The prediction and the experimental discovery of topological insulators has set the stage for a novel type of electronic devices. In contrast to conventional metals or semiconductors, this new class of materials exhibits peculiar transport properties at the sample surface, as conduction channels emerge at the topological boundaries of the system. In specific materials with strong spin-orbit coupling, a particular form of a two-dimensional topological insulator, the quantum spin Hall state, can be observed. Here, the respective one-dimensional edge channels are helical in nature, meaning that there is a locking of the spin orientation of an electron and its direction of motion. Due to the symmetry of time-reversal, elastic backscattering off interspersed impurities is suppressed in such a helical system, and transport is approximately ballistic. This allows in principle for the realization of novel energy-efficient devices, ``spintronic`` applications, or the formation of exotic bound states with non-Abelian statistics, which could be used for quantum computing. The present work is concerned with the general transport properties of one-dimensional helical states. Beyond the topological protection mentioned above, inelastic backscattering can arise from various microscopic sources, of which the most prominent ones will be discussed in this Thesis. As it is characteristic for one-dimensional systems, the role of electron-electron interactions can be of major importance in this context. First, we review well-established techniques of many-body physics in one dimension such as perturbative renormalization group analysis, (Abelian) bosonization, and Luttinger liquid theory. The latter allow us to treat electron interactions in an exact way. Those methods then are employed to derive the corrections to the conductance in a helical transport channel, that arise from various types of perturbations. Particularly, we focus on the interplay of Rashba spin-orbit coupling and electron interactions as a source of inelastic single-particle and two-particle backscattering. It is demonstrated, that microscopic details of the system, such as the existence of a momentum cutoff, that restricts the energy spectrum, or the presence of non-interacting leads attached to the system, can fundamentally alter the transport signature. By comparison of the predicted corrections to the conductance to a transport experiment, one can gain insight about the microscopic processes and the structure of a quantum spin Hall sample. Another important mechanism we analyze is backscattering induced by magnetic moments. Those findings provide an alternative interpretation of recent transport measurements in InAs/GaSb quantum wells. / Mit der Vorhersage und der experimentellen Entdeckung von topologischen Isolatoren wurde die Grundlage für eine vollkommen neue Art von elektronischen Bauelementen geschaffen. Diese neue Klasse von Materialien zeichnet sich gegenüber herkömmlichen Metallen und Halbleitern durch besondere Transporteigenschaften der Probenoberfläche aus, wobei elektrische Leitung in Randkanälen an den topologischen Grenzflächen des Systems stattfindet. Eine spezielle Form des zweidimensionalen topologischen Isolators stellt der Quanten-Spin-Hall-Zustand dar, welcher in bestimmten Materialien mit starker Spin-Bahn-Kopplung beobachtet werden kann. Die hier auftretenden eindimensionalen Leitungskanäle sind von helikaler Natur, was bedeutet, dass die Orientierung des Spins eines Elektrons und seine Bewegungsrichtung fest miteinander gekoppelt sind. Aufgrund von Symmetrien wie Zeitumkehr ist elastische Rückstreuung an eventuell vorhandenen Störstellen in solchen helikalen Kanälen verboten, sodass elektrische Leitung als nahezu ballistisch betrachtet werden kann. Prinzipiell bieten sich dadurch neue Möglichkeiten zur Konstruktion von energieeffizienten Transistoren, “Spintronik“-Bauelementen, oder zur Erzeugung von speziellen Zuständen, die für den Betrieb eines Quantencomputers benutzt werden könnten. Die vorliegende Arbeit beschäftigt sich mit den allgemeinen Transporteigenschaften von eindimensionalen, helikalen Randzuständen. Neben dem oben erwähnten topologischen Schutz gibt es zahlreiche Störquellen, die inelastische Rückstreuprozesse induzieren. Die wichtigsten davon werden im Rahmen dieser Dissertation beleuchtet. Entscheidend wirkt hierbei oft die Rolle von Elektron-Elektron-Wechselwirkungen, welche in eindimensionalen Systemen generell von großer Bedeutung ist. Zunächst werden bewährte Techniken der Festkörperphysik wie etwa Abelsche Bosonisierung (mithilfe derer Wechselwirkungen in einer Raumdimension exakt berücksichtigt werden können), die Theorie von Luttinger Flüssigkeiten, oder die störungstheoretische Renormierungsgruppenanalyse rekapituliert. Diese Methoden werden im Weiteren benutzt, um die Korrekturen zum Leitwert eines