SOUSA, Ariel Adorno de. Vazamentos de corrente e ineficiência de transporte em nanoestruturas semicondutoras investigadas através de propagação de pacotes de onda. 2015. 149 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2015. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-06-11T18:23:58Z No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-06-11T18:24:41Z (GMT) No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) / Made available in DSpace on 2015-06-11T18:24:41Z (GMT). No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) Previous issue date: 2015 / Advances in growth techniques have made possible the fabrication of quasi one-dimensional semiconductor structures on nanometric scales, called quantum dots, wires, wells and rings. Interest in these structures has grown considerably not only due to their possible applications in electronic devices and to their easy chemical manipulation, but also because they offer the possibility of experimentally exploring several aspects of quantum confinement, scattering and interference phenomena. In particular, in this work, we investigate the electronic and transport properties in quantum wells, wires and rings, whose dimensions can be achieved experimentally. For this purpose, we solve the time-dependent Schrödinger equation using the split-operator method in two dimensions. We address four different problems: in the first one, the electronic transport properties of a mesoscopic branched out quantum ring are discussed in analogy to the Braess Paradox of game theory, which, in simple words, states that adding an extra path to a traffic network does not necessarily improves its overall flow. In this case, we consider a quantum ringindex{Quantum ring} with an extra channel in its central region, aligned with the input and output leads. This extra channel plays the role of an additional path in a similar way as the extra roads in the classical Braess paradox. Our results show that in this system, surprisingly the transmission coefficient decreases for some values of the extra channel width, similarly to the case of traffic networks in the original Braess problem. We demonstrate that such transmission reduction in our case originates from both quantum scattering and interference effects, and is closely related to recent experimental results in a similar mesoscopic system. In the second work of this thesis, we extend the first system by considering different ring geometries, and by investigating the effects of an external perpendicular magnetic field and of obstructions to the electrons pathways on the transport properties of the system. For narrow widths of the extra channel, it is possible to observe Aharonov-Bohm oscillations in the transmission probability. More importantly, the Aharonov-Bohm phase acquired by the wave function in the presence of the magnetic field allows one to verify in which situations the transmission reduction induced by the extra channel is purely due to interference. We simulate a possible closure of one of the paths by applying a local electrostatic potential, which can be seen as a model for the charged tip of an atomic force microscope (AFM). We show that positioning the AFM tip in the extra channel suppresses the transmission reduction due to the Braess paradox, thus demonstrating that closing the extra path improves the overall transport properties of the system. In the third work, we analyze the tunneling of wave packets between two semiconductor quantum wires separated by a short distance. We investigate the smallest distance at which a significant tunneling between the semiconduting wires still occur. This work is of fundamental importantance for the manufacturing of future nanostructured devices, since it provides information on the minimum reasonable distances between the electron channels in miniaturized electronic circuits, where quantum tunnelling and interference effects will start to play a major role. In the last work of this thesis, we investigate the binding energy of the electron-impurity pair in a GaN/HfO2 quantum well. We consider simultaneously the contributions of all interactions in the self-energy due to the dielectric constant mismatch between materials. We investigate the electron-impurity bound states in quantum wells of several widths, and compared the results for different impurity positions. / Os avanços nas técnicas de crescimento tornaram possível a fabricação de estruturas semicondutoras quase-unidimensionais em escalas nanométricas, chamadas pontos, fios, poços e anéis quânticos. Interesse nessas estruturas