I. Theory of Laser Driven Molecular Wires.II. Light Diffraction by Colloidal Crystals - Numerical Simulations for Realistic Finite Systems Using Single Scattering Theory.

Part I considers electron transport through a molecular bridge coupled to two metal electrodes in the presence of a monochromatic ac radiation field. Coherent current flow through the wire is calculated within a nondissipative one-electron tight binding model of the quantum dynamics. Using Floquet theory, the field-driven molecular wire is mapped to an effective time- independent quantum system characterized by a tight-binding Hamiltonian with the same essential structure as the nondriven analog. Thus, the Landauer formalism and scattering Green's Function methods for computing current flow through the wire, which have been profitably applied to the molecular wire problem in the absence of driving, can also be used to analyze the corresponding field-driven system.The theory developed here is applied to an experimentally relevant system, namely a xylyl-dithiol molecule in contact at either end with gold electrodes. Net current through the wire is calculated for two - STM and molecular junction - configurations of the electrode-wire-electrode system for a range of experimental inputs, including bias and the intensity and frequency of the laser. Via absorption/emission of photons, the electron tunneling occurs through an interference of many pathways and may lead to a significantly enhanced laser-driven current at experimentally accessible laser field strengths.In Part II we apply a single particle scattering methodology to calculate diffraction efficiencies of finite Crystalline Colloidal Arrays (CCA's). We developed an extension of the well-known Kinematic theory and tested it by comparing computed light scattering efficiencies with exact results for 1D slab model. We discuss some applications of the method to finite CCA's of different shapes and sizes. In particular, the dependence of diffraction intensities on the incident angle is analyzed near the Bragg diffraction maximum for several different crystal planes. We also study the effect of the incident beam shape and cross sectional profile on the CCA diffraction. Finally, the effective penetration depth for the incident light is calculated and compared for several incident directions, and the effect of stacking faults on diffraction efficiencies is analyzed using the methodology developed herein

Electromagnetic Analysis and Design of Semiconductor Qubit Structures for the Realization of the Quantum Computer

Ph.DDOCTOR OF PHILOSOPH

Simulation of multigate SOI transistors with silicon, germanium and III-V channels

In this work by employing numerical three-dimensional simulations we study the electrical performance and short channel behavior of several multi-gate transistors based on advanced SOI technology. These include FinFETs, triple-gate and gate-all-around nanowire FETs with different channel material, namely Si, Ge, and III-V compound semiconductors, all most promising candidates for future nanoscale CMOS technologies. Also, a new type of transistor called “junctionless nanowire transistor” is presented and extensive simulations are carried out to study its electrical characteristics and compare with the conventional inversion- and accumulation-mode transistors. We study the influence of device properties such as different channel material and orientation, dimensions, and doping concentration as well as quantum effects on the performance of multi-gate SOI transistors. For the modeled n-channel nanowire devices we found that at very small cross sections the nanowires with silicon channel are more immune to short channel effects. Interestingly, the mobility of the channel material is not as significant in determining the device performance in ultrashort channels as other material properties such as the dielectric constant and the effective mass. Better electrostatic control is achieved in materials with smaller dielectric constant and smaller source-to-drain tunneling currents are observed in channels with higher transport effective mass. This explains our results on Si-based devices. In addition to using the commercial TCAD software (Silvaco and Synopsys TCAD), we have developed a three-dimensional Schrödinger-Poisson solver based on the non-equilibrium Green’s functions formalism and in the framework of effective mass approximation. This allows studying the influence of quantum effects on electrical performance of ultra-scaled devices. We have implemented different mode-space methodologies in our 3D quantum-mechanical simulator and moreover introduced a new method to deal with discontinuities in the device structures which is much faster than the coupled-mode-space approach

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

Propriétés électroniques et thermoélectriques des hétérostructures planaires de graphène et de nitrure de bore

