isolare strati di spessore quasi-atomico di TMDs, detti “monostrati”, con proprietà spesso molto diverse dal materiale bulk originario. Il WTe2 nella sua forma a monostrato, è stato recentemente oggetto di interesse scientifico, in quanto teoricamente predetto essere un isolante topologico (TI) bidimensionale. Un TI è un materiale che internamente si comporta come un isolante elettrico ma che sulla superficie manifesta stati conduttivi. Lo scopo di questa tesi è studiare le proprietà si trasporto di monostrati di WTe2 in micro-dispositivi realizzati con opportune tecniche di nanofabbricazione. L'ossidazione della superficie esterna del WTe2, dovuta ad una non-perfetta stabilità in aria, influenza significativamente il trasporto elettronico in cristalli costituiti da pochi strati atomici ed è causa di una transizione metallo-isolante. Una possibile soluzione per evitare la degradazione del materiale consiste nell' “incapsulamento” di un monostrato di WTe2 fra materiali 2D chimicamente inerti, come il nitruro di boro esagonale. A tale proposito, si è sviluppata una tecnica di “trasferimento” che permette di sollevare e allineare con precisione micrometrica strati di spessore atomico di differenti materiali, assemblando eterostrutture di van der Waals. Campioni selezionati sono studiati mediante misure di magneto-transporto a bassa temperatura (fino a 0.250 K). I dati analizzati evidenziano l'esistenza di un gap di energia in monostrati di WTe2 e la presenza di una corrente localizzata ai bordi del sistema, coerentemente con l'ipotesi di un isolante topologico 2D.

To study transport properties, one needs to investigate the system of interest when coupled to biased external baths. This requires solving a master equation for this open quantum system. Obtaining this solution is very challenging, especially for large systems. This limits applications of the theories of open quantum systems, especially insofar as studies of transport in large quantum systems, of interest in condensed matter, is concerned. In this thesis, I propose three efficient methods to solve the Redfield equation --- an example of such a master equation. The first is an open-system Kubo formula, valid in the limit of weak bias. The second is a solution in terms of Green's functions, based on a BBGKY (Bogoliubov--Born--Green--Kirkwood--Yvon)-like hierarchy. In the third, the Redfield equation is mapped to a generalized Fokker-Planck equation using the coherent-state representation. All three methods, but especially the latter two, have much better efficiency than direct methods such as numerical integration of the Redfield equation via the Runge-Kutta method. For a central system with a d-dimensional Hilbert space, the direct methods have complexity of d³, while that of the latter two methods is on the order of order of polynomials of log d. The first method, besides converting the task of solving the Redfield equation to solving the much easier Schrödinger's equation, also provides an even more important conceptual lesson: the standard Kubo formula is not applicable to open systems. Besides these general methodologies, I also investigate transport properties of spin systems using the framework of the Redfield equation and with direct methods. Normal energy and spin transport is found for integrable but interacting systems. This conflicts with the well-known conjecture linking anomalous conductivity to integrability, and it also contradicts the relationship, suggested by some, between gapped systems (Jz > Jxy) and normal spin conductivity. I propose a new conjecture, linking anomalous transport to the existence of a mapping of the problem to one for non-interacting particles.

In this thesis, we have developed a parallel GPU accelerated code for carrying out transport calculations within the Non-Equilibrium Green's Function (NEGF) framework using the Tight-Binding (TB) model. We also discuss the theoretical, modelling, and computational issues that arise in this implementation. We demonstrate that a heterogenous implementation with CPUs and GPUs is superior to single processor, multiple processor, and massively parallel CPU-only implementations. The GPU-Matlab Interface (GMI) developed in this work for use in our NEGF-TB code is not application specific and can be used by researchers in any field without previous knowledge of GPU programming or multi-threaded programming. We also demonstrate that GMI competes very well with commercial packages.Finally, we apply our heterogenous NEGF-TB code to the study of electronic transport properties of Si nanowires and nanobeams. We investigate the effect of several kinds of structural defects on the conductance of such devices and demonstrate that our method can handle systems of over 200,000 atoms in a reasonable time scale while using just 1-4 GPUs.
