This thesis comprises detailed experimental and theoretical investigations of the transport properties of one-dimensional nanostructures. Most of the work is dedicated to the exploration of the fascinating effects occurring in single wall carbon nanotubes (SWCNT). These particular nanostructures gained an overwhelming interest in the past two decades due to its outstanding electronic and mechanical features. We have investigated the properties of a novel family of carbon nanostructures, named here as Y-shaped rings. The studies show that they present very interesting quantum interference effects. A high structural stability under tensile strain and elevated temperatures is observed. Within the semi-classical potential adopted, the critical strain values of structure rupture lie in the same range of their pristine SWCNT counterparts. This is directly verified by the first observations of these ring-like structures in a transmission electron microscopy. A merging process of asymmetric into symmetric rings is investigated in-situ under electron beam irradiation at high temperatures. The electronic properties of these systems are theoretically studied using Monte Carlo simulations and environment dependent tight-binding calculations. From our results, we address the possibility of double-slit like interference processes of counter-propagating electron waves in the ring-like structures. The nature of well defined, sharp peaks in the density of states are determined as the discrete eigenenergies of the central loop part. Furthermore, the formation and dispersion of standing waves inside the ring is shown to originate from the quantum-dot like confinement of each branch between the leads. The obtained dispersion relation is shown to be the same occurring in purely one-dimensional quantum dots of similar geometries. Furthermore, Fabry-Perot-like interferences are observed. We established at the IFW a bottom-up processing route to fabricate nanotube based electronic devices. The SWCNTs are grown by chemical vapor deposition and we present a detailed study of the different approaches to obtain individual nanotubes suitable for a successful integration into electronic devices. Wet-chemistry and ultra-thin films as well as ferritin were employed as catalyst particles in the growth of SWCNT samples. By adjusting the optimized process parameters, we can control the obtained yield from thick nanotube forests down to just a couple of free-standing individual SWCNTs. The nanotubes are localized, contacted by standard e-beam lithography and characterized at ambient- as well as liquid helium temperatures. We usually obtain quite transparent contacts and the devices exhibit metallic or a mixed metallic/semiconducting behavior. The well-known memory effect upon gate voltage sweeping as well as single electron tunneling in the Coulomb blockade regime are addressed.

This thesis comprises detailed experimental and theoretical investigations of the transport properties of one-dimensional nanostructures. Most of the work is dedicated to the exploration of the fascinating effects occurring in single wall carbon nanotubes (SWCNT). These particular nanostructures gained an overwhelming interest in the past two decades due to its outstanding electronic and mechanical features. We have investigated the properties of a novel family of carbon nanostructures, named here as Y-shaped rings. The studies show that they present very interesting quantum interference effects. A high structural stability under tensile strain and elevated temperatures is observed. Within the semi-classical potential adopted, the critical strain values of structure rupture lie in the same range of their pristine SWCNT counterparts. This is directly verified by the first observations of these ring-like structures in a transmission electron microscopy. A merging process of asymmetric into symmetric rings is investigated in-situ under electron beam irradiation at high temperatures. The electronic properties of these systems are theoretically studied using Monte Carlo simulations and environment dependent tight-binding calculations. From our results, we address the possibility of double-slit like interference processes of counter-propagating electron waves in the ring-like structures. The nature of well defined, sharp peaks in the density of states are determined as the discrete eigenenergies of the central loop part. Furthermore, the formation and dispersion of standing waves inside the ring is shown to originate from the quantum-dot like confinement of each branch between the leads. The obtained dispersion relation is shown to be the same occurring in purely one-dimensional quantum dots of similar geometries. Furthermore, Fabry-Perot-like interferences are observed. We established at the IFW a bottom-up processing route to fabricate nanotube based electronic devices. The SWCNTs are grown by chemical vapor deposition and we present a detailed study of the different approaches to obtain individual nanotubes suitable for a successful integration into electronic devices. Wet-chemistry and ultra-thin films as well as ferritin were employed as catalyst particles in the growth of SWCNT samples. By adjusting the optimized process parameters, we can control the obtained yield from thick nanotube forests down to just a couple of free-standing individual SWCNTs. The nanotubes are localized, contacted by standard e-beam lithography and characterized at ambient- as well as liquid helium temperatures. We usually obtain quite transparent contacts and the devices exhibit metallic or a mixed metallic/semiconducting behavior. The well-known memory effect upon gate voltage sweeping as well as single electron tunneling in the Coulomb blockade regime are addressed.