tem crescido consideravelmente, não só devido às suas possíveis aplicações em dispositivos eletrônicos e à sua manipulação química fácil, mas também porque eles oferecem a possibilidade de explorar experimentalmente vários aspectos de confinamento quântico, espalhamento e fenômenos de interferência. Em particular, neste trabalho, investigamos as propriedades eletrônicas e de transporte em poços quânticos, fios e anéis, cujas dimensões podem ser alcançados experimentalmente. Para isto, resolvemos a equação de Schrödinger dependente do tempo utilizando o método Split-operator em duas dimensões. Nesta tese, abordamos quatro trabalhos, sendo o primeiro uma analogia ao Paradoxo de Braess para um sistema mesoscópico. Para isso, utilizamos um anel quântico com um canal adicional na região central, alinhado com os canais de entrada e saída. Este canal extra faz o papel do caminho adicional em uma rede de tráfego na teoria dos jogos, similar ao caso do paradoxo de Braess. Calculamos as auto-energias e a evolução temporal para o anel quântico. Surpreendentemente, o coeficiente de transmissão para algumas larguras do canal extra diminuiu, semelhante ao que acontece com redes de tráfego, onde a presença de uma via extra não necessariamente melhora o fluxo total. Com a analise dos resultados obtidos, foi possível determinar que neste sistema o paradoxo ocorre devido a efeitos de interferência e de espalhamento quântico. No segundo trabalho, foi feita uma extensão do primeiro, (i) aplicando-se um campo magnético, onde foi possível obter o efeito Aharonov-Bohm para pequenos valores do canal extra e controlar efeitos de interferência responsáveis pelo paradoxo mencionado, e (ii) fazendo também a aplicação de um potencial que simula a ponta de um microscópio de força atômica (AFM) interagindo com a amostra - este potencial é repulsivo e simula um possível fechamento do caminho em que o pacote de onda se propaga. Assim, neste trabalho, realizamos uma contra-prova do primeiro, onde observamos que com o posicionamento da ponta do AFM sobre canal extra, se diminui o efeito de redução de corrente devido ao paradoxo de Braess. No terceiro trabalho, realizamos uma análise de tunelamento entre dois fios quânticos separados por uma certa distância e calculamos qual a menor distância para qual ocorre tunelamento significativo nesse sistema eletrônico. Este trabalho é de fundamental importância para o manufaturamento de dispositivos nanoestruturados, porque nos permite investigar qual a distância mínima para a construção de um circuito eletrônico sem que haja interferências nas transmissões das informações. No quarto e último trabalho desta tese, investigamos a energia de ligação do elétron-impureza em GaN/HfO2 para um poço quântico. Consideramos simultaneamente as contribuições de todas as interações das auto-energias devido ao descasamento das constantes dielétricas entre os materiais. Foram estudados poços largos e estreitos, comparando os resultados para diferentes posições da impureza e a contribuição da auto-energia para o sistema.

This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems. Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry. In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique. Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally. In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states. The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.

This work is about the properties of several low dimensional, small systems of interacting particles. We demonstrate that interaction between particles in the low dimensional small systems can lead to many unexpected effects. We considered electrons in a Luttinger liquid, in a superconducting state, and atoms in a magneto-optical trap. Using bosonization techniques we calculated the thermopower of a Luttinger liquid wire with an impurity. We predicted the appearance of a phase dependent force and resonant phase dependent magnetization in the nanoscopic superconductor - normal metal superconductor (or superconductor - two dimensional electron gas - superconductor) junction. We also considered plasma oscillations inside thin superconducting tubes and rings and predicted that the velocities of the plasmons in these systems are periodic functions of the magnetic flux. By considering neutral atoms in a harmonic trap we discovered that strongly repelling atoms do not form Bose-Einstein condensate at zero temperature but tend to occupy different orbitals with small mutual overlap, forming crystallite structures similar to Wigner molecules of electrons inside a quantum dot.