Dans cette thèse, nous présentons un logiciel qui effectue des calculs de transport quantique en utilisant conjointement la théorie des fonctions de Green hors équilibre (non equilibrium Green function, NEGF) et le modèle des liens étroits (tight-binding model, TB). Notre logiciel tire avantage du parallélisme inhérent aux algorithmes utilisés en plus d'être accéléré grâce à l'utilisation de processeurs graphiques (GPU). Nous abordons également les problèmes théoriques, géométriques et numériques qui se posent lors de l'implémentation du code NEGF-TB. Nous démontrons ensuite qu'une implémentation hétérogène utilisant des CPU et des GPU est supérieure aux implémentations à processeur unique, à celles à processeurs multiples, et même aux implémentations massivement parallèles n'utilisant que des CPU. Le GPU-Matlab Interface (GMI) présenté dans cette thèse fut développé pour des fins de calculs de transport quantique NEGF-TB. Néanmoins, les capacités de GMI ne se limitent pas à l'utilisation que nous en faisons ici et GMI peut être utilisé par des chercheurs de tous les domaines n'ayant pas de connaissances préalables de la programmation GPU ou de la programmation "multi-thread". Nous démontrons également que GMI compétitionne avantageusement avec des logiciels commerciaux similaires.Enfin, nous utilisons notre logiciel NEGF-TB pour étudier certaines propriétés de transport électronique de nanofils de Si et de Nanobeams. Nous examinons l'effet de plusieurs sortes de lacunes sur la conductance de ces structures et démontrons que notre méthode peut étudier des systèmes de plus de 200 000 atomes en un temps raisonnable en utilisant de un à quatre GPU sur un seul poste de travail.

Relativistic kinetic theory provides a transport equation for classical, spinless, colored particles in a non-Abelian external field. We review the methods of solution used in the literature to find the transport coefficients for quark and gluon systems. Most authors use the relaxation time approximation of the Boltzmann equation to compute the transport coefficients, but this method has shortcomings in mixtures. We use the Chapman Enskog (CE) method to solve the classical transport equations for quarks and gluons for the transport coefficients. The differential crosssections describing the particle interaction are obtained from the lowest order scattering diagrams of quantum chromodynamics. We study a pure quark system, a pure gluon system and a quark antiquark (qq) mixture. For mixtures of quarks, antiquarks and gluons, we find the shear viscosity, heat conductivity and cross-coefficients. The coefficients pertaining to qq mixtures, namely the thermal diffusion, diffusion and Dufour coefficient, the viscosities and heat conductivity are obtained and the conductivity of a qq mixture in an external field is computed. We compare our transport coefficients to others in the literature by rewriting them in terms of characteristic relaxation times. Although our results are generally larger than others, they are of the same order of magnitude, with important implications for quark-gluon (QG) plasma signatures. The quark to gluon shear viscosity ratio is found to be ~5 times the number of quark flavors, emphasising the importance of quarks in dynamical QG calculations. The coefficients for a field-free qq mixture indicate no qq separation in the presence of a temperature gradient. In the CE method, the transport coefficients depend naturally on a logarithmic factor due to the divergent scattering cross-sections, reflecting the plasma shielding effects. This logarithm is evaluated by relating it to typical plasma parameters. We apply our results to the QG phase in the early universe and ultra-relativistic heavy ion collisions. A comparison of the QG to pion transport coefficients at the quark-hadron phase transition shows that the latter are ~10³ smaller. Dissipative effects increase the plasma lifetime, resulting in a longer high energy density and temperature plasma phase.

