In many current hybrid systems, thin adsorbate layers (e.g., graphene, dichalcogenides, or molecular layers) reside on a substrate support (e.g., glass, silver, silicon). The interaction between the two materials is often so weak that the internal structure of each material is retained, especially its lattice constant. The low interaction then leads to "only" to weak modifications of the structure, which nevertheless can be of central importance for the properties of the hybrid system. In the proposed project, such structural effects will be investigated using classical two-body potentials as used in molecular dynamics. With the help of suitable optimization algorithms, the resulting structures and pattern formations can then be identified.

Organic dye molecules absorb light in the visible spectral range. In the experiment, they are often deposited on weakly interacting metal surfaces (e.g., to simultaneously examine their electrons using a scanning tunneling microscope). However, the metal reflects light, so that the absorption is disturbed by the molecule - or the adsorbed molecules interfere with the perfect reflectivity of the metal.

 

In the proposed topic, the optical properties of the metal-adsorbate complex should be investigated by means of electrodynamics. In this case, suitable dielectric constants are assigned to the metal and the adsorbate layer, from which the reflectivity (and all other optical properties) can be calculated using Maxwell equations and boundary conditions.

The empirical tight-binding method makes it possible to describe the electronic structure of solids in an efficient and conceptually simple way - often focused on the electronic band structure. In this work, electron-hole excitations, i.e. excitons, are to be investigated on the basis of the band structure - these are responsible for the optical properties of a material. For this, it is necessary to extend the tight-binding model by a suitably parameterized Coulomb interaction between electrons and holes and then to solve the equation of motion of a correlated electron-hole pair.

The scattered-theoretical method makes it possible to treat nanoscale systems that are not subject to periodic boundary conditions. This includes for example the treatment of electronic transport through tunneling barriers or nanowires. Similarly, the scattering of electrons on surfaces and interfaces of solids can be treated well with this methodology. First of all, simple model systems (potential barrier, double barrier) are to be dealt with in this work in order to familiarize oneself with formalism and the underlying physics. In a second step, the scattering of electrons on magnetic layer systems could be investigated. In these systems, the strength of the transmission depends on the orientation of the electron spin. This also makes them interesting with regard to possible applications.

Weyl semi-metals are solids in which the uppermost valence and the lowest conduction band touch each other with linear dispersion at the Fermi level. The points of contact known as Weyl nodes always appear in pairs in the Brillouin zone and give rise to surface states with very interesting properties (e.g. Fermi arcs). Recently, the realization of the Weyl half-metal phase in a 3D solid was experimentally demonstrated using TaAs as an example. In this work, the electronic structure of Wey semi-metals and their surfaces will first be investigated in the context of simple models (tight-binding, k · p-theory) considering the spin-orbit coupling. These studies can be extended by ab initio calculations.

Polymers (long hydrocarbon chains) are currently being intensively studied for a variety of applications. Optical spectroscopy can provide valuable information about the geometric structure and electronic excitations of a polymer. In order to interpret the results obtained, appropriate theoretical investigations are essential. In this work, the optical properties of selected polymers are to be calculated within the framework of the many-particle perturbation theory. In particular, the influence of excitons (electron-hole pairs) on the optical spectra should be considered.