Graphene is a fascinating 2-dimensional material exhibiting outstanding electronic, thermal and mechanical properties. Is this expected to have a huge potential for a wide range of applications, in particular in electronics. However, this material also suffers from a strong drawback for most electronic devices due to the gapless character of its band structure, which makes it difficult to switch off the current. For thermoelectric applications, the high thermal conductance of this material is also a strong limitation. Hence, many challenges have to be taken up to make it useful for actual applications. This thesis work focuses on the theoretical investigation of a new strategy to modulate and control the properties of graphene that consists in assembling in-plane heterostructures of graphene and Boron Nitride (BN). It allows us to tune on a wide range the bandgap, the thermal conductance and the Seebeck coefficient of the resulting hybrid nanomaterial. The work is performed using atomistic simulations based on tight binding (TB), force constant (FC) models for electrons and phonons, respectively, coupled with the Green's function formalism for transport calculation. The results show that thanks to the tunable bandgap, it is possible to design graphene/BN based transistors exhibiting high on/off current ratio in the range 10⁴-10⁵. We also predict the existence hybrid quantum states at the zigzag interface between graphene and BN with appealing electron transport. Finally this work shows that by designing properly a graphene ribbon decorated with BN nanoflakes, the phonon conductance is strongly reduced while the bandgap opening leads to significant enhancement of Seebeck coefficient. It results in a thermoelectric figure of merit ZT larger than one at room temperature.Les excellentes propriétés électroniques, thermiques et mécaniques du graphène confèrent à ce matériau planaire (bi-dimensionnel) un énorme potentiel applicatif, notamment en électronique. Néanmoins, ce matériau présente de sérieux inconvénients qui pourraient limiter son champ d'applications. Par exemple, sa structure de bandes électronique sans bande interdite rend difficile le blocage du courant dans un dispositif. De plus, pour les applications thermoélectriques, sa forte conductance thermique est aussi une forte limitation. Il y a donc beaucoup de défis à relever pour rendre ce matériau vraiment utile pour des applications. Cette thèse porte sur l'étude des propriétés électroniques et thermoélectriques dans les hétérostructures planaires constituées de graphène et de nitrure de bore hexagonal (BN). Différentes configuration de ce nouveau matériau hybride permettent de moduler la bande interdite, la conductance thermique et le coefficient Seebeck. Cette étude a été menée au moyen de calculs atomistiques basés sur les approches des liaisons fortes (TB) et du modèle à constantes de force (FC). Le transport d'électrons et de phonons a été simulé dans le formalisme des fonctions de Green hors équilibre. Les résultats montrent que, grâce à la modulation de la bande interdite, des transistors à base d'hétérostructures de BN et de graphène peuvent présenter un très bon rapport courant passant / bloqué d'environ 10⁴ à 10⁵. En outre, nous montrons l'existence d'états quantiques hybrides à l'interface zigzag entre le graphène et le BN donnant lieu à des propriétés de transport électronique très intéressantes. Enfin, ce travail montre qu'en agençant correctement des nano-flocons de BN sur les côtés d'un nanoruban de graphène, la conductance des phonons peut être fortement réduite alors que l'ouverture de bande interdite conduit à un accroissement important du coefficient Seebeck. Il en résulte qu'un facteur de mérite thermoélectrique ZT plus grand que l'unité peut être réalisé à température ambiante

Low-dimensional quantum systems

We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended t-V model of fermions with interactions of finite range is investigated. The model exhibits a phase transition between liquid and insulating regimes. We use various analytical approaches to generalise previous theoretical studies. We devise a strong coupling expansion to go beyond first-order perturbation theory. The method is insensitive to the presence or the lack of integrability of the system. We extract the ground state energy and critical parameters of the model near the Mott insulating commensurate density. A summary of the methods used is provided to give a broader view of their advantages and disadvantages. We also study the possible charge-density-wave phases that exist when the model is at the critical density. A complete description of phase diagrams of the model is provided: at low critical densities the phases are defined analytically, and at higher critical densities we tackle this problem computationally. We also provide a future outlook for determining the phases that occur at non-zero temperature. Secondly, we investigate Mott-Wannier complexes of two (excitons), three (trions) and four (biexcitons) charge carriers in two-dimensional semiconductors. The fermions interact through an effective interaction of a form introduced by Keldysh. Our study also includes impurity-bound complexes. We provide a classification of trions and biexcitons in transition-metal dichalcogenides, which incorporates the difference of spin polarisation between molybdenum- and tungsten-based materials. Using the diffusion Monte Carlo method, which is statistically exact for these systems, we extract binding energies of the complexes for a complete set of parameters of the model. Our results are compared with theoretical and experimental work on transition-metal dichalcogenides. Agreement is found for excitonic and trionic results, but we also observe a large discrepancy in the theoretical biexcitonic binding energies as compared to the experimental values. Possible reasons for this are outlined. Simple interpolation formulas for binding energies are provided, that can be used to easily determine the values within the accuracy of 5% for any two-dimensional semiconductor. We also calculate contact pair densities, which in the future can be used in the determination of the contact interaction