L’étude de l’interaction entre la lumière et la matière n’a cessé de susciter un intérêt croissant au fil des années. L’amélioration des techniques de fabrication des cavités électromagnétiques permet aujourd’hui de coupler ces cavités à des nanocircuits, se faisant, combinant les champs de l’optique quantique et de la nanoélectronique. À cela s’ajoute enfin la démonstration expérimentale de la possibilité d’utiliser un microscope à effet tunnel comme cavité plasmonique couplée au transport électronique. Cette thèse propose un cadre théorique basé sur l’électrodynamique quantique en cavité, permettant l’étude du couplage entre le transport électronique dans une jonction moléculaire et le champ électromagnétique d’une cavité. L’attention est portée sur le régime de transfert tunnel séquentiel des électrons, auquel est adapté l’utilisation les calculs basés sur l’usage de la matrice densité. Ce régime permet d’établir les equations maîtresses régissant l’évolution temporelle de la matrice densité, ainsi qu’un schéma de calcul numérique du courant électronique et des propriétés statistiques des photons dans la cavité quand il n’est pas possible d’obtenir un résultat analytique. Dans un premier temps, l’attention est portée sur un modele de jonction moléculaire à une orbitale. En effet, l’existence d’un courant électronique signifie que la charge de la molécule fluctue et cette fluctuation se couple au champ électromagnétique de la cavité. L’étude de ce premier système est faite dans le régime, expérimentalement pertinent, de fort taux d’amortissement κ ≥ kBT du mode de la cavité et de couplage lumière–matière arbitrairement élevé. Ce modèle met en évidence l’équivalence du couplage électron–photon et du couv plage électron–phonon pour un unique niveau électronique. Ce couplage électron–phonon est étudié depuis longtemps en nanoélectronique sous le nom de principe Franck–Condon. La caractéristique courant–tension du circuit fait apparaitre une évolution par paliers ou seuils inelastiques, chacun séparé par l’énergie d’un photon. Ce phénomène correspond à une dissipation d’énergie, par émission de photons dans la cavité, médiée par le courant électronique. Pour cette étude, une formule du courant électronique prenant en compte l’effet de l’amortissement de la cavité(facteur de qualité Q ≈ 10) a été dérivée. Cela a permis de montrer que la largeur des sauts du courant est contrôlée par κ plutôt que la température. Ce modèle démontre la possibilité d’obtenir divers régimes d’émission de lumière par passage de courant au sein de la jonction. Pour une importante différence de potentiel entre les électrodes de la jonction, cette théorie prédît un important groupement («bunching») des photons émis dans la cavité. La fonction de corrélation de deux photons à temps égaux g(2)(0) atteint alors une valeur de l’ordre de κ/Γ, où Γ est le taux de transfert tunnel des électrons. En revanche, au premier seuil de transfert inélastique des électrons, cette théorie prédît une émission de lumière non–classique provoquée par le courant électronique moléculaire à un niveau (la jonction se comporte alors comme une source à un photon). Enfin, nous avons montré qu’en présence d’une source de voltage dépendant du temps appliqué à la cavité, le courant dc présente des paliers analogues à ceux obtenus dans le régime Franck–Condon. La théorie développée dans cette thèse est ensuite appliquée à une jonction moléculaire à deux niveaux électroniques. Dans ce scénario, le mode de la cavité se couple à la transition électronique entre les deux orbitales moléculaires. L’effet des fluctuations des charges de chaque orbitale est négligé. Dans ce cadre, nous avons étudié le cas d’un couplage cavité-molécule de type dipolaire électrique. L’attention est portée principalement sur le régime de couplage faible entre le dipole de la molécule et le mode de la cavité. [...]