This work presents a joint theoretical and experimental investigation of the electronic structure of quasi one-dimensional cuprates and vanadates. Electron energy-loss spectroscopy in transmission was employed to measure the momentum-dependent loss function of Li2CuO2, CuGeO3, V2O5 and NaV2O5. The comparison between the experimental data and the results from bandstructure as well as cluster calculations allows an explanation of the mobility and correlations of the electrons in these systems. The investigation of the electronic structure of the structurally related cuprates Li2CuO2 and CuGeO3 is exemplary for the study of the transition from a quasi zero-dimensional to a quasi one-dimensional system. In contrast to Li2CuO2 where the electron transitions are strongly localized, the excited states in CuGeO3 can be assigned to the electron hopping to the nearest-neighboured CuO4 plaquettes. The shift of spectral weight from the high energy to the low energy region with increasing coupling between the plaquettes, observed in edge-sharing CuO2 chains, is confirmed by the applied cluster modell. The momentum dependent loss functions of NaV2O5 deliver information about the mobility and correlations of electrons in a quarter-filled ladder system which determine the transition from the charge ordered state into the unordered state at 34 K. Thcontributions of the 3d electrons to the EELS spectra of NaV2O5 are filtered by comparing these spectra with the loss functions of the structurally related V2O5 (d0 configuration). For NaV2O5 the picture of linear chains of V-O-V rungs containing a single d electron in a molecular orbital-like state is confirmed. The comparison of the experimentally determined optical conductivities and those derived from the bandstructrure calculations yield a good agreement upon adoption of an on-site Coulomb interaction U = 2-3 eV. In contrast to the strongly anisotropic hopping within the ladder plane the intersite Coulomb interactions V are about the same size. These interactions are the driving force for the transition from an unordered state at room temperature into a zigzag ordered state observed at low temperatures. / In einer Kombination aus experimentellen und theoretischen Methoden wurden in dieser Arbeit die Elektronenstrukturen von quasi-eindimensionalen Kupraten und Vanadaten untersucht. Dazu wurde die impulsabhängige Verlustfunktion mit Hilfe der Elektronen-Energieverlustspektroskopie in Transmission an Einkristallen von Li2CuO2, CuGeO3, V2O5 und NaV2O5 gemessen. Der Vergleich der experimentellen Daten mit Ergebnissen aus Bandstruktur- und Cluster-Rechnungen erlaubte Rückschlüsse auf die Beweglichkeit und Korrelationen der Elektronen in diesen Systemen. Die Untersuchung der elektronischen Anregungen in den strukturell sehr ähnlichen Kupraten Li2CuO2 und CuGeO3 ist beispielhaft für das Studium des Übergangs von einem quasi-nulldimensionalen zu einem quasi-eindimensionalen System. In Li2CuO2 finden die elektronischen Übergänge vorwiegend lokal auf der CuO4-Plakette statt. Dagegen findet man in CuGeO3 angeregte Zustände, die als das Hüpfen der Elektronen auf benachbarte Plaketten interpretiert werden können. Das angewandte Cluster-Modell bestätigt für eine zunehmende Kopplung zwischen den Plaketten die in eckenverbundenen Kupratketten beobachtete Verschiebung des spektralen Gewichts vom hoch- zum niederenergetischen Bereich. Die Verlustfunktionen von NaV2O5 liefern wertvolle Informationen über die Freiheitsgrade und Korrelationen der Elektronen in einem viertelgefüllten Leitersystem, die wesentlich den Phasenübergang zwischen geordneter und ungeordneter Ladung bei 34 K bestimmen. Die Beiträge der 3d-Elektronen von NaV2O5 zu den EELS-Spektren konnten durch eine vergleichende Studie der Verlustfunktionen des strukturell verwandten V2O5, das keine d-Elektronen besitzt, separiert werden. Die Beschreibbarkeit der Elektronenstruktur in NaV2O5 durch ein effektives Modell einfach besetzter, molekülähnlicher V-O-V-Sprossen wird bestätigt. Die Coulomb-Wechselwirkung U kann in diesem Modell auf den Wertebereich zwischen 2 und 3 eV eingeschränkt werden. Im Gegensatz zu den stark anisotropen Hüpfwahrscheinlichkeiten in der Leiterebene sind die Coulomb-Wechselwirkungen V zwischen Elektronen auf benachbarten Vanadiumplätzen nahezu von gleicher Größe. Diese Wechselwirkungen sind die treibende Kraft für den Übergang von einem ungeordneten Zustand bei Raumtemperatur in einen zickzackgeordneten Grundzustand bei tiefen Temperaturen.