Gegenstand dieser Arbeit sind Wellenphänomene in mesoskopischen Ringstrukturen. In Teil I der Arbeit befassen wir uns mit spinabhängigem Transport von Elektronen in effektiv eindimensionalen Ringen in Gegenwart inhomogener Magnetfelder. Wir benutzen die exakten Lösungen der Schrödinger-Gleichung im allgemeinen nicht-adiabatischen Fall in einem Transfer-Matrix-Formalismus und untersuchen Auswirkungen von geometrischen Phasen auf den Magnetwiderstand. Für den Spezialfall eines Magnetfeldes in der Ringebene sagen wir einen interessanten Spin-Flip-Effekt vorher, der die Steuerung der Polarisationsrichtung von Elektronen über einen externen Aharonov-Bohm-Fluß erlaubt. Optische mesoskopische Systeme sind Thema von Teil II dieser Arbeit. Wir betrachten zweidimensionale annulare Strukturen, charakterisiert durch unterschiedliche Brechungsindizes, sowohl im klassischen Bild der geometrischen Optik als auch mit Wellenmethoden auf der Grundlage der Maxwellschen Gleichungen. Insbesondere diskutieren wir erstmals eine Streumatrixbeschreibung optischer Mikroresonatoren und wenden sie auf das dielektrische annulare Billard an. Ein Vergleich der Ergebnisse des Wellen- und Strahlenbildes liefert eine gute Übereinstimmung, jedoch sind im Grenzfall großer Wellenlängen von der Ordnung der Systemabmessungen Korrekturen zum Strahlenbild nötig. Wir zeigen am Beispiel von Fresnel-Gesetzen für gekrümmte Oberflächen erstmals, daß der Goos-Hänchen-Effekt diese Korrekturen quantitativ erfaßt. Ausgehend von der Wellenbeschreibung leiten wir neue analytische Formeln für verallgemeinerte Fresnel-Gesetze für beide möglichen Polarisationsrichtungen ab. Die Anwendung des Strahlenbildes erlaubt eine schlüssige Interpretation eines Experiments mit einer quadrupolaren Glasfaser, außerdem schlagen wir Strahlenkonzepte als Grundlage der Konstruktion von Mikrolasern mit maßgeschneiderten Charakteristika vor. / In this work we investigate wave phenomena in mesoscopic systems using different theoretical approaches. In Part I, we focus on effectively one-dimensional electronic ring structures and address the phenomenon of geometric phases in spin-dependent electronic transport in the presence of non-uniform magnetic fields. In the general non-adiabatic case, exact solutions of the Schrödinger equation are used in a transfer matrix formalism to compute the transmission probability through the ring. In the magneto-conductance we identify clear signatures of interference effects due to geometric phases, for example in rings where the non-uniform field is created by a central micromagnet. For the special case of an in-plane magnetic field we predict an interesting spin-flip effect that allows one to control the spin polarization of electrons by applying an external Aharonov-Bohm flux. Optical mesoscopic systems are the subject of Part II. We consider two-dimensional annular structures characterized by different refractive indices, and apply classical methods from geometric optics as well as wave concepts based on Maxwell's equations. For the first time, an S-matrix approach is successfully employed in the description of resonances in optical microresonators; in particular we propose the dielectric annular billiard as an attractive model system. Comparing ray and wave pictures, we find general agreement, except for large wavelengths of the order of the system size, where corrections to the ray model are necessary. The Goos-Hänchen effect as an extension of the ray picture is shown to quantitatively account for wave modifications of Fresnel's laws due to curved interfaces. We derive novel analytical expressions for the corrected Fresnel formulas for both polarizations of light. Motivated by the successful ray description, we give a conclusive interpretation of a recent filter experiment on a quadrupolar glass fibre, and suggest novel concepts for microresonator-based lasers.

