@phdthesis{Blumenstein2012,
  author    = {Blumenstein, Christian},
  title     = {One-Dimensional Electron Liquid at a Surface: Gold Nanowires on Ge(001)},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-72801},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Selbstorganisierte Nanodr{\"a}hte auf Halbleiteroberfl{\"a}chen erm{\"o}glichen die Untersuchung von Elektronen in niedrigen Dimensionen. Interessanterweise werden die elektronischen Eigenschaften des Systems von dessen Dimensionalit{\"a}t bestimmt, und das noch {\"u}ber das Quasiteilchenbild hinaus. Das quasi-eindimensionale (1D) Regime zeichnet sich durch eine schwache laterale Kopplung zwischen den Ketten aus und erm{\"o}glicht die Ausbildung einer Peierls Instabilit{\"a}t. Durch eine Nesting Bedingung in der Fermi Fl{\"a}che kommt es zu einer Bandr{\"u}ckfaltung und damit zu einem isolierenden Grundzustand. Dies wird begleitet von einer neuen {\"U}berstruktur im Realraum, die mit dem Nestingvektor korrespondiert. In fr{\"u}heren Nanodrahtsystemen wurde ein solcher Effekt gezeigt. Dazu geh ̈oren Indium Ketten auf Si(111) und die Gold rekonstruierten Substrate Si(553) und Si(557). Die Theorie sagt jedoch einen weiteren Zustand voraus, der nur im perfekten 1D Grenzfall existiert und der bei geringster Kopplung mit h{\"o}heren Dimensionen zerst{\"o}rt wird. Dieser Zustand wird Tomonaga-Luttinger Fl{\"u}ssigkeit (TLL) genannt und f{\"u}hrt zu einem Zusammenbruch des Quasiteilchenbildes der Fermi-Fl{\"u}ssigkeit. Hier sind nur noch kollektive Anregungen der Elektronen erlaubt, da die starke laterale Einschr{\"a}nkung zu einer erh{\"o}hten Kopplung zwischen den Teilchen f{\"u}hrt. Dadurch treten interessante Effekte wie Spin-Ladungs-Trennung auf, bei dem sich die Ladung und der Spin eines Elektrons entkoppeln und getrennt voneinander durch den Nanodraht bewegen k{\"o}nnen. Bis heute wurde solch ein seltener Zustand noch nicht an einer Oberfl{\"a}che beobachtet. In dieser Arbeit wird ein neuer Ansatz zur Herstellung von besser definierten 1D Ketten gew{\"a}hlt. Dazu wird die Au-rekonstruierte Ge(001) Nanodraht-Oberfl{\"a}che untersucht. F{\"u}r die Pr{\"a}paration des Substrates wird ein neues Rezept entwickelt, welches eine langreichweitig geordnete Oberfl{\"a}che erzeugt. Um das Wachstum der Nanodr{\"a}hte zu optimieren wird das Wachstums-Phasendiagramm ausgiebig untersucht. Außerdem werden die strukturellen Bausteine der Ketten sehr genau beschrieben. Es ist bemerkenswert, dass ein struktureller Phasen{\"u}bergang der Ketten oberhalb von Raumtemperatur gefunden wird. Aufgrund von spektroskopischen Untersuchungen kann eine Peierls Instabilit{\"a}t als Ursache ausgeschlossen werden. Es handelt sich um einen 3D-Ising-Typ {\"U}bergang an dem das Substrat ebenfalls beteiligt ist. Die Untersuchungen zur elektronischen Struktur der Ketten zeigen zwei deutliche Erkennungsmerkmale einer TLL: Ein potenzgesetzartiger Verlauf der Zustandsdichte und universales Skalenverhalten. Daher wird zum ersten Mal eine TLL an einer Oberfl{\"a}che nachgewiesen, was nun gezielt lokale Untersuchungen und Manipulationen erm{\"o}glicht. Dazu geh{\"o}ren (i) Dotierung mit Alkalimetallen, (ii) die Untersuchung von Kettenenden und (iii) die einstellbare Kopplung zwischen den Ketten durch zus{\"a}tzliche Goldatome. Damit wird ein wichtiger Beitrag zu theoretischen Vorhersagen und Modellen geliefert und somit das Verst{\"a}ndnis korrelierter Elektronen vorangetrieben.},
  subject      = {Nanodraht},
  language  = {en}
}
@phdthesis{Meyer2013,
  author    = {Meyer, Sebastian},
  title     = {Model System for Correlation Phenomena in Reduced Dimensions - Gold-induced Atomic Chains on Germanium},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-77723},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {Atomic chains, often called nanowires, form in a self-organized process after the adsorption of metal atoms. These wires are spatially well confined representing a close approach of a true one-dimensional structure. The low-dimensional architecture thereby often leads to anisotropic electronic states with vanishing interchain interaction. In the presence of weak coupling to the substrate a one-dimensional metal can experience a phase transition according to Peierls into an insulating ground state upon temperature, which is accompanied by a periodic lattice distortion. Without any coupling a strict onedimensional regime is reached, where the common Fermi liquid description breaks down with the quasi-particles being replaced by collective excitations of spin and charge. This state is referred to as a Tomonaga-Luttinger liquid (TLL), which has been observed so far only in anisotropic bulk materials. An experimental fingerprint for both phenomena can be obtained from the electronic states close to the chemical potential, i.e. the Fermi energy. Using a semiconducting substrate provides the best observation conditions since any bulk projection onto the interesting bands is avoided. In case of Au/Ge(001) the growth of gold-induced chains is guided by the dimerized bare Ge (2×1) reconstruction yielding two different domains of wires rotated by 90° going from one terrace to the next by a single height step. The superior wetting capabilities of gold on germanium enables a complete coverage of the Ge(001) surface with longrange ordered wires. Their length scale and defect density is limited by the underlying substrate, for which a cleaning procedure is introduced based on wet-chemical etching followed by thermal dry oxidation. The band structure of Au/Ge(001) is investigated by angle-resolved photoelectron spectroscopy as a function of temperature. Two states are observed: a two-dimensional metallic state with hole-like dispersion and a one-dimensional electron pocket, whose band-integrated spectral function does not show the typical Fermi distribution at the chemical potential. Instead, a decrease of spectral weight applies following a power-law. This behavior can be well explained within the Tomonaga-Luttinger liquid theory which replaces the Fermi-Landau formalism in strictly one-dimensional systems. To enable theoretical modeling, a structural analysis was performed on the basis of surface x-ray diffraction (SXRD). From the in-plane scattering data a Patterson-map could be extracted leading to in-plane distances between gold atoms in the unit cell. This provides the first step towards a complete structural model and therefore towards a band structure calculation. First successful attempts have been made to manipulate the system by controlled adsorption of potassium. Here, an n-type doping effect is observed for submonolayer coverage whereas slightly increased coverages in combination with thermal energy lead to a new surface reconstruction.},
  subject      = {Nanodraht},
  language  = {en}
}
@phdthesis{Geissler2017,
  author    = {Geißler, Florian},
  title     = {Transport properties of helical Luttinger liquids},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-153450},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {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.},
  subject      = {Topologischer Isolator},
  language  = {en}
}