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Os avanÃos nas tÃcnicas de crescimento tornaram possÃvel a fabricaÃÃo de estruturas semicondutoras quase-unidimensionais em escalas nanomÃtricas, chamadas pontos, fios, poÃos e anÃis quÃnticos. Interesse nessas estruturas tem crescido consideravelmente, nÃo sà devido Ãs suas possÃveis aplicaÃÃes em dispositivos eletrÃnicos e à sua manipulaÃÃo quÃmica fÃcil, mas tambÃm porque eles oferecem a possibilidade de explorar experimentalmente vÃrios aspectos de confinamento quÃntico, espalhamento e fenÃmenos de interferÃncia. Em particular, neste trabalho, investigamos as propriedades eletrÃnicas e de transporte em poÃos quÃnticos, fios e anÃis, cujas dimensÃes podem ser alcanÃados experimentalmente. Para isto, resolvemos a equaÃÃo de SchrÃdinger dependente do tempo utilizando o mÃtodo Split-operator em duas dimensÃes. Nesta tese, abordamos quatro trabalhos, sendo o primeiro uma analogia ao Paradoxo de Braess para um sistema mesoscÃpico. Para isso, utilizamos um anel quÃntico com um canal adicional na regiÃo central, alinhado com os canais de entrada e saÃda. Este canal extra faz o papel do caminho adicional em uma rede de trÃfego na teoria dos jogos, similar ao caso do paradoxo de Braess. Calculamos as auto-energias e a evoluÃÃo temporal para o anel quÃntico. Surpreendentemente, o coeficiente de transmissÃo para algumas larguras do canal extra diminuiu, semelhante ao que acontece com redes de trÃfego, onde a presenÃa de uma via extra nÃo necessariamente melhora o fluxo total. Com a analise dos resultados obtidos, foi possÃvel determinar que neste sistema o paradoxo ocorre devido a efeitos de interferÃncia e de espalhamento quÃntico. No segundo trabalho, foi feita uma extensÃo do primeiro, (i) aplicando-se um campo magnÃtico, onde foi possÃvel obter o efeito Aharonov-Bohm para pequenos valores do canal extra e controlar efeitos de interferÃncia responsÃveis pelo paradoxo mencionado, e (ii) fazendo tambÃm a aplicaÃÃo de um potencial que simula a ponta de um microscÃpio de forÃa atÃmica (AFM) interagindo com a amostra - este potencial à repulsivo e simula um possÃvel fechamento do caminho em que o pacote de onda se propaga. Assim, neste trabalho, realizamos uma contra-prova do primeiro, onde observamos que com o posicionamento da ponta do AFM sobre canal extra, se diminui o efeito de reduÃÃo de corrente devido ao paradoxo de Braess. No terceiro trabalho, realizamos uma anÃlise de tunelamento entre dois fios quÃnticos separados por uma certa distÃncia e calculamos qual a menor distÃncia para qual ocorre tunelamento significativo nesse sistema eletrÃnico. Este trabalho à de fundamental importÃncia para o manufaturamento de dispositivos nanoestruturados, porque nos permite investigar qual a distÃncia mÃnima para a construÃÃo de um circuito eletrÃnico sem que haja interferÃncias nas transmissÃes das informaÃÃes. No quarto e Ãltimo trabalho desta tese, investigamos a energia de ligaÃÃo do elÃtron-impureza em GaN/HfO2 para um poÃo quÃntico. Consideramos simultaneamente as contribuiÃÃes de todas as interaÃÃes das auto-energias devido ao descasamento das constantes dielÃtricas entre os materiais. Foram estudados poÃos largos e estreitos, comparando os resultados para diferentes posiÃÃes da impureza e a contribuiÃÃo da auto-energia para o sistema. / Advances in growth techniques have made possible the fabrication of quasi one-dimensional semiconductor structures on nanometric scales, called quantum dots, wires, wells and rings. Interest in these structures has grown considerably not only due to their possible applications in electronic devices and to their easy chemical manipulation, but also because they offer the possibility of experimentally exploring several aspects of quantum confinement, scattering and interference phenomena. In particular, in this work, we investigate the electronic and transport properties in quantum wells, wires and rings, whose dimensions can be achieved experimentally. For this purpose, we solve the time-dependent SchrÃdinger equation using the split-operator method in two dimensions. We address four different problems: in the first one, the electronic transport properties of a mesoscopic branched out quantum ring are discussed in analogy to the Braess Paradox of game theory, which, in simple words, states that adding an extra path to a traffic network does not necessarily improves its overall flow. In this case, we consider a quantum ringindex{Quantum ring} with an extra channel in its central region, aligned with the input and output leads. This extra channel plays the role of an additional path in a similar way as the extra roads in the classical Braess paradox. Our results show that in this system, surprisingly the transmission coefficient decreases for some values of the extra channel width, similarly to the case of traffic networks in the original Braess problem. We demonstrate that such transmission reduction in our case originates from both quantum scattering and interference effects, and is closely related to recent experimental results in a similar mesoscopic system. In the second work of this thesis, we extend the first system by considering different ring geometries, and