Quantum gauge theory simulation with ultracold atoms

The study of ultracold atoms constitutes one of the hottest areas of atomic, molecular, and optical physics and quantum optics. The experimental and theoretical achievements in the last three decades in the control and manipulation of quantum matter at macroscopic scales lead to the so called third quantum revolution. Concretely, the recent advances in the studies of ultracold gases in optical lattices are particularly impressive. The very precise control of the diverse parameters of the ultracold gas samples in optical lattices provides a system that can be reshaped and adjusted to mimic the behaviour of other many-body systems: ultracold atomic gases in optical lattices act as genuine quantum simulators. The understanding of gauge theories is essential for the description of the fundamental interactions of our physical world. In particular, gauge theories describe one of the most important class of systems which can be addressed with quantum simulators. The main objective of the thesis is to study the implementation of quantum simulators for gauge theories with ultracold atomic gases in optical lattices. First, we analyse a system composed of a non-interacting ultracold gas in a 2D lattice under the action of an exotic and external gauge field related to the Heisenberg-Weyl gauge group. We describe a novel method to simulate the gauge degree of freedom, which consists of mapping the gauge coordinate to a real and perpendicular direction with respect to the 2D space of positions. Thus, the system turns out to be a 3D insulator with a non-trivial topology, specifically, a quantum Hall insulator. Next, we study an analog quantum simulation of dynamical gauge fields by considering spin-5/2 alkaline-earth atoms in a 2D honeycomb lattice. In the strongly repulsive regime with one particle per site, the ground state is a chiral spin liquid state with broken time reversal symmetry. The spin fluctuations around this configuration are given in terms of an emergent U(1) gauge theory with a Chern-Simons toplogical term. We also address the stability of the three lowest lying states, showing a common critical temperature. We consider experimentally measurable signatures of the mean field states, which can also be key insights for revealing the gauge structure . Then, we introduce the notion of constructive approach for the lattice gauge theories, which leads to a family of gauge theories, the gauge magnets. This family corresponds to quantum link models for the U(1) gauge theory, which consider a truncated dimensional representation of the gauge group. First of all, we (re)discover the phase diagram of the gauge magnet in 2+1 D. Then, we propose a realistic implementation of a digital quantum simulation of the U(1) gauge magnet by using Rydberg atoms, considering that the amount of resources needed for the simulation of link models is drastically reduced as the local Hilbert space shrinks from infinity to 2D (qubit). Finally, motivated by the advances in the simulation of open quantum systems, we turn to consider some aspects concerning the dynamics of correlated quantum many body systems. Specifically we study the time evolution of a quench protocol that conserves the entanglement spectrum of a bipartition. We consider the splitting of a critical Ising chain in two independent chains, and compare it with the case of joining two chains, which does not conserve the entanglement spectrum. We show that both quenches are both locally and globally distinguishable. Our results suggest that this conservation plays a fundamental role in both the out-of-equilibrium dynamics and the subsequent equilibration mechanismL'estudi dels àtoms ultrafreds constitueix una de les àrees més actives de la física atòmica, molecular, òptica i de l'òptica quàntica. Els èxits teòrics i experimentals de les tres últimes dècades sobre el control i la manipulació de la matèria quàntica en escala macroscòpica condueix a l'anomenada tercera revolució quàntica. Concretament, els recents avenços en els estudis dels àtoms ultrafred en xarxes òptiques proporcionen un sistema que es pot reajustar i reorganitzat per imitar el comportament d'altres sistemes de molts cossos: els gasos d'àtoms ultrafreds en xarxes òptiques actuen com a genuïns simuladors quàntics. La comprensió de les teories de gauge és clau per a la descripció de les interaccions fonamentals del nostre món físic. Particularment, les teories de gauge descriuen una de les més importants classes de sistemes que poden ser tractats amb simuladors quàntics. L'objectiu principal de la tesi és estudiar la implementació de simuladors quàntics de teories de gauge amb gasos d'àtoms ultrafreds en xarxes òptiques. En primer lloc, analitzem un sistema format per un gas ultrafred no interaccionant en una xarxa 2D sota l'acció d'un camp de gauge exòtic i extern provinent del grup de gauge de Heisenberg-Weyl. Descrivim un nou mètode per simular el grau de llibertat gauge, que consisteix a associar la coordenada gauge a una coordenada real i perpendicular a l'espai 2D de les posicions. Així, el sistema resultar ser un aïllant 3D amb topologia no trivial, concretament un aïllant Hall quàntic. Seguidament, estudiem un simulador quàntic analògic de camps de gauge dinàmics amb àtoms alcalinoterris en una xarxa hexagonal. Al régim fortament repulsiu amb un àtom en cada