The study of light–matter interaction has drawn through the years more and more interest. With the improvement of the techniques used for building electromagnetic cavities, it is now possible to couple cavities with nanocircuits merging the fields of quantum optics and nanoelectronics.Not only that, but some experiments also reported the possibility to use a scanning tunneling microscope as a plasmonic cavity coupled with electronic transport. In this thesis a theoretical framework is proposed, based on mesoscopic quantum electrodynamics, for studying the coupling between electronic transport in a molecular junction and the electromagnetic field of a cavity. This thesis focuses on the sequential tunneling regime for the electrons and use density matrix approach. This allows to derive the master equation as well as a computational scheme to compute electronic current and the photon statistic when it is not possible to obtain analytical results. First, a single–level model for the molecule in the junction is studied. Indeed the electronic current induces a fluctuation of the charge on the molecule that couples with the electromagnetic field in the cavity. The investigations on this system are done in the experimentally relevant limit of large damping rate κ for the cavity mode and arbitrary strong light–matter coupling strength. This model shows the equivalence between the electron–photon coupling for a single level and the electron– phonon coupling that has long been studied in nanoelectronics known as the Franck–Condon principle. The current–voltage characteristics show steps, each separated by the energy of a photon, as the electron tunneling dissipate some energy in the cavity mode. In this work a formula has been derived for the electronic current taking into account the damping of the cavity. This allows to show that the width of the current’s steps are controlled by κ rather than the temperature. The single-level junction shows interesting light–emission regimes. At large bias voltage this theory predicts strong photon bunching of the order κ/Γ where Γ is the electronic tunneling rate. However, at the first inelastic threshold the theory predicts current–driven non–classical light emission from the single–level junction. Finally the investigation of the effect of a strong external drive of the cavity on the electronic current shows a quantization of the current that is linked to the Franck–Condon effect. Finally the theory is applied to a double–level model for the molecular junction inspired by quantum optics. In this scenario, the cavity mode couples to the electronic transition between the two states of the molecule. The effect of the charge fluctuations for each single electronic level is neglected. Therefore the coupling is a dipolar coupling in this case. The focus is mainly on the weak coupling regime. The electronic current shows the Rabi splitting due to the hybridization of the cavity mode and the molecule. Electronic tunneling can occur into these hybridized states and is responsible for light emission in the cavity in a iii single tunneling process. Light antibunching is seen in the weak coupling regime since our model predicts that only single photon emission is possible during a tunneling event in this case. Though the intermediate coupling regime is only briefly treated, the strong coupling regime is shown to be similar to two independent single level
El estudio de las interacciones entre luz y materia ha atraído un interés creciente a lo largo de los años. La mejora de las técnicas de fabricación de las cavidades electromagnéticas permite hoy conjugar las cavidades con nanocircuitos, combinando así los campos de la óptica cuántica y de la nanoelectrónica. Se añade a eso la posibilidad de usar un microscopio con efecto túnel a modo de cavidad plasmónica combinada con el transporte electrónico que fue demostrado en numerosas experiencias. Esa tesis propone un cuadro teórico basado en la electrodinámica mesoscópica, permitiendo el estudio de la combinación del transporte electrónico dentro de una unión molecular con el campo electromagnético de una cavidad. El foco se centra en el régimen túnel secuencial de los electrones, a cual está apto el uso de la matriz densidad para los cálculos. Ese régimen permite establecer ecuaciones claves que rigen el desarrollo temporal de la matriz densidad, tal como un esquema de cálculo numérico de la corriente electrónica y de la estadística de los fotones en la cavidad cuando no es posible obtener un resultado analítico. Primero se estudia un modelo de un solo nivel electrónico para la molécula. En efecto, la existencia de una corriente electrónica significa que la carga en la molécula fluctúa y esa fluctuación se combina con el campo electromagnético de la cavidad. El estudio de ese sistema se hace en el limite, experimentalmente pertinente, del ratio alto de la amortiguación κ del modo de la cavidad y del acoplo luz–materia arbitrariamente alto. Ese modelo demuestra la equivalencia del acoplo electrón– fotón para un nivel electrónico y el acoplo electrón–fonón que se ha estudiado desde hace