by investigating the effects of an external perpendicular magnetic field and of obstructions to the electrons pathways on the transport properties of the system. For narrow widths of the extra channel, it is possible to observe Aharonov-Bohm oscillations in the transmission probability. More importantly, the Aharonov-Bohm phase acquired by the wave function in the presence of the magnetic field allows one to verify in which situations the transmission reduction induced by the extra channel is purely due to interference. We simulate a possible closure of one of the paths by applying a local electrostatic potential, which can be seen as a model for the charged tip of an atomic force microscope (AFM). We show that positioning the AFM tip in the extra channel suppresses the transmission reduction due to the Braess paradox, thus demonstrating that closing the extra path improves the overall transport properties of the system. In the third work, we analyze the tunneling of wave packets between two semiconductor quantum wires separated by a short distance. We investigate the smallest distance at which a significant tunneling between the semiconduting wires still occur. This work is of fundamental importantance for the manufacturing of future nanostructured devices, since it provides information on the minimum reasonable distances between the electron channels in miniaturized electronic circuits, where quantum tunnelling and interference effects will start to play a major role. In the last work of this thesis, we investigate the binding energy of the electron-impurity pair in a GaN/HfO2 quantum well. We consider simultaneously the contributions of all interactions in the self-energy due to the dielectric constant mismatch between materials. We investigate the electron-impurity bound states in quantum wells of several widths, and compared the results for different impurity positions.

This work presents a joint theoretical and experimental investigation of the electronic structure of quasi one-dimensional cuprates and vanadates. Electron energy-loss spectroscopy in transmission was employed to measure the momentum-dependent loss function of Li2CuO2, CuGeO3, V2O5 and NaV2O5. The comparison between the experimental data and the results from bandstructure as well as cluster calculations allows an explanation of the mobility and correlations of the electrons in these systems. The investigation of the electronic structure of the structurally related cuprates Li2CuO2 and CuGeO3 is exemplary for the study of the transition from a quasi zero-dimensional to a quasi one-dimensional system. In contrast to Li2CuO2 where the electron transitions are strongly localized, the excited states in CuGeO3 can be assigned to the electron hopping to the nearest-neighboured CuO4 plaquettes. The shift of spectral weight from the high energy to the low energy region with increasing coupling between the plaquettes, observed in edge-sharing CuO2 chains, is confirmed by the applied cluster modell. The momentum dependent loss functions of NaV2O5 deliver information about the mobility and correlations of electrons in a quarter-filled ladder system which determine the transition from the charge ordered state into the unordered state at 34 K. Thcontributions of the 3d electrons to the EELS spectra of NaV2O5 are filtered by comparing these spectra with the loss functions of the structurally related V2O5 (d0 configuration). For NaV2O5 the picture of linear chains of V-O-V rungs containing a single d electron in a molecular orbital-like state is confirmed. The comparison of the experimentally determined optical conductivities and those derived from the bandstructrure calculations yield a good agreement upon adoption of an on-site Coulomb interaction U = 2-3 eV. In contrast to the strongly anisotropic hopping within the ladder plane the intersite Coulomb interactions V are about the same size. These interactions are the driving force for the transition from an unordered state at room temperature into a zigzag ordered state observed at low temperatures. / In einer Kombination aus experimentellen und theoretischen Methoden wurden in dieser Arbeit die Elektronenstrukturen von quasi-eindimensionalen Kupraten und Vanadaten untersucht. Dazu wurde die impulsabhängige Verlustfunktion mit Hilfe der Elektronen-Energieverlustspektroskopie in Transmission an Einkristallen von Li2CuO2, CuGeO3, V2O5 und NaV2O5 gemessen. Der Vergleich der experimentellen Daten mit Ergebnissen aus Bandstruktur- und Cluster-Rechnungen erlaubte Rückschlüsse auf die Beweglichkeit und Korrelationen der Elektronen in diesen Systemen. Die Untersuchung der elektronischen Anregungen in den strukturell sehr ähnlichen Kupraten Li2CuO2 und CuGeO3 ist beispielhaft für das Studium des Übergangs von einem quasi-nulldimensionalen zu einem quasi-eindimensionalen System. In Li2CuO2 