lloc, l'estat fonamental és un líquid espinorial quiral amb la simetria d'inversió temporal trencada. Les fluctuacions d'espín al voltant d'aquesta configuració vénen descrites per una teoria gauge U(1) emergent amb un terme topològic de Chern-Simons. També tractem l'estabilitat dels tres estats amb mínima energia, tot observant una temperatura crítica comuna. Considerem indicis experimentals mesurables dels estats de camp mitjà, que poden ser claus per revelar l'estructura gauge. A continuació, introduïm un enfoc constructiu per a teories gauge en el reticle, la qual porta a una família de teories de gauge, els magnets de gauge. Aquesta família es correspon amb els models d'enllaços quàntics de la teoria gauge U(1). Primer, (re)descobrim el diagrama de fases del magnet de gauge en 2+1 D. Després, proposem una implementació realista d'un simulador quàntic digital del magnet de gauge U(1) amb àtoms de Rydberg, considerant que el nombre de recursos necessaris per a la simulació dels models d'enllaços es redueix dràsticament pel fet que l'espai d' Hilbert local disminueix de dimensió infinita a 2 (bit quàntic). Finalment, motivats pels avenços en la simulació de sistemes quàntics oberts, considerem alguns aspectes de la dinàmica de sistemes quàntics correlacionats de molts cossos. Específicament, estudiem l'evolució temporal en un protocol de canvi sobtat que conserva l'espectre d'entrellaçament d'una bipartició. Considerem la ruptura d'una cadena d'Ising en dues cadenes independents i ho comparem amb la unió de dues cadenes, la qual no conserva l'espectre d'entrellaçamentEl estudio de los átomos ultrafríos constituye una de las áreas mas activas de la física atómica, molecular, óptica y de la óptica cuántica. Los logros teóricos y experimentales de las tres últimas décadas sobre el control y la manipulación de la materia cuántica a escala macroscópica conducen a la denominada tercera revolución cuántica. Concretamente, los avances recientes en los estudios de átomos ultrafríos en redes ópticas proporcionan un sistema que puede ser reajustado y reorganizado para imitar el comportamiento de otros sistemas de muchos cuerpos: los gases de átomos ultrafríos en redes ópticas actúan como genuinos simuladores cuánticos. La comprensión de las teorías de gauge es clave para la descripción de la interacciones fundamentales de nuestro mundo físico. En particular, las teorías de gauge describen una de las mas importante clase de sistemas que pueden ser abordados con simuladores cuánticos. El objetivo principal de la tesis es estudiar la implementación de simuladores cuánticos de teorías de gauge con gases de átomos ultrafríos en redes ópticas. En primer lugar, analizamos un sistema formado por un gas ultrafrío no interactuante en una red 2D, bajo la acción de un campo de gauge exótico y externo descrito por el grupo de gauge de Heisenberg-Weyl. Describimos un método novedoso para simular el grado de libertad gauge , que consiste en asociar la coordenada gauge a una coordenada real y perpendicular al espacio 2D de las posiciones. Así, el sistema resulta ser un aislante 3D con una topología no trivial, específicamente un aislante Hall cuántico. Seguidamente, estudiamos un simulador cuántico analógico de campos de gauge dinámicos, considerando átomos alcalinotérreos en una red hexagonal. En el régimen fuertemente repulsivo con una átomo en cada sitio, el estado fundamental es un liquido espinorial quiral con la simetría de inversión temporal rota. Las fluctuaciones de espín alrededor de dicha configuración vienen dadas en términos de una teoría de gauge U(1) emergente con un término topológico de Chern-Simons. También tratamos la estabilidad de los tres estados con mínima energía, observando una temperatura crítica común. Consideramos indicios experimentales medibles de los estados de campo medio, que pueden claves para revelar la estructura de gauge. A continuación, introducimos la noción del enfoque constructivo para teorías de gauge en el retículo, lo que conduce a una familia de teorías de gauge, los magnetos de gauge. Esta familia se corresponde con los modelos de enlaces cuánticos para la teoría de gauge U(1), los cuales consideran una representación dimensional truncada del grupo de gauge. Primeramente, (re)descubrimos el diagrama de fases del magneto de gauge en 2+1D. Seguidamente, proponemos un implementación realista de un simulador cuántico digital del magneto de gauge U(1) usando átomos de Rydberg, considerando que el número de recursos necesarios para la simulación de los modelos de enlace está drásticamente reducido debido a que el espacio de Hilbert local disminuye de infinitas dimensiones a 2 (bit cuántico). Finalmente, motivados por los avances en la simulación de sistemas cuánticos abiertos, consideramos algunos aspectos sobre la dinámica de sistemas cuánticos correlacionados de muchos cuerpos . Específicamente, estudiamos la evolución temporal en un protocolo de cambio súbito que conserva el espectro de entrelazamiento de una bipartición. Consideramos la ruptura de una cadena de Ising en dos cadenas independientes y lo comparamos con la unión de dos cadenas, la cual no conserva el espectro de entrelazamiento. Estos dos cambios abruptos son localmente y globalmente distinguibles. Nuestro resultado sugiere que la mencionada conservación juega un papel fundamental en la dinámica fuera de equilibrio y en el consiguiente equilibrio