mucho tiempo en el campo de la nanoelectrónica bajo el nombre del principio de Franck–Condon. La característica corriente– tensión del circuito hace aparecer una evolución de escalones, cada uno separado por la energía de un fotón. Eso corresponde a una disipación de energía por parte de los electrones al modo de la cavidad durante el proceso de transporte. En ese trabajo se derivó una ecuación para la corriente electrónica que toma en cuenta el efecto de la amortiguación de la cavidad. Esto demuestra que la anchura de los saltos en la corriente está controlada por κ más que por la temperatura. El modelo de un solo nivel muestra también regímenes inesperados de emisión de luz. En el límite de voltaje alto entre los electrodos de la unión molecular, la teoría predice una agrupación («bunching») de los fotones emitidos dentro de la cavidad. La correlación entre dos fotones emitidos alcanza un valor del orden de κ/Γ donde Γ es el ratio de tunelamiento de los electrones. Sin embargo, en el primer umbral de transferencia inelástica esa teoría iv predice una emisión de luz no-clásica provocada por la corriente electrónica. Por fin, el estudio del impacto de una fuerte excitación externa del modo de la cavidad muestra también una cuantización de la corriente relacionada al efecto Franck–Condon. Finalmente, la teoría desarrollada en esta tesis está aplicada también a una unión molecular de dos niveles electrónicos inspirada de la óptica cuántica. En ese escenario el modo de la cavidad está acoplado con la transición electrónica entre dos orbitales moleculares. El efecto de fluctuaciones de carga en cada orbital no se tiene en cuenta. Entonces en ese marco el acoplo es solo dipolar. Se centra la atención principalmente en el régimen del acoplo débil. La corriente electrónica muestra la huella de oscilaciones de Rabi como resultado de la hibridación del modo de la cavidad con la molécula. El transporte de electrones se puede ocurrir mediante estos estados híbridos. Entonces el traslado de un único electrón es responsable de la emisión de un fotón en la cavidad. Se observa el desagrupamiento («anti-bunching») de la luz emitida

Thesis (Ph. D.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Electrical Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Nanoscale wires and molecules have remarkable electrical properties that make them well suited for new electronic devices. The projected device densities result in very small separation distances and therefore the possibility of device-device interactions. However, we do not know what impacts wire-wire interactions might have on the properties of closely spaced devices. If two quantum wires interact, what types of effects will there be on transport properties such as conductance? How would the coupling strength, length of wire, position of contact, or the energy of the electrons affect conductance? Understanding the effects of the interactions will assist the construction of efficient nanoscale devices.This thesis examined the effects of interaction on the low-field conductance using a simple classical model and two quantum models of coupled quantum wires fabricated electrostatically in the two-dimensional electron gas at the interface of the heterostructure A1GaAs/GaAs. We considered the effect of position and length of an interaction between two parallel quantum wires formed by hard wall boundaries and connected to electron reservoirs. Our second model consisted of two artificial molecular wires, i.e., parallel chains of quantum dots. We used a one-electron Schrodinger equation in the envelope approximation, a tight-binding Hamiltonian, and a recursive Green's function method to study the electron transport properties. Multi-parameter computations using a fortran-95 computer model provided data for an analysis of the relationships among conductance, the interaction strength, interaction location, and electron energy.In contrast to the monotonic changes predicted by the classical model, the lowfield conductance of interacting hard wall quantum wires varies in an oscillatory manner with the perturbing interaction strength and position. For electron energies below the first conductance plateau, Breit-Wigner resonances appear as a consequence of coupling. These conductance properties are explained with reference to quasi-bound states created by reflections at the end boundaries of the wires and the separating wall.At low electron energies, the conductance signature of a symmetric artificial molecule composed of serial quantum dots is a band of resonances. Coupled artificial molecular wires display a split-off molecular band with an energy separation that grows with the coupling strength and a bandwidth that narrows. The position of the Fermi energy relative to the molecular band states plays a dominant role in determining the lowfield conductance of interacting artificial molecules. The conductance variation with coupling ranges from oscillatory to monotonic, depending on the Fermi energy. Varying the atom-atom coupling position in the molecular wires causes a relatively small shift in the resonance band energies.