finden die elektronischen Übergänge vorwiegend lokal auf der CuO4-Plakette statt. Dagegen findet man in CuGeO3 angeregte Zustände, die als das Hüpfen der Elektronen auf benachbarte Plaketten interpretiert werden können. Das angewandte Cluster-Modell bestätigt für eine zunehmende Kopplung zwischen den Plaketten die in eckenverbundenen Kupratketten beobachtete Verschiebung des spektralen Gewichts vom hoch- zum niederenergetischen Bereich. Die Verlustfunktionen von NaV2O5 liefern wertvolle Informationen über die Freiheitsgrade und Korrelationen der Elektronen in einem viertelgefüllten Leitersystem, die wesentlich den Phasenübergang zwischen geordneter und ungeordneter Ladung bei 34 K bestimmen. Die Beiträge der 3d-Elektronen von NaV2O5 zu den EELS-Spektren konnten durch eine vergleichende Studie der Verlustfunktionen des strukturell verwandten V2O5, das keine d-Elektronen besitzt, separiert werden. Die Beschreibbarkeit der Elektronenstruktur in NaV2O5 durch ein effektives Modell einfach besetzter, molekülähnlicher V-O-V-Sprossen wird bestätigt. Die Coulomb-Wechselwirkung U kann in diesem Modell auf den Wertebereich zwischen 2 und 3 eV eingeschränkt werden. Im Gegensatz zu den stark anisotropen Hüpfwahrscheinlichkeiten in der Leiterebene sind die Coulomb-Wechselwirkungen V zwischen Elektronen auf benachbarten Vanadiumplätzen nahezu von gleicher Größe. Diese Wechselwirkungen sind die treibende Kraft für den Übergang von einem ungeordneten Zustand bei Raumtemperatur in einen zickzackgeordneten Grundzustand bei tiefen Temperaturen.

Cette thèse présente une étude des propriétés électroniques de systèmes de basse dimension à base de métaux et de semiconducteurs. La première partie de l'étude traite le confinement de l'état de Shockley dans des nanostructures tridimensionnelles d'Ag(111), par des mesures STM/STS à très basse température (5 K). Nous avons d'abord analysé en détail la structure en énergie et la distribution spatiale des modes confinés. Nous avons ensuite mis à profit la nature discrète du spectre en énergie pour étudier le temps de vie des quasiparticules. Un comportement typique de liquide de Fermi est mis en évidence, et nous montrons que le mécanisme de diffusion dominant est associé au couplage électron-phonon. La contribution extrinsèque provenant du confinement partiel de l'onde électronique a également été obtenue. Une loi d'échelle est observée avec la taille des nanostructures, ce qui permet d'extraire un coefficient de réflexion plus important que dans de simples ilôts monoatomiques. La seconde partie de l'étude est consacrée aux couches ultra-minces semiconductrices obtenues par dépôts d'alcalins (K, Rb, Cs) sur la surface Si(111):B-[racine]3. Ce travail résout la controverse concernant la nature de l'état fondamental de ce système, et notamment l'origine de la reconstruction 2[racine]3 obtenue à la saturation du taux de couverture. La compréhension en amont de la structure cristallographique permet d'élucider les propriétés électroniques. Nous montrons qu'une approche à un électron, conduisant à un isolant de bandes, décrit le système de manière convaincante, malgré l'indication de forts effets polaroniques. Ce résultat est le fruit d'une étude approfondie combinant des techniques diverses et complémentaires (LEED, ARPES, XPS, STM/STS et calcul DFT) / This thesis is devoted to the electronic properties of low-dimensional systems based on metal and semiconducting materials. The first part deals with the Shockley state confinement in Ag(111) nanostructures, by means of very-low temperature (5 K) STM/STS measurements. We study the electronic structure and spatial distribution of the confined modes. Then the discrete nature of the electronic spectrum allows one to yield the quasiparticule lifetime. A Fermi-liquid behaviour is evidenced and we show that the dominant decay mechanism is attributed to the electron-phonon coupling. The extrinsic contribution arising from the partial confinement of the electronic wave is obtained as well. A scaling law with the nanostructure width is demonstrated, from which we deduce a higher reflection amplitude than in monoatomic islands. In the second part of the thesis, we study semiconducting ultra-thin films produced by alkali (K, Rb, Cs) deposition on the Si(111):B-[root of]3 surface. This work solves the controversy concerning the ground state of this system, and especially the nature of the 2[root of]3 surface recontruction obtained at saturation coverage. Prior understanding of the crystallographic structure allows to elucidate the electronic properties. We show that a one-electron picture, leading to a band insulator scenario, gives a good description of the system, in spite of strong polaronic effects. This conclusion results from an in-depth, combined study of complementary techniques (LEED, ARPES, XPS, STM/STS and DFT calculations).