helikalen Transportkanals zu berechnen, welche aufgrund von ausgewählten Störungen auftreten können. Ein Fokus liegt hierbei auf dem Zusammenspiel vonWechselwirkungen und Rashba Spin-Bahn-Kopplung als Quelle inelastischer Ein-Teilchen- oder Zwei-Teilchen-Rückstreuung. Mikroskopische Details wie etwa die Existenz einer Impulsobergrenze, welche das Energiespektrum beschränkt, oder die Anwesenheit von wechselwirkungsfreien Spannungskontakten, sind dabei von grundsätzlicher Bedeutung. Die charakteristische Form der vorhergesagten Korrekturen kann dazu dienen, die Struktur und die mikroskopischen Vorgänge im Inneren einer Quanten-Spin- Hall-Probe besser zu verstehen. Ein weiterer grundlegender Mechanismus ist Rückstreuung verursacht durch magnetische Momente. Aus der entsprechenden Analyse der Korrekturen zur Leitfähigkeit ergeben sich interessante Übereinstimmungen mit aktuellen Experimenten in InAs/GaSb Quantentrögen.

Single-wall carbon nanotubes (SWCNTs) are a fascinating material because they exhibit many outstanding properties. Due to their unique geometric structure, they are a paradigm for one-dimensional systems. Furthermore, depending on their chirality, they can be either metallic or semiconducting. The SWCNT are arranged in bundles of some ten nanotubes with a random distribution of semiconducting and metallic tubes. They are thus one-dimensional objects embedded in a three-dimensional arrangement, the bundles. In this thesis, the metallic ground state of one-dimensional (1D) and three-dimensional (3D) systems is investigated on the basis of SWCNTs, using angle-integrated photoemission spectroscopy. In particular, a transition from a 1D to a 3D metallic system, induced by a charge transfer, is studied on SWCNTs and C60 peapods. In general, the metallic ground state of materials is greatly influenced by correlation effects. In classical three-dimensional metals, electron-electron interaction mainly leads to a renormalization of the charge carrier properties (e.g. effective mass), as described in Landau's Fermi liquid theory. One-dimensional metals are influenced to a greater extent by interactions. In fact, the Landau-quasiparticle picture breaks down due to the Peierls instability. Instead, one-dimensional metals are described by Tomonaga-Luttinger liquid (TLL) theory which predicts unusual properties such as spin-charge separation and non-universal power laws in some physical properties such as the electronic density of states (DOS). Angle-integrated photoemission spectroscopy provides direct access to the DOS and as such directly addresses the power law renormalization of a TLL. It is first shown, that the bundles of single-wall carbon nanotubes indeed exhibit a power law scaling of the electronic density of states is observed as it is expected from TLL theory. The main part of the thesis is devoted to the investigation of the metallic ground state of SWCNTs upon functionalization. In general, functionalization is a controlled modification of the structural and/or electronic properties of SWCNT. It can be carried out e.g. by doping with electron donors or acceptors, by filling the nanospace inside the tubes with molecules or by substituting carbon atoms. First, the behavior of the SWCNT upon chemical doping was probed. The overall modification of the electronic band structure can be explained well by a rigid band shift model. The one-dimensional character of the metallic tubes in the bundle is retained at low doping, but when the semiconducting tubes in the sample are also rendered metallic by the charge transfer, a Fermi edge emerges out of the power law renormalization of the spectral weight, signifying a transition to a three-dimensional metallic behavior. This can be explained by an increased interaction between the tubes in the bundle. A crossover from a Tomonaga-Luttinger liquid to a Fermi liquid is observed. The filling of SWCNTs with C60 molecules leads to the formation of so-called peapods. It raises questions concerning the role of the additional bands originating from the C60 filling in the one-dimensional system. In the pristine state, the states of the C60 filling were found to have no influence on the metallic ground state. The TLL power law scaling of the density of states is observed. The overall interaction between the SWCNT host and the C60 filling is small. Upon doping however, the modified band structure leads to a qualitative change in the crossover from a TLL to a Fermi liquid. Upon doping, also states in the conduction band of the C60 are filled. The evolution of the power law scaling at intermediate doping can be interpreted as an opening of an additional conduction channel of one-dimensional metallic chains of C60 inside the tubes. This is in good agreement with transport experiments. Upon further doping, a Fermi edge similar to the highly doped SWCNTs is observed.

