Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Polyphenylene dendrimers

The main goals of this work were the design, synthesis, and characterization of new functional polyphenylene dendrimers. Polyphenylene dendrimers are highly branched, monodisperse macromolecules consisting exclusively of benzene rings. They can be obtained in high yield by a repetitive Diels-Alder cycloaddition - deprotection protocol. Their shape-persistent dendritic scaffold allows to obtain nanoparticles with functional groups in defined relative orientation. In the first chapter polyphenylene dendrimers with a pyrene core are presented. The focus of the investigations was upon the shielding efficiency of dendritic shells of different generations upon the pyrene-functionality in the core. The herein presented materials combine high quantum efficiency, good solubility and improved film forming properties making them possible candidates for several applications in electronic devices. The defined functionalization of polyphenylene dendrimers often requires a great synthetic effort, since for every desired function the appropriate building block has to be synthesized. To overcome these disadvantages, a new functionalization concept based upon benzophenone precursors has been developed. This new concept has successfully been applied for the functionalization of the dendritic core, the dendrimer shell, and the dendrimer surface. To investigate the accessibility and reactivity of the embedded groups, many functions of different size and nature were introduced. Moreover, suitable precursors for the synthesis of dendrimer entrapped species, trityl cations, trityl radicals, and ketyl radical anions, were obtained. The combination of the synthetic protocols of core- and surface-functionalization resulted in a new type of functional molecules, highly interesting from the point of electron transfer processes. A polyphenylene dendron was used to arrange a triphenylamine donor and a perylene acceptor moiety in a defined spatial distance and orientation. The in-depth photophysical investigation of a first model compound is reported. The herein presented functionalized dendrimers are highly interesting as well from the point of view of fundamental research (looking into the optic and electronic properties of such unique shape persistent structures) as from the point of view of their potential application as tailor-made nanomaterials in the field of optoelectronics.