Department of Physics and Astronomy

In this thesis, integrated quantum devices defined using a split gate technique are studied experimentally. These integrated devices provide a novel platform to investigate the property of quantum systems, such as spin polarization, via non-local measurement. Information extracted from these integrated devices leads to a comprehensive understanding of the puzzling phenomenon such as the 0.7 anomaly. Meanwhile, these devices are possibly suitable for studying quantum entanglement because perturbation due to measurement is minimized in the non-local setup. Devices demonstrated here are also promising to be used as a building block such as quantum injector/detector or quantum bus (which is a information channel where quantum information can be transported coherently) for more complicated quantum systems. In the first experiment, a transverse electron focusing in n-type GaAs heterojunction is present where pronounced splitting of odd focusing peaks are observed. From the asymmetry of sub-peaks of the first focusing spin polarization is extracted directly, this provides direct evidence for intrinsic spin polarization in a quasi-one-dimensional system. Parameters which may affect transverse electron focusing are studied systemically. Changing the shape of the injector, thus tuning the adiabaticity of the injection process, can influence the presence of peak splitting or not, with the sharp (non-adiabatic) injector the peak splitting is absent while peak splitting is observed with the flat (adiabatic) injector. Adjusting the length of injector affects the spin polarization, the longer the channel the higher the spin polarization can be achieved. This highlights the role of exchange interaction which results in the spin polarization in the quasi-1D channel. Applying a dc source-drain bias leads to such a result, peak splitting is preserved with negative bias while it smears out with positive bias when the bias is above a particular value (0.5 mV in the experiment), this proves the existence of spin-gap. In the second experiment, the coupling between different quantum devices are investigated by using an integrated quantum device consisting of an QPC and electronic cavity, where the cavity is defined with the arc-shaped gate and an inclined reflector. Unique features such as the double-peak structure occurs in the 1D-2D transition regime of the arc-QPC and 5 fine oscillations associated with conductance plateaus and 0.7 anomaly are observed when the reflector voltage is sufficiently negative and these features smear out when the reflector voltage is less negative. The double-peak structure and fine oscillations are proved to arise from the coupling between the discrete states in the QPC and continuum cavity state by the manifestation of Fano resonance via tuning reflector voltage or small transverse magnetic field. In the third experiment, quantum interference in a double-cavity system is studied by magneoresistance measurement. An unique evolution of the line shape of the magnetoresistance are observed, the magnetoresistance has a Lorentzian shape, corresponding to ergodic and chaotic motion, when the injector conductance is sufficiently small and then alters into linear line shape arising from non-ergodic and regular motion when injector is opens a bit more and finally a Lorentzian shape when the injector opens even further. Apart from the line shape, the strength of the magnetoresistance is found to fluctuate with injector conductance, it is enhanced at conductance plateaus and weakens elsewhere. Such behaviours are likely to arise from both deformation of the arc-shaped potential barrier at the vicinity of injector and detector QPC as well as the non-uniform spatial distribution of the cavity state.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (p. 87-90).
We have studied the transport of magnetization and energy in systems of spins 1/2 on a lattice at high temperature. This work was motivated by recent experiments which observed "spin diffusion" among the dipolar coupled nuclear spins of the insulator calcium fluoride, under conditions where it was appropriate to neglect the coupling to any heat reservoir. The dynamics under these conditions is coherent and reversible, yet signatures of irreversibility (i.e. diffusion) are typically observed. This state of affairs poses a formidable conceptual puzzle. In this thesis we present both phenomenological and microscopic models of spin diffusion, retaining the important aspects of statistical approaches to transport while incorporating relevant quantum effects. These methods allow an efficient calculation of energy diffusion for a long- range interaction, which has largely been an intractable problem. We study transport in two different limits, that where the XY term of the spin Hamiltonian is dominant, and that where it can be treated as a perturbation compared to the Ising term. In the case of dipolar couping, both limits are found to show slightly more rapid diffusion of inter spin energy than magnetization, in qualitative agreement with experiments.
by Daniel Greenbaum.