Thema der vorliegenden Arbeit ist die Untersuchung ausgewählter niederdimensionaler Schichtgittersysteme, wobei das Hauptinteresse in der Erforschung der elektronischen Struktur im Zusammenhang mit Interkalationsexperimenten liegt. Einkristalline Graphit-, TiSe2- und TaSe2-Proben wurden vor und nach der Interkalation mit winkelaufgelöster Photoemission, Fermi- und Isoenergieflächenmessungen und Elektronenbeugung (LEED) analysiert. Als Interkalationsmaterialien wurden U, Eu, Gd und Cs verwendet. Die experimentellen Daten wurden mit Ergebnissen von LDA-LCAO-Bandstrukturrechnungen und Simulationen im Rahmen eines Single-Impurity-Anderson-Modells verglichen. Neben dem Einfluß unterschiedlicher Valenzelektronen der interkalierten Atome auf den Einlagerungsprozeß werden Fragen zum Lokalisierungsverhalten von 4f- und 5f-Zuständen und zu den Veränderungen in der Dimensionalität der Verbindungen durch die Einlagerung diskutiert. Ein weiterer Schwerpunkt dieser Arbeit befaßt sich mit Untersuchungen zur temperaturabhängigen Ausbildung von Ladungsdichtewellen in 1T-TaSe2. / Subject of the present thesis are investigations of selected low-dimensional layered lattice systems, with the principal goal to study the electronic structure in relation to intercalation experiments. Single-crystalline graphite-, TiSe2 - and TaSe2- samples were analyzed by angle-resolved photoemission, Fermi- and isoenergy-surface measurements, and low energy electron diffraction experiments before and after intercalation. U, Eu, Gd, and Cs were used as materials for the intercalation process. The experimental results were compared with theoretical LDA-LCAO band-structure calculations and with simulations in the framework of a single-impurity Anderson model. In addition to the influence of different numbers of valence electrons from intercalated atoms, questions concerning the localization of 4f and 5f states and changes in the dimensionality of the compounds due to the intercalation process are discussed. Investigations of the temperature dependent formation of charge density waves in 1T-TaSe2 complete this work.

This thesis presents the work done on electronic transport in various interacting and non-interacting systems in one and two dimensions. The systems under study are: an interacting quantum dot [1], a non-interacting quantum wire and a ring in which time-dependent potentials are applied [2], an interacting quantum wire and networks of multiple quantum wires with resistive regions [3, 4], one-dimensional edge stages of a two-dimensional topological insulator [5], and a hybrid system of two-dimensional surface states of a three-dimensional topological insulator and a superconductor [6]. In the first chapter, we introduce a number of concepts which are used in the rest of the thesis, such as scattering theory, Landauer conductance formula, quantum wires, bosonization, topological insulators and superconductor. In the second chapter, we study transport through a quantum dot with interacting electrons which is connected to two reservoirs. The quantum dot is modeled by two sites within a tight-binding model with spinless electrons. Using the Lippman-Schwinger method, we write down an exact two-particle wave function for the dot-reservoir system with the interaction localized in the region of the dot. We discuss the phenomena of two-particle resonance and rectification. In the third chapter, we study pumping in two kinds of one-dimensional systems: (i) an infinite line connected to reservoirs at the two ends, and (ii) an isolated ring. The infinite line is modeled by the Dirac equation with two time-independent point-like backscatterers that create a resonant barrier. We demonstrate that even if the reservoirs are at the same chemical potential, a net current can be driven through the channel by the application of one or more time-dependent point-like potentials. When the left-right symmetry is broken, a net current can be pumped from one reservoir to the other by applying a time-varying potential at only one site. For a finite ring, we model the system by a tight-binding model. The ring is isolated in the sense that it is not connected to any reservoir or environment. The system is driven by one or more time-varying on-site potentials. We develop an exact method to calculate the current averaged over an infinite amount of time by converting it to the calculation of the current carried by certain states averaged over just one time period. Using this method, we demonstrate that an oscillating potential at only one site cannot pump charge, and oscillating potentials