No description available.

Gegenstand dieser Arbeit sind Wellenphänomene in mesoskopischen Ringstrukturen. In Teil I der Arbeit befassen wir uns mit spinabhängigem Transport von Elektronen in effektiv eindimensionalen Ringen in Gegenwart inhomogener Magnetfelder. Wir benutzen die exakten Lösungen der Schrödinger-Gleichung im allgemeinen nicht-adiabatischen Fall in einem Transfer-Matrix-Formalismus und untersuchen Auswirkungen von geometrischen Phasen auf den Magnetwiderstand. Für den Spezialfall eines Magnetfeldes in der Ringebene sagen wir einen interessanten Spin-Flip-Effekt vorher, der die Steuerung der Polarisationsrichtung von Elektronen über einen externen Aharonov-Bohm-Fluß erlaubt. Optische mesoskopische Systeme sind Thema von Teil II dieser Arbeit. Wir betrachten zweidimensionale annulare Strukturen, charakterisiert durch unterschiedliche Brechungsindizes, sowohl im klassischen Bild der geometrischen Optik als auch mit Wellenmethoden auf der Grundlage der Maxwellschen Gleichungen. Insbesondere diskutieren wir erstmals eine Streumatrixbeschreibung optischer Mikroresonatoren und wenden sie auf das dielektrische annulare Billard an. Ein Vergleich der Ergebnisse des Wellen- und Strahlenbildes liefert eine gute Übereinstimmung, jedoch sind im Grenzfall großer Wellenlängen von der Ordnung der Systemabmessungen Korrekturen zum Strahlenbild nötig. Wir zeigen am Beispiel von Fresnel-Gesetzen für gekrümmte Oberflächen erstmals, daß der Goos-Hänchen-Effekt diese Korrekturen quantitativ erfaßt. Ausgehend von der Wellenbeschreibung leiten wir neue analytische Formeln für verallgemeinerte Fresnel-Gesetze für beide möglichen Polarisationsrichtungen ab. Die Anwendung des Strahlenbildes erlaubt eine schlüssige Interpretation eines Experiments mit einer quadrupolaren Glasfaser, außerdem schlagen wir Strahlenkonzepte als Grundlage der Konstruktion von Mikrolasern mit maßgeschneiderten Charakteristika vor. / In this work we investigate wave phenomena in mesoscopic systems using different theoretical approaches. In Part I, we focus on effectively one-dimensional electronic ring structures and address the phenomenon of geometric phases in spin-dependent electronic transport in the presence of non-uniform magnetic fields. In the general non-adiabatic case, exact solutions of the Schrödinger equation are used in a transfer matrix formalism to compute the transmission probability through the ring. In the magneto-conductance we identify clear signatures of interference effects due to geometric phases, for example in rings where the non-uniform field is created by a central micromagnet. For the special case of an in-plane magnetic field we predict an interesting spin-flip effect that allows one to control the spin polarization of electrons by applying an external Aharonov-Bohm flux. Optical mesoscopic systems are the subject of Part II. We consider two-dimensional annular structures characterized by different refractive indices, and apply classical methods from geometric optics as well as wave concepts based on Maxwell's equations. For the first time, an S-matrix approach is successfully employed in the description of resonances in optical microresonators; in particular we propose the dielectric annular billiard as an attractive model system. Comparing ray and wave pictures, we find general agreement, except for large wavelengths of the order of the system size, where corrections to the ray model are necessary. The Goos-Hänchen effect as an extension of the ray picture is shown to quantitatively account for wave modifications of Fresnel's laws due to curved interfaces. We derive novel analytical expressions for the corrected Fresnel formulas for both polarizations of light. Motivated by the successful ray description, we give a conclusive interpretation of a recent filter experiment on a quadrupolar glass fibre, and suggest novel concepts for microresonator-based lasers.