Ph.D.

This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.

Depuis l'avènement des nanotechnologies, une grande quantité de matériaux sont façonnés à l'échelle du nanomètre par des techniques diverses et l'intégration de ces nanostructures demande une caractérisation de leur structure électronique. La microscopie à effet tunnel est adaptée à ces études car elle permet l'adressage de nanostructures uniques pour mesurer leur structure électronique. Nous rapportons ici l'étude du transport électronique dans deux types de nanostructures: des nanotubes de carbone simple paroi déposés sur une surface d'or et des atomes uniques de silicium sur un substrat de silicium. Dans la première étude, le couplage faible entre un nanotube et le substrat permet d'accéder à la densité d'états unidimensionnelle des nanotubes et autorise la formation de défauts ponctuels, ayant des états localisés dans la bande interdite des nanotubes. Cette modification, réversible, de la structure atomique des nanotubes de carbone amène des opportunités concernant la modification controlée et à volonté de leurs propriétés électroniques. La deuxième étude vise à caractériser la dynamique des porteurs dans une liaison pendante de silicium énergétiquement isolée de tout autre état électronique sur une surface Si(111). L'analyse du transport révèle un courant inélastique mettant en oeuvre la recombinaison non radiative des électrons de la pointe avec des trous capturés par l'état de la liaison pendante, grâce à l'émission de vibrations. La spectroscopie à effet tunnel montre de plus que l'on peut caractériser l'efficacité de capture d'un état quantique unique, en connaissant son niveau d'énergie, sa fonction d'onde, sa section de capture et le couplage électron-phonon.

We use a quantum master equation approach to study the transport properties of a triple quantum dot ring. Unlike double quantum dots and triple quantum dot chains, this geometry gives two transport paths with a relative phase sensitive to magnetic flux via the Aharonov-Bohm effect. This gives rise to a coherent population trapping effect and what is known as a "dark state". Unlike other master equation techniques valid only in the high bias voltage limit, our treatment reproduces such results as well as giving an analytic zero-bias conductance formula. As well as providing a more robust signature of this "dark state" physics, our model further predicts a negative differential resistance in connection with high bias rectification already predicted.
Nous utilisons une approche d´equation quantique maîtresse pour étudier les propriétés de transport des points quantiques triples en forme d'anneau. Contrairement aux points quantiques doubles et triples en forme de chaînes, cette géométrie offre deux chemins pour le transport avec une phase quantique relative qui est sensible au flux magnétique en raison de l'effet Aharonov-Bohm. Ceci méne à un effet de piégeage de population cohérent et cela est connu sous le nom d'un "état sombre". Contrairement à d'autres techniques d'équation maîtresse qui sont seulement valides dans la limite d'un potentiel électrique élevé, notre méthode reproduit les résultats de ces derniers en plus de donner une expression analytique pour la conductance différentielle de zéro potentiel électrique. En plus de donner une optique plus robuste de la physique "d´etats sombres", notre modèle prédit une résistance différentielle négative qui est reliée au phénomène déjà prédit de rectification à potentiel élevé.

In this thesis, we present a theory to calculate the time-dependent current flowing through an arbitrary noninteracting nanoscale phase-coherent device connected to arbitrary noninteracting external leads, in response to sharp step- and square-shaped voltage pulses. Our analysis is based on the Keldysh nonequilibrium Green's functions formalism, and provides an exact analytical solution to the transport equations in the far from equilibrium, nonlinear response regime. The essential feature of our solution is that it does not rely on the commonly used wideband approximation where the coupling between device scattering region and leads is taken to be independent of energy, and as such provides a way to perform transient transport calculations from first principles on realistic systems, taking into account the detailed electronic structure of the device scattering region and the leads. As an illustration of the general theory, we perform a toy model calculation for a quantum dot with Lorentzian linewidth and show how interesting finite-bandwidth effects arise in the time-dependent current dynamics. Finally, we describe possible generalizations of our theory to the cases of superconducting leads (an example of broken symmetry) and one-dimensional leads in the Luttinger liquid regime (an example of an interacting system).

