Topological and unconventional superconductivity (SC) are focal topics of this SFB 1170. Yet, pub- lished results predominantly consist of theoretical work; successful reports in the scientific literature are rare and heavily disputed. For example, the existence of topological SC in doped or interca- lated host materials has never been rigorously proven by confirming the coexistence of surface SC and a topological surface state (TSS). Similarly, it has been controversially discussed whether Majorana fermions reported for magnetic chains on strongly spin-orbit–coupled SC exist or rather represent non-topological Shiba states. In this project we will pursue customized approaches to investigate (i) superconducting-doped topological insulators and (ii) strongly spin-orbit–coupled superconductor-ferromagnet hybrids to study unconventional superconductivity. In preliminary work performed towards part (i) of this project, we studied the structural and electronic properties of two potential topological SC, i.e., Nb- and Tl-doped V2VI3 compounds with tetradymite structure, which both turned out to be normal conducting at the surface, potentially due to n-type surface band bend- ing effects. Within this project, we will p-dope these surfaces by appropriate adsorbates, such as C60, and investigate alternate topological SCs, such as Cu- or Sr-doped Bi2Se3. Furthermore, (ii) we will study two-dimensional islands and atom-by-atom–assembled atomic chains on strongly spin-orbit–coupled superconductors by spin-polarized STM and STS. Towards this goal we will utilize substrate materials which combine a high critical temperature with suitability for atomic resolution, such as Nb(110). We will use our expertise in surface science, thin-film epitaxy, and atomic manip- ulation together with an improved energy resolution we will achieve by a new 3He-cooled cryostat requested here to overcome existing limitations and test theoretical proposals with high spatial and energy resolution.