Single-wall carbon nanotubes (SWCNTs) are a fascinating material because they exhibit many outstanding properties. Due to their unique geometric structure, they are a paradigm for one-dimensional systems. Furthermore, depending on their chirality, they can be either metallic or semiconducting. The SWCNT are arranged in bundles of some ten nanotubes with a random distribution of semiconducting and metallic tubes. They are thus one-dimensional objects embedded in a three-dimensional arrangement, the bundles. In this thesis, the metallic ground state of one-dimensional (1D) and three-dimensional (3D) systems is investigated on the basis of SWCNTs, using angle-integrated photoemission spectroscopy. In particular, a transition from a 1D to a 3D metallic system, induced by a charge transfer, is studied on SWCNTs and C60 peapods. In general, the metallic ground state of materials is greatly influenced by correlation effects. In classical three-dimensional metals, electron-electron interaction mainly leads to a renormalization of the charge carrier properties (e.g. effective mass), as described in Landau's Fermi liquid theory. One-dimensional metals are influenced to a greater extent by interactions. In fact, the Landau-quasiparticle picture breaks down due to the Peierls instability. Instead, one-dimensional metals are described by Tomonaga-Luttinger liquid (TLL) theory which predicts unusual properties such as spin-charge separation and non-universal power laws in some physical properties such as the electronic density of states (DOS). Angle-integrated photoemission spectroscopy provides direct access to the DOS and as such directly addresses the power law renormalization of a TLL. It is first shown, that the bundles of single-wall carbon nanotubes indeed exhibit a power law scaling of the electronic density of states is observed as it is expected from TLL theory. The main part of the thesis is devoted to the investigation of the metallic ground state of SWCNTs upon functionalization. In general, functionalization is a controlled modification of the structural and/or electronic properties of SWCNT. It can be carried out e.g. by doping with electron donors or acceptors, by filling the nanospace inside the tubes with molecules or by substituting carbon atoms. First, the behavior of the SWCNT upon chemical doping was probed. The overall modification of the electronic band structure can be explained well by a rigid band shift model. The one-dimensional character of the metallic tubes in the bundle is retained at low doping, but when the semiconducting tubes in the sample are also rendered metallic by the charge transfer, a Fermi edge emerges out of the power law renormalization of the spectral weight, signifying a transition to a three-dimensional metallic behavior. This can be explained by an increased interaction between the tubes in the bundle. A crossover from a Tomonaga-Luttinger liquid to a Fermi liquid is observed. The filling of SWCNTs with C60 molecules leads to the formation of so-called peapods. It raises questions concerning the role of the additional bands originating from the C60 filling in the one-dimensional system. In the pristine state, the states of the C60 filling were found to have no influence on the metallic ground state. The TLL power law scaling of the density of states is observed. The overall interaction between the SWCNT host and the C60 filling is small. Upon doping however, the modified band structure leads to a qualitative change in the crossover from a TLL to a Fermi liquid. Upon doping, also states in the conduction band of the C60 are filled. The evolution of the power law scaling at intermediate doping can be interpreted as an opening of an additional conduction channel of one-dimensional metallic chains of C60 inside the tubes. This is in good agreement with transport experiments. Upon further doping, a Fermi edge similar to the highly doped SWCNTs is observed.