The AC phase-coherent transport in mesoscopic structures is studied via a scattering approach. A general theory is presented under the guidance of two physical principles: charge and current conservation, gauge invariance. As the AC response is intrinsically a many-body problem, we have to treat the scattering problem and the charge redistribution effects in a self-consistent manner.
One quantity of particular interest is the mesoscopic capacitance. In mesoscopic structures where the electric screening length is comparable to the geometric size, the experimentally relevant capacitance is no longer due to geometry alone but to the electro-chemical potential and the capacitance crucially depends on the density of states of the conductor. Furthermore, the phase-coherent nature of the carrier motion leads to striking asymmetric effects in the magneto-capacitance. The general theory is put forth into numerical simulations where the theory is justified.
The study of AC transport in mesoscopic structures should not only help us to better understand the physics of many-body systems, but should also provide valuable knowledge in characterizing and controlling small electronic devices which is of great technological importance.

In this thesis, We will focus on discussing the Andreev tunneling and Josephson tunneling of underdoped cuprate superconductors. In particular, we emphasize how the pseudogap of the underdoped cuprate influences these tunneling behaviors. Our calculation is based on the theory of YRZ Green’s function in which the pseudogap acts as a precursor to the undoped Mott insulator. In the study of Andreev tunneling, the tunneling spectroscopy we obtained exhibits a two-gap feature, i. e., a small energy gap associated with Andreev reflection in the transparent limit and a large gap associated with single particle tunneling. Our results are in good agreement with the two-gap scenario observed in tunneling experiments for underdoped cuprate. In the study of Josephson tunneling, we aimed to test the proposal of “cooperon physics” by examining the Josephson coupling between two optimally doped (or overdoped) cuprate superconductors separated by a barrier of an underdoped-cuprate in its pseudogap state with finiteenergy cooperon excitation. Our calculation shows a significant contribution from the cooperon excitation to the Josephson coupling, which is comparable to that from nodal quasiparticles. Moreover, our results give a good description of the temperature-dependent enhanced Josephson tunneling revealed in experiments.
published_or_final_version
Physics
Doctoral
Doctor of Philosophy

Discrete spatial symmetries affect ergodic transport through two-dimensional mesoscopic systems with chaos-inducing geometries and coherence lengths greater than the system's size. This thesis looks at those effects in symmetries both commuting and anticommuting with the current. Additionally the validity of the fractal Weyl law for quantum systems with mixed phase space is examined. Calculating the joint probability distribution of transmission eigenvalues of systems with discrete symmetries using random matrix theory shows that in the orthogonal universality class the transmission eigenvalues show repulsion of every second eigenvalue. For lead-preserving symmetries this behaviour is a result of superposition of independent sequences, while for symmetries mapping leads onto each other different one-point weights in the probability distribution prevent such an interpretation. This has the largest effect for narrow leads, as confirmed by numerical calculations. Microscopical understanding of symmetry effects is gained using a semiclassical approach to calculate the weak localization corrections and universal conductance fluctuations of systems where symmetry is broken by disturbing the internal symmetry of the system or displacing the leads. Duplicating random matrix theory results for perfect symmetry, this approach shows that symmetry effects vanish fast for small deviations from symmetry over a large part of the system while arbitrary deviations with a width smaller than the lead width have finite effect. Symmetry effects will show whenever leads overlap in part with mirrored leads. These results are confirmed with a crossover of random matrix ensembles. We examine the statistics of resonances in open systems with a mixed phase space. For this, we introduce a Husimi representation of decaying states based on the Schur decomposition of the time evolution operator. Applying this method to the open kicked rotator shows that a modified fractal Weyl law holds, which is cormected to emerging quantum-to-classical correspondence.