at two or more sites are necessary to pump charge. Further we study the dependence of the pumped current on the phases and the amplitudes of the oscillating potentials at two sites. In the fourth chapter, we study the effect of resistances present in an extended region in a one-dimensional quantum wire described by a Tomonaga-Luttinger liquid model. We combine the concept of a Rayleigh dissipation function with the technique of bosonization to model the dissipative region. In the DC limit, we find that the resistance of the dissipative patch adds in series to the contact resistance. Using a current splitting matrix M to describe junctions, we study in detail the conductances of: a three-wire junction with resistances and a parallel combination of resistances. The conductance and power dissipated in these networks depend in general on the resistances and the current splitting matrices that make up the network. We also show that the idea of a Rayleigh dissipation function can be extended to couple two wires; this gives rise to a finite transconductance analogous to the Coulomb drag. In the fifth chapter, we study the effect of a Zeeman field coupled to the edge states of a two-dimensional topological insulator. These edge states form two one-dimensional channels with spin-momentum locking which are protected by time-reversal symmetry. We study what happens when time-reversal symmetry is broken by a magnetic field which is Zeeman-coupled to the edge states. We show that a magnetic field over a finite region leads to Fabry-P´erot type resonances and the conductance can be controlled by changing the direction of the magnetic field. We also study the effect of a static impurity in the patch that can backscatter electrons in the presence of a magnetic field. In the sixth chapter, we use the Blonder-Tinkham-Klapwijk formalism to study trans-port across a line junction lying between two orthogonal topological insulator surfaces and a superconductor (which can have either s-wave or p-wave pairing). The charge and spin conductances across such a junction and their behaviors as a function of the bias voltage applied across the junction and various junction parameters are studied. Our study reveals that in addition to the zero conductance bias peak, there is a non-zero spin conductance for some particular spin states of the triplet Cooper pairs. We also find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for a p-wave symmetry of the superconductor order parameter.

Thema der vorliegenden Arbeit ist die Untersuchung ausgewählter niederdimensionaler Schichtgittersysteme, wobei das Hauptinteresse in der Erforschung der elektronischen Struktur im Zusammenhang mit Interkalationsexperimenten liegt. Einkristalline Graphit-, TiSe2- und TaSe2-Proben wurden vor und nach der Interkalation mit winkelaufgelöster Photoemission, Fermi- und Isoenergieflächenmessungen und Elektronenbeugung (LEED) analysiert. Als Interkalationsmaterialien wurden U, Eu, Gd und Cs verwendet. Die experimentellen Daten wurden mit Ergebnissen von LDA-LCAO-Bandstrukturrechnungen und Simulationen im Rahmen eines Single-Impurity-Anderson-Modells verglichen. Neben dem Einfluß unterschiedlicher Valenzelektronen der interkalierten Atome auf den Einlagerungsprozeß werden Fragen zum Lokalisierungsverhalten von 4f- und 5f-Zuständen und zu den Veränderungen in der Dimensionalität der Verbindungen durch die Einlagerung diskutiert. Ein weiterer Schwerpunkt dieser Arbeit befaßt sich mit Untersuchungen zur temperaturabhängigen Ausbildung von Ladungsdichtewellen in 1T-TaSe2. / Subject of the present thesis are investigations of selected low-dimensional layered lattice systems, with the principal goal to study the electronic structure in relation to intercalation experiments. Single-crystalline graphite-, TiSe2 - and TaSe2- samples were analyzed by angle-resolved photoemission, Fermi- and isoenergy-surface measurements, and low energy electron diffraction experiments before and after intercalation. U, Eu, Gd, and Cs were used as materials for the intercalation process. The experimental results were compared with theoretical LDA-LCAO band-structure calculations and with simulations in the framework of a single-impurity Anderson model. In addition to the influence of different numbers of valence electrons from intercalated atoms, questions concerning the localization of 4f and 5f states and changes in the dimensionality of the compounds due to the intercalation process are discussed. Investigations of the temperature dependent formation of charge density waves in 